Giant brains; or, Machines that think

*** START OF THE PROJECT GUTENBERG EBOOK 68991 *** Transcriber’s Notes: Underscores “_” before and after a word or phrase indicate _italics_ in the original text. A single underscore after a symbol indicates a subscript. Small capitals have been converted to SOLID capitals. Illustrations have been moved so they do not break up paragraphs. Typographical and punctuation errors have been silently corrected. GIANT BRAINS OR MACHINES THAT THINK EDMUND CALLIS BERKELEY Consultant in Modern Technology President, E. C. Berkeley and Associates JOHN WILEY & SONS, INC., NEW YORK CHAPMAN & HALL, LIMITED, LONDON Copyright, 1949 by EDMUND CALLIS BERKELEY _All Rights Reserved_ _This book or any part thereof must not be reproduced in any form without the written permission of the publisher._ Second Printing, February, 1950 Printed in the United States of America To my friends, whose help and instruction made this book possible PREFACE The Subject, Purpose, and Method of this Book The subject of this book is a type of machine that comes closer to being a brain that thinks than any machine ever did before 1940. These new machines are called sometimes mechanical brains and sometimes sequence-controlled calculators and sometimes by other names. Essentially, though, they are machines that can handle information with great skill and great speed. And that power is very similar to the power of a brain. These new machines are important. They do the work of hundreds of human beings for the wages of a dozen. They are powerful instruments for obtaining new knowledge. They apply in science, business, government, and other activities. They apply in reasoning and computing, and, the harder the problem, the more useful they are. Along with the release of atomic energy, they are one of the great achievements of the present century. No one can afford to be unaware of their significance. In this book I have sought to tell a part of the story of these new machines that think. Perhaps you, as you start this book, may not agree with me that a machine can think: the first chapter of this book is devoted to the discussion of this question. My purpose has been to tell enough about these machines so that we can see in general how they work. I have sought to explain some giant brains that have been built and to show how they do thinking operations. I have sought also to talk about what these machines can do in the future and to judge their significance for us. It seems to me that they will take a load off men’s as great as the load that printing took off men’s writing: a tremendous burden lifted. We need to examine several of the new mechanical brains: Massachusetts Institute of Technology’s differential analyzer, Harvard’s IBM automatic sequence-controlled calculator, Moore School’s ENIAC (Electronic Numerical Integrator and Calculator), and Bell Laboratories’ general-purpose relay calculator. These are described in the sequence in which they were finished between the years 1942 and 1946. We also have to go on some excursions—for instance, the nature of language and of symbols, the meaning of thinking, the human brain and nervous system, the future design of machinery that can think, and a little algebra and logic. I have also sought to discuss the relations between machines that think and human society—what we can foresee as likely to happen or be needed as a result of the remarkable invention of machines that can think. READING THIS BOOK This book is intended for everyone. I have sought to put it together in such a way that any reader can select from it what he wants. Perhaps at first reading you want only the main thread of the story. Then read only what seems interesting, and skip whatever seems uninteresting. The subheadings should help to tell you what to read and what to skip. Nearly all the chapters can be read with little reference to what goes before, although some reference to the supplements in the back may at times be useful. Perhaps your memory of physics is dim, like mine. The little knowledge of physics needed is explained here and there throughout the book, and the index should tell where to find any explanation you may want. Perhaps it is a long time since you did any algebra. Then Supplement 2 on mathematics may hold something of use to you. Two sections (one in Chapter 5 and one in Chapter 6) labeled as containing some rather mathematical details may be skipped with no great loss. Perhaps you are unacquainted with logic that uses symbols—the branch of logic called mathematical logic. In fact, very few people are familiar with it. No discussion in the book hinges on understanding this subject, except for Chapter 9 where a machine that calculates logical truth is described. In all other chapters you may freely skip all references to mathematical logic. But, if you are curious about the subject and how it can be usefully applied in the field of mechanical brains, then begin with the introduction to the subject in Chapter 9, and note the suggestions in the section entitled “Algebra of Logic” in Supplement 2. In any case, glance at the table of contents, the chapter headings and subheadings, and the supplements at the back. These should give an idea of how the book is put together and how you may select what may be interesting to you. Please do not read this book straight from beginning to end unless that way proves to be congenial to you. If you are not interested in technical details, skip most of the middle chapters, which describe existing mechanical brains. If, on the other hand, you want more details than this book contains, look up references in Supplement 3. Here are listed, with a few comments, over 250 books, articles, and pamphlets related to the subject of machinery for computing and reasoning. These cover many parts of the field; some parts, however, are not yet covered by any published information. There are no photographs in this book, although there are over 80 drawings. Photographs of these complicated machines can really show very little: panels, lights, switches, wires, and other kinds of hardware. What is important is the way the machine works inside. This cannot be shown by a photograph but may be shown by schematic drawings. In the same way, a photograph of a human being shows almost nothing about how he thinks. UNDERSTANDING THIS BOOK I have tried to write this book so that it could be understood. I have attempted to explain machinery for computing and reasoning without using technical words any more than necessary. To do this seemed to be easy in some places, much harder in others. As a test of this attempt, a count has been made of all the different words in the book that have two syllables or more, that are used for explaining, and that are not themselves defined. There are fewer than 1800 of these words. In Supplement 1, entitled “Words and Ideas,” I have digressed to discuss further the problem of explanation and understanding. Every now and then in the book, along comes a word or a phrase that has a special meaning, for example, the name of something new. When it first appears, it is put in italics and is explained or defined. In addition, all the words and phrases having special meaning appear again in the index, and next to each is the page number of its explanation or definition. In many places, I have talked of mechanical brains as if they were living. For example, instead of “capacity to store information” I have spoken of “memory.” Of course, the machines are not living; but they do have individuality, responsiveness, and other traits of living beings, just as a political party pictured as a living elephant does. Besides, to treat things as persons is a help in making any subject vivid and understandable, as every song writer and cartoonist illustrates. We speak of “Old Man River” and “Father Time”; we may speak of a ship or a locomotive as “she”; and the crew on the first Harvard sequence-controlled calculator has often called her “Bessy, the Bessel engine.” Let us pause a little longer on the subject of understanding. What is the understanding of something new? It is a state of knowing, a process of knowing more and more. The more we know about something new, the better we understand it. It is possible for almost anybody to understand almost anything, I believe. What is mainly needed in order to grasp an idea is a good collection of true statements about it and some practice in using those statements in situations. For example, no one has ever seen or touched the separate scraps of electricity called electrons. But electrons have been described and measured; hundreds of thousands of people work with electrons; they know and use true statements about electrons. In effect, these people understand electrons. Probably the hardest task of an author is to make his statements understandable yet accurate. It is too much to hope for complete success. I shall be very grateful to any reader who points out to me the statements that he has not understood or that are in error. As to the views I have expressed, I do not expect every reader to agree with me. In fact, I shall be glad if many a reader disagrees with me. For then someone else may say to both of us, “You’re both right and both wrong—the truth lies atwixt and atween you.” Thoughtful and tolerant disagreement is the finest climate for scientific progress. BASIC FACTS Many of the mechanical brains described in this book will do good work for years; but their design is already out of date. Many organizations are hard at work finding new tricks in electronics, materials, and engineering and making new mechanical brains that are better and faster. In spite of future developments, though, the basic facts about mechanical brains will endure. These basic facts are drawn from the principles of thinking, of mathematics, of science, of engineering, etc. These facts govern all handling of information. They do not depend very much on human or mechanical energy. They do not depend very much on signs. They do not depend very much on the century, or the language, or the country. For example, “II et III V sunt,” the Romans may have said; “deux et trois font cinq,” say the French; “2 + 3 = 5,” say the mathematicians; and we say, “two and three make five.” The main effort in this book has been to make clear the basic facts about mechanical brains, for they are now a masterly instrument for obtaining new knowledge. EDMUND CALLIS BERKELEY New York 11, N. Y. _June 30, 1949_ ACKNOWLEDGMENTS This book has been over seven years in the making and has evolved through many different plans for its contents. It springs essentially from the desire to see human beings use their knowledge better: we know enough, but how are we to use what we know? Machines that handle information, that make knowledge accessible, are a long step in the direction of using what we know. For help in causing this desire to come to fruition, I should like to express my indebtedness especially to Professor (then Commander, U.S.N.R.) Howard H. Aiken of Harvard University, whose stimulus, while I was stationed for ten months in 1945-46 in his laboratory, was very great. I should also like to express my appreciation to Mr. Harry J. Volk, whose vision and enthusiasm greatly encouraged me in the writing of this book. For careful reviews and helpful comments on the chapters dealing with existing mechanical brains, I am especially grateful to Dr. Franz L. Alt, Mr. E. G. Andrews, Professor Samuel H. Caldwell, Dr. Grace M. Hopper, Mr. Theodore A. Kalin, and Dr. John W. Mauchly, who are experts in their fields. Dr. Ruth P. Berkeley, Dr. Rudolf Flesch, Mr. J. Ross Macdonald, Dr. Z. I. Mosesson, Mr. Irving Rosenthal, Mr. Max S. Weinstein, and many others have been true friends in reading and commenting upon many parts of the manuscript. Mr. Frank W. Keller devoted much time and skill to converting my rough sketches into illustrations. Mr. Murray B. Ritterman has been of invaluable help in preparing and checking much of the bibliography. Miss Marjorie L. Black has helped very greatly in turning scraps of paper bearing sentences into an excellent manuscript for the printer. For permission to use the quotations on various pages in Chapters 11 and 12, I am indebted to the kindness of: E. P. Dutton & Co., for quotations from _Frankenstein_, by Mary W. Shelley, Everyman’s Library, No. 616. Samuel French, for quotations from _R. U. R._, by Karel Čapek.[1] _Modern Industry_, for a quotation from the issue of February 15, 1947. [1] Copyright 1923 by Doubleday, Page and Co.; all rights reserved; quotations reprinted by permission of Karel Čapek and Samuel French. Responsibility for the statements and opinions expressed in this book is solely my own. These statements and opinions do not necessarily represent the views of any organization with which I may be or have been associated. To the best of my knowledge and belief no information contained in this book is classified by the Department of Defense of the United States. EDMUND CALLIS BERKELEY CONTENTS 1. CAN MACHINES THINK? What Is a Mechanical Brain? 1 2. LANGUAGES: Systems for Handling Information 10 3. A MACHINE THAT WILL THINK: The Design of a Very Simple Mechanical Brain 22 4. COUNTING HOLES: Punch-Card Calculating Machines 42 5. MEASURING: Massachusetts Institute of Technology’s Differential Analyzer No. 2 65 6. ACCURACY TO 23 DIGITS: Harvard’s IBM Automatic Sequence-Controlled Calculator 89 7. SPEED—5000 ADDITIONS A SECOND: Moore School’s ENIAC (Electronic Numerical Integrator and Calculator) 113 8. RELIABILITY—NO WRONG RESULTS: Bell Laboratories’ General-Purpose Relay Calculator 128 9. REASONING: The Kalin-Burkhart Logical-Truth Calculator 144 10. AN EXCURSION: The Future Design of Machines That Think 167 11. THE FUTURE: Machines That Think, and What They Might Do for Men 180 12. SOCIAL CONTROL: Machines That Think, and How Society May Control Them 196 SUPPLEMENTS 1. Words and Ideas 209 2. Mathematics 214 3. References 228 INDEX 257 Chapter 1 CAN MACHINES THINK? WHAT IS A MECHANICAL BRAIN? Recently there has been a good deal of news about strange giant machines that can handle information with vast speed and skill. They calculate and they reason. Some of them are cleverer than others—able to do more kinds of problems. Some are extremely fast: one of them does 5000 additions a second for hours or days, as may be needed. Where they apply, they find answers to problems much faster and more accurately than human beings can; and so they can solve problems that a man’s life is far too short to permit him to do. That is why they were built. These machines are similar to what a brain would be if it were made of hardware and wire instead of flesh and nerves. It is therefore natural to call these machines _mechanical brains_. Also, since their powers are like those of a giant, we may call them _giant brains_. Several giant mechanical brains are now at work finding out answers never before known. Two are in Cambridge, Mass.; one is at Massachusetts Institute of Technology, and one at Harvard University. Two are in Aberdeen, Md., at the Army’s Ballistic Research Laboratories. These four machines were finished in the period 1942 to 1946 and are described in later chapters of this book. More giant brains are being constructed. Can we say that these machines really think? What do we mean by thinking, and how does the human brain think? HUMAN THINKING We do not know very much about the physical process of thinking in the human brain. If you ask a scientist how flesh and blood in a human brain can think, he will talk to you a little about nerves and about electrical and chemical changes, but he will not be able to tell you very much about how we add 2 and 3 and make 5. What men know about the way in which a human brain thinks can be put down in a few pages, and what men do not know would fill many libraries. Injuries to brains have shown some things of importance; for example, they have shown that certain parts of the brain have certain duties. There is a part of the brain, for instance, where sights are recorded and compared. If an accident damages the part of the brain where certain information is stored, the human being has to relearn—haltingly and badly—the information destroyed. We know also that thinking in the human brain is done essentially by a process of storing information and then referring to it, by a process of learning and remembering. We know that there are no little wheels in the brain so that a wheel standing at 2 can be turned 3 more steps and the result of 5 read. Instead, you and I store the information that 2 and 3 are 5, and store it in such a way that we can give the answer when questioned. But we do not know the register in our brain where this particular piece of information is stored. Nor do we know how, when we are questioned, we are able automatically to pick up the nerve channels that lead into this register, get the answer, and report it. Since there are many nerves in the brain, about 10 billion of them, in fact, we are certain that the network of connecting nerves is a main part of the puzzle. We are therefore much interested in nerves and their properties. NERVES AND THEIR PROPERTIES A single nerve, or _nerve cell_, consists of a _cell nucleus_ and a _fiber_. This fiber may have a length of anything from a small fraction of an inch up to several feet. In the laboratory, successive impulses can be sent along a nerve fiber as often as 1000 a second. Impulses can travel along a nerve fiber in either direction at a rate from 3 feet to 300 feet a second. Because the speed of the impulse is far less than 186,000 miles a second—the speed of an electric current—the impulse in the nerve is thought by some investigators to be more chemical than electrical. We know that a nerve cell has what is called an _all-or-none response_, like the trigger of a gun. If you stimulate the nerve up to a certain point, nothing will happen; if you reach that point, or cross it,—bang!—the nerve responds and sends out an impulse. The strength of the impulse, like the shot of the gun, has no relation whatever to the amount of the stimulation. [Illustration: FIG. 1. Scheme of a nerve cell.] The structure between the end of one nerve and the beginning of the next is called a _synapse_ (see Fig. 1). No one really knows very much about synapses, for they are extremely small and it is not easy to tell where a synapse stops and other stuff begins. Impulses travel through synapses in from ½ to 3 thousandths of a second. An impulse travels through a synapse only in one direction, from the head (or _axon_) of one nerve fiber to the foot (or _dendrite_) of another. It seems clear that the activity in a synapse is chemical. When the head of a nerve fiber brings in an impulse to a synapse, apparently a chemical called _acetylcholine_ is released and may affect the foot of another fiber, thus transmitting the impulse; but the process and the conditions for it are still not well understood. It is thought that nearly all information is handled in the brain by groups of nerves in parallel paths. For example, the eye is estimated to have about 100 million nerves sensitive to light, and the information that they gather is reported by about 1 million nerves to the part of the brain that stores sights. Not much more is yet known, however, about the operation of handling information in a human brain. We do not yet know how the nerves are connected so that we can do what we do. Probably the greatest obstacle to knowledge is that so far we cannot observe the detailed structure of a living human brain while it performs, without hurting or killing it. BEHAVIOR THAT IS THINKING Therefore, we cannot yet tell what thinking is by observing precisely how a human brain does it. Instead, we have to define thinking by describing the kind of behavior that we call thinking. Let us consider some examples. When you and I add 12 and 8 and make 20, we are thinking. We use our minds and our understanding to count 8 places forward from 12, for example, and finish with 20. If we could find a dog or a horse that could add numbers and tell answers, we would certainly say that the animal could think. With no trouble a machine can do this. An ordinary 10-column adding machine can be given two numbers like 1,378,917,766 and 2,355,799,867 and the instruction to add them. The machine will then give the answer, 3,734,717,633, much faster than a man. In fact, the mechanical brain at Harvard can add a number of 23 digits to another number of 23 digits and get the right answer in ³/₁₀ of a second. Or, suppose that you are walking along a road and come to a fork. If you stop, read the signpost, and then choose left or right, you are thinking. You know beforehand where you want to go, you compare your destination with what the signpost says, and you decide on your route. This is an operation of logical choice. A machine can do this. The mechanical brain now at Aberdeen which was built at Bell Laboratories can examine any number that comes up in the process of a calculation and tell whether it is bigger than 3 (or any stated number) or smaller. If the number is bigger than 3, the machine will choose one process; if the number is smaller than 3, the machine will choose another process. Now suppose that we consider the basic operation of all thinking: in the human brain it is called learning and remembering, and in a machine it is called storing information and then referring to it. For example, suppose you want to find 305 Main Street in Kalamazoo. You look up a map of Kalamazoo; the map is information kindly stored by other people for your use. When you study the map, notice the streets and the numbering, and then find where the house should be, you are thinking. A machine can do this. In the Bell Laboratories’ mechanical brain, for example, the map could be stored as a long list of the blocks of the city and the streets and numbers that apply to each block. The machine will then hunt for the city block that contains 305 Main Street and report it when found. A machine can handle information; it can calculate, conclude, and choose; it can perform reasonable operations with information. A machine, therefore, can think. THE DEFINITION OF A MECHANICAL BRAIN Now when we speak of a machine that thinks, or a mechanical brain, what do we mean? Essentially, a _mechanical brain_ is a machine that handles information, transfers information automatically from one part of the machine to another, and has a flexible control over the sequence of its operations. No human being is needed around such a machine to pick up a physical piece of information produced in one part of the machine, personally move it to another part of the machine, and there put it in again. Nor is any human being needed to give the machine instructions from minute to minute. Instead, we can write out the whole program to solve a problem, translate the program into machine language, and put the program into the machine. Then we press the “start” button; the machine starts whirring; and it prints out the answers as it obtains them. Machines that handle information have existed for more than 2000 years. These two properties are new, however, and make a deep break with the past. How should we imagine a mechanical brain? One way to think of a mechanical brain is shown in Fig. 2. We see here a railroad line with four stations, marked _input_, _storage_, _computer_, and _output_. These stations are joined by little gates or switches to the main railroad line. We can imagine that numbers and other information move along this railroad line, loaded in freight cars. _Input_ and _output_ are stations where numbers or other information go in and come out, respectively. _Storage_ is a station where there are many platforms and where information can be stored. The _computer_ is a special station somewhat like a factory; when two numbers are loaded on platforms 1 and 2 of this station and an order is loaded on platform 3, then another number is produced on platform 4. [Illustration: FIG. 2. Scheme of a mechanical brain.] We see also a tower, marked _control_. This tower runs a telegraph line to each of its little watchmen standing by the gates. The tower tells them when to open and when to shut which gates. Now we can see that, just as soon as the right gates are shut, freight cars of information can move between stations. Actually the freight cars move at the speed of electric current, thousands of miles a second. So, by closing the right gates each fraction of a second, we can flash numbers and information through the system and perform operations of reasoning. Thus we obtain a mechanical brain. In general, a mechanical brain is made up of: 1. A quantity of registers where information (numbers and instructions) can be stored. 2. Channels along which information can be sent. 3. Mechanisms that can carry out arithmetical and logical operations. 4. A control, which guides the machine to perform a sequence of operations. 5. Input and output devices, whereby information can go into the machine and come out of it. 6. Motors or electricity, which provide energy. THE KINDS OF THINKING A MECHANICAL BRAIN CAN DO There are many kinds of thinking that mechanical brains can do. Among other things, they can: 1. Learn what you tell them. 2. Apply the instructions when needed. 3. Read and remember numbers. 4. Add, subtract, multiply, divide, and round off. 5. Look up numbers in tables. 6. Look at a result, and make a choice. 7. Do long chains of these operations one after another. 8. Write out an answer. 9. Make sure the answer is right. 10. Know that one problem is finished, and turn to another. 11. Determine _most_ of their own instructions. 12. Work unattended. They do these things much better than you or I. They are fast. The mechanical brain built at the Moore School of Electrical Engineering at the University of Pennsylvania does 5000 additions a second. They are reliable. Even with hundreds of thousands of parts, the existing giant brains have worked successfully. They have remarkably few mechanical troubles; in fact, for one of the giant brains, a mechanical failure is of the order of once a month. They are powerful. The big machine at Harvard can remember 72 numbers each of 23 digits at one time and can do 3 operations with these numbers every second. The mechanical brains that have been finished are able to solve problems that have baffled men for many, many years, and they think in ways never open to men before. Mechanical brains have removed the limits on complexity of routine: the machine can carry out a complicated routine as easily as a simple one. Already, processes for solving problems are being worked out so that the mechanical brain will itself determine more than 99 per cent of all the routine orders that it is to carry out. But, you may ask, can they do any kind of thinking? The answer is no. No mechanical brain so far built can: 1. Do intuitive thinking. 2. Make bright guesses, and leap to conclusions. 3. Determine _all_ its own instructions. 4. Perceive complex situations outside itself and interpret them. A clever wild animal, for example, a fox, can do all these things; a mechanical brain, not yet. There is, however, good reason to believe that most, if not all, of these operations will in the future be performed not only by animals but also by machines. Men have only just begun to construct mechanical brains. All those finished are children; they have all been born since 1940. Soon there will be much more remarkable giant brains. WHY ARE THESE GIANT BRAINS IMPORTANT? Most of the thinking so far done by these machines is with numbers. They have already solved problems in airplane design, astronomy, physics, mathematics, engineering, and many other sciences, that previously could not be solved. To find the solutions of these problems, mathematicians would have had to work for years and years, using the best known methods and large staffs of human computers. These mechanical brains not only calculate, however. They also remember and reason, and thus they promise to solve some very important human problems. For example, one of these problems is the application of what mankind knows. It takes too long to find understandable information on a subject. The libraries are full of books: most of them we can never hope to read in our lifetime. The technical journals are full of condensed scientific information: they can hardly be understood by you and me. There is a big gap between somebody’s knowing something and employment of that knowledge by you or me when we need it. But these new mechanical brains handle information very swiftly. In a few years machines will probably be made that will know what is in libraries and that will tell very swiftly where to find certain information. Thus we can see that mechanical brains are one of the great new tools for finding out what we do not know and applying what we do know. Chapter 2 LANGUAGES: SYSTEMS FOR HANDLING INFORMATION As everyone knows, it is not always easy to think. By _thinking_, we mean computing, reasoning, and other handling of information. By _information_ we mean collections of ideas—physically, collections of marks that have meaning. By _handling_ information, we mean proceeding logically from some ideas to other ideas—physically, changing from some marks to other marks in ways that have meaning. For example, one of your hands can express an idea: it can store the number 3 for a short while by turning 3 fingers up and 2 down. In the same way, a machine can express an idea: it can store information by arranging some equipment. The Harvard mechanical brain can store 132 numbers between 0 and 99,999,999,999,999,999,999,999 for days. When you want to change the number stored by your fingers, you move them: perhaps you need a half second to change the number stored by your fingers from 3 to 2, for example. In the same way, a machine can change a stored number by changing the arrangement of some equipment: the electronic brain Eniac can change a stored number in ¹/₅₀₀₀ of a second. LANGUAGES Since it is not always easy to think, men have given much attention to devices for making thinking easier. They have worked out many _systems for handling information_, which we often call _languages_. Some languages are very complete and versatile and of great importance. Others cover only a narrow field—such as numbers alone—but in this field they may be remarkably efficient. Just what is a language? Every language is both a _scheme for expressing meanings_ and _physical equipment_ that can be handled. For example, let us take _spoken English_. The scheme of spoken English consists of more than 150,000 words expressing meanings, and some rules for putting words together meaningfully. The physical equipment of spoken English consists of (1) sounds in the air, and (2) the ears of millions of people, and their mouths and voices, by which they can hear and speak the sounds of English. For another example, let us take numbers expressed in the _Arabic numerals_ and the rules of arithmetic. The scheme of this language contains only ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 or their equivalents, and some rules for combining them. Sufficient physical equipment for this language might very well be a ten-column desk calculating machine with its counter wheels, gears, keys, etc. If we tried to exchange the physical equipment of these two languages, we would be blocked: the desk calculating machine cannot possibly express the meaningful combinations of 150,000 words, and sounds in the air are not permanent enough to express the steps of division of one large number by another. SCHEMES FOR EXPRESSING MEANINGS If we examine languages that have existed, we can observe a number of schemes for expressing meanings. In the table on pp. 12-13 is a rough list of a dozen of them. From among these we can choose the schemes that are likely to be useful in mechanical brains. Schemes 11 and 12 are the schemes that have been predominantly used in machinery for computing. Scheme 12 consisting of combinations of just two marks, ✓, ✕, provides one of the best codes for mechanical handling of information. This scheme, called _binary coding_ (see Supplement 2), is also useful for measuring the quantity of information. QUANTITY OF INFORMATION How should we measure the quantity of information? The smallest unit of information is a “yes” or a “no,” a check mark (✓) or a cross (✕), an impulse in a nerve or no impulse, a 1 or a 0, black or white, good or bad, etc. This twofold difference is called a _binary digit_ of information (see Supplement 2). It is the convenient _unit of information_. SCHEMES FOR EXPRESSING MEANINGS EXAMPLE: /————————————————^—————————————————\ PRINCIPLE SIGN USED IN SIGNIFICANCE NAME OF NO. OF SCHEME SCHEME (1) (2) (3) (4) (5) (6) _Sounds_ 1. Sound of new Bobwhite[2] Spoken kind of quail, Imitative; word is like English so called bowwow sound of from its note theory referent 2. An utterance Pooh![2] Spoken The speaker Pooh-pooh becomes a English expresses theory new word disdain 3. New word is Chortle[2] Spoken “Chuckle” Analogical like another English; and word invented by “snort” Lewis Carroll, blended 1896 4. Word has Mother[2] Spoken Female Historical been used English parent through the ages _Sights_ 5. Picture [picture Egyptian; Picture of Imitative; is like of eye] Ojibwa eye and pictographic referent (American tears, to Indian) mean grief 6. Pattern is 5 English; Five; Ideographic; symbol of French; cinq; mathematical; an idea German; fünf; symbolic; etc. etc. numeric _Mapping of Sounds_ 7. Object [picture Possible Picture of Rebus- pictured of knot] English a knot to writing; has the mean “not” phonographic wanted sound 8. Pattern is [picture Ancient Sign for Syllable- symbol for of star] Cypriote the writing a large (island of syllable sound unit Cyprus) _mu_ 9. Pattern is Ʒ International The sound Phonetic symbol for Phonetic _zh_, as writing a small Alphabet of _s_ in alphabetic sound unit 87 characters “measure” writing; _Mapping of Sights or Symbols_ 10. Systematic ENIAC Abbreviations, Initial Alphabetic combinations etc. letters coding of 26 of a letters 5-word title 11. Systematic 135-03-1228 Abbreviations, Social Numeric combinations nomenclature, Security coding of 10 digits etc. No. of a person 12. Systematic ✓,✕,✕,✓,✓ Checking “yes,” Binary combinations lists, “no,” coding of 2 marks etc. “no,” “yes,” “yes,” respectively [2] The preceding word is the spoken word, not the written one. With 2 units of information or 2 binary digits (1 or 0) we can represent 4 pieces of information: 00, 01, 10, 11 With 3 units of information we can represent 8 pieces of information: 000, 001, 010, 011, 100, 101, 110, 111 With 4 units of information we can represent 16 pieces of information: 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 Now 4 units of information are sufficient to represent a _decimal digit_ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and allow 6 possibilities to be left over; 3 units of information are not sufficient. For example, we may have: 0 0000 5 0101 1 0001 6 0110 2 0010 7 0111 3 0011 8 1000 4 0100 9 1001 We say, therefore, that a decimal digit 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 is _equivalent_ to 4 units of information. Thus a table containing 10,000 numbers, each of 10 decimal digits, is equivalent to 400,000 units of information. One of the 26 letters of the alphabet is equivalent to 5 units of information, for, 5 binary digits (1 or 0) have 32 possible arrangements, and these are enough to provide for the 26 letters. Any printed information in English can be expressed in about 80 characters consisting of 10 numerals, 52 capital and small letters, and some 18 punctuation marks and other types of marks; 6 binary digits (1 or 0) have 64 possible arrangements, and 7 binary digits (1 or 0) have 128 possible arrangements. Each character in a printed book, therefore, is roughly equivalent to 7 units of information. It can be determined that a big telephone book or a big reference dictionary stores printed information at the rate of about 1 billion units of information per cubic foot. If the 10 billion nerves in the human brain could independently be impulsed or not impulsed, then the human brain could conceivably store 10 billion units of information. The largest library in the world is the Library of Congress, containing 7 million volumes including pamphlets. It stores about 100 trillion units of information. We can thus see the significance of a _quantity of information_ from 1 unit to 100 trillion units. No distinction is here made between information that reports facts and information that does not. For example, a book of fiction about persons who never existed is still counted as information, and, of course, much instruction and entertainment may be found in such a source. PHYSICAL EQUIPMENT FOR HANDLING INFORMATION The first thing we want to do with information is _store_ it. The second thing we want to do is _combine_ it. We want equipment that makes these two processes easy and efficient. We want equipment for handling information that: 1. Costs little. 2. Holds much information in little space. 3. Is _permanent_, when we want to keep the information. 4. Is _erasable_, when we want to remove information. 5. Is _versatile_, holds easily any kind of information, and allows operations to be done easily. The amount of human effort needed to handle information correctly depends very much on the properties of the physical equipment expressing the information, although the laws of correct reasoning are independent of the equipment. For example, the great difficulty with spoken sounds as physical equipment for handling information is the trouble of storing them. The technique for doing so was mastered only about 1877 when Thomas A. Edison made the first phonograph. Even with this advance, no one can glance at a soundtrack and tell quickly what sounds are stored there; only by turning back the machine and listening to a groove can we determine this. It was not possible for the men of 2000 B.C. to wait thousands of years for the storing of spoken sounds. The problem of storing information was accordingly taken to other types of physical equipment. PHYSICAL EQUIPMENT FOR HANDLING INFORMATION PHYSICAL ARRANGED OPERATED OR LOW LITTLE PERM- ERAS- VERS- NO. OBJECTS IN OR ON PRODUCED BY COST? SPACE? ANENT? ABLE? ATILE? (1) (2) (3) (4) (5) (6) (7) (8) (9) _Mind_ 1. Nerve Human Body ✕ ✓✓ ✓ ✓ ✓✓ cells brain _Sounds_ 2. Sounds Air Voice ✓✓ ✓✓ ✕✕ ✓✓ ✓✓ 3. Sound- Wax Machines ✓ ✓ ✓✓ ✕ ✓✓ tracks cylinders, and phonograph motors records _Sights_ 4. Marks Sand Stick ✓ ✕ ✓ ✓✓ ✕ 5. Colored Cave Paintbrush ✕ ✕ ✓ ✕ ✕✕ painting walls, and paints canvases, etc. 6. Marks, Clay, Stylus, ✕✕ ✓ ✓✓ ✕✕ ✓ inscript- stone chisel ions 7. Marks Slate Chalk ✓ ✕ ✓ ✓✓ ✓ 8. Marks Paper, Pen ✓✓ ✓ ✓ ✕ ✓✓ parchment, and ink, etc. pencil 9. Letters, Paper, Printing ✓✓ ✓✓ ✓✓ ✕✕ ✓✓ etc. books, press, etc. movable type, motor, and hands 10. Photo- Film, Camera ✓ ✓✓ ✓ ✕✕ ✓✓ graphs prints, etc. 11. Letters, Paper, Typewriter ✓ ✓✓ ✓ ✕ ✓✓ etc. mimeograph and stencil, fingers etc. _Body_ 12. Gestures Space Body ✓ ✕ ✕✕ ✓✓ ✕✕ 13. Fingers Hands Body ✕ ✕ ✕✕ ✓✓ ✕✕ _Objects_ 14. Pebbles Slab Hands ✓✓ ✓ ✓ ✓ ✕✕ 15. Knots String Hands ✓✓ ✓ ✓ ✓ ✕✕ 16. Tallies, Stick Knife ✓✓ ✓ ✓✓ ✕✕ ✕✕ notches 17. Beads Rods in Hands ✓ ✓ ✓ ✓✓ ✕✕ a frame, abacus 18. Ruled Rulers, Hands, ✓ ✓ ✓ ✓ ✓ lines, scales, pressure, pointers dials etc. _Machines_ 19. Counter Desk Motor ✓ ✓ ✓ ✓✓ ✓ wheels, calculating and gears, machines, hands keys, fire-control lights, instruments, etc. etc. 20. Punched Punch card Motor ✓✓ ✓✓ ✓ ✕ ✓✓ cards machinery, and and teletype, input paper etc. instructions tape 21. Relays Dial Motor ✕ ✓ ✓ ✓✓ ✓✓ telephone, and other input machinery instructions 22. Elect- Machinery Motor ✓ ✓ ✓ ✓✓ ✓✓ ronic and tubes input instructions 23. Magnetic Machinery Motor ✓✓ ✓✓ ✓✓ ✓✓ ✓✓ surfaces: and wire, input tape, instructions discs 24. Delay Machinery Motor ✕ ✓ ✕ ✓✓ ✓✓ lines: and electric, input acoustic instructions 25. Electro- Machinery Motor ✕ ✓✓ ✕ ✓✓ ✓✓ static and storage input tubes instructions ✓✓ yes, very. ✓ yes, adequately. ✕ not generally. ✕✕ not at all. What are the types of physical equipment for handling information, and which are the good ones? In the table on pp. 16-17 is a rough list of 25 types of physical equipment for handling information. ✓✓ means “yes, very;” ✓ means “yes, adequately;” ✕ means “not generally;” ✕✕ means “not at all.” For example, our _fingers_ (see No. 13) as a device for handling information are very expensive for most cases. They take up a good deal of space. Certainly they are very temporary storage; any information they may express is very erasable; and what we can express with them alone is very limited. Yet, with a _typewriter_ (see No. 11), our fingers become versatile and efficient. In fact, our fingers can make 4 strokes a second; we can select any one of about 38 keys; and, since each key is equivalent to 5 or 6 units of information, the effective speed of our fingers may be about 800 units of information a second. LANGUAGES OF PHYSICAL OBJECTS The use of pebbles (see No. 14) for keeping track of numerical information is shown in the history of the words containing the root _calc_-of the word _calculate_. The Latin word _calcis_ meant pertaining to lime or limestone, and the Latin word _calculus_ derived from it meant first a small piece of limestone, and later any small stone, particularly a pebble used in counting. All three of these meanings have left descendants: “chalk,” “calcite,” “calcium,” relating in one way or another to lime; in medicine, “calculus,” referring to stones in the kidneys or elsewhere in the body; and in mathematics, “calculate,” “calculus,” referring to computations, once done with pebbles. The pebbles, and the slab (for which the ancient Greek word is _abax_) on which they were arranged and counted, were later replaced, for ease in handling, by groups of beads strung on rods and placed in a frame (see No. 17). These constituted the _abacus_ (see Supplement 2 and the figure there). This was the first calculating machine. It is still used all over Asia; in fact, even today more people use the abacus for accounting than use pencil and paper. The skill with which the abacus can be used was shown in November 1946 in a well-publicized contest in Japan. Kiyoshi Mastuzaki, a clerk in the Japanese communications department, using the abacus, challenged Private Thomas Wood of the U. S. Army, using a modern desk calculating machine, and defeated him in a speed contest involving additions, subtractions, multiplications, and divisions. The heaps of small pebbles, the notches in sticks, and the abacus had the advantage of being visible and comparatively permanent. Storing and reading were relatively easy. They were rather compact and easy to manipulate, certainly much easier than spoken words. But they were subject to disadvantages also. Moving correctly from one arrangement to another was difficult, since there was no good way for storing intermediate steps so that the process could be easily verified. Furthermore, these devices applied to specified numbers only. Also, there was no natural provision for recording what the several numbers belonged to. This had to be recorded with the help of another language, writing. The language of physical objects was picked up from obscurity by the invention of motors and the demands of commerce and business. Commencing in the late 1800’s, _desk calculating machines_ (see No. 19) were constructed to meet mass calculation requirements. They would add, subtract, multiply, and divide specific numbers with great accuracy and speed. But until recently they still were adjuncts to the other languages, for they provided figures one at a time for insertion in the spaces on the ledger pages or calculation sheets where figures were called for. Beginning in the 1920’s, a remarkable change has taken place. Instead of performing single operations, machines have been developed to perform chains of operations with many kinds of information. One of these machines is the _dial telephone_: it can select one of 7 million telephones by successive sorting according to the letters and digits of a telephone number. Another of these machines is a _fire-control instrument_, a mechanism for controlling the firing of a gun. For example, in a modern anti-aircraft gun the mechanism will observe an enemy plane flying at several hundred miles an hour, convert the observations into gun-aiming directions, and determine the aiming directions fast enough to shoot down the plane. _Punch-card machinery_, machines handling information expressed as punched holes in cards, enable the fulfillment of social security legislation, the production of the census, and countless operations of banks, insurance companies, department stores, and factories. And, finally, in 1942 the first _mechanical brain_ was finished at Massachusetts Institute of Technology. THE CRUCIAL DEVICES FOR MECHANICAL BRAINS Let us consider the two modern physical devices for handling information which make mechanical brains possible. These are _relays_ and _electronic tubes_ (Nos. 21 and 22). The last three kinds of equipment listed in the table (_magnetic surfaces_, No. 23; _delay lines_, No. 24; and _electrostatic storage tubes_, No. 25) were not included in any mechanical brains functioning by the middle of 1948. The discussion of them is therefore put off to Chapter 10, where we talk about the future design of mechanical brains. [Illustration: FIG. 1. Relay] Figure 1 shows a simple relay. There are two electrical circuits here. One has two terminals—Pickup and Ground. The other has three terminals—Common, Normally Open, and Normally Closed. When current flows through the coil of wire around the iron, it makes the iron a magnet; the magnet pulls down the flap of iron above, overcoming the force of the spring. When there is no current through the coil, the iron is not a magnet, and the flap is held up by the spring. Now suppose that there is current in Common. When there is no current in Pickup, the current from Common will flow through the upper contact, to the terminal marked Normally Closed. When there is current in Pickup, the current from Common will flow through the lower contact, to the terminal marked Normally Open. Thus we see that a relay expresses a “yes” or a “no,” a 1 or 0, a binary digit, a unit of information. A relay costs $5 to $10. It is rather expensive for storing a single unit of information. The fastest it can be changed from 1 to 0, or vice versa, is about ¹/₁₀₀ of a second. [Illustration: FIG. 2. Electronic tube.] Figure 2 shows a simple electronic tube. It has three parts—the Cathode, the Grid, and the Plate. The Grid actually is a coarse net of metal wires. Electrons can flow from the Cathode to the Plate, provided the voltage on the Grid is such as to permit them to flow. So we can see that an electronic tube is a very simple on-off device and expresses a “yes” or a “no,” a 1 or 0, a binary digit, a unit of information. A simple electronic tube suitable for calculating purposes costs 50 cents to a $1, only ⅒ the cost of a relay. It can be changed from 1 to 0, or back again, in 1 millionth of a second. Relays have been widely used in the mechanical brains so far built, and electronic tubes are the essence of Eniac. In the next chapter, we shall see how physical equipment for handling information can be put together to make a simple mechanical brain. Chapter 3 A MACHINE THAT WILL THINK: THE DESIGN OF A VERY SIMPLE MECHANICAL BRAIN We shall now consider how we can design a very simple machine that will think. Let us call it Simon, because of its predecessor, Simple Simon. SIMON, THE VERY SIMPLE MECHANICAL BRAIN By designing Simon, we shall see how we can put together physical equipment for handling information in such a way as to get a very simple mechanical brain. At every point in the design of Simon, we shall make the simplest possible choice that will still give us a machine that: handles information, transfers information automatically from one part of the machine to another, and has control over the sequence of operations. Simon is so simple and so small, in fact, that it could be built to fill up less space than a grocery-store box, about 4 cubic feet. If we know a little about electrical work, we will find it rather easy to make Simon. What do we do first to design the very simple mechanical brain, Simon? SIMON’S FLESH AND NERVES—REPRESENTING INFORMATION The first thing we have to decide about Simon is how information will be represented: as we put it into Simon, as it is moved around inside of Simon, and as it comes out of Simon. We need to decide what physical equipment we shall use to make Simon’s flesh and nerves. Since we are taking the simplest convenient solution to each problem, let us decide to use: _punched paper tape_ for putting information in, _relays_ (see Chapter 2) and wires for storing and transferring information, and _lights_ for putting information out. [Illustration: TWO-HOLED TAPE READER: Simon’s left ear that listens to numbers and operations. FOUR-HOLED TAPE READER: Simon’s right ear that listens to instructions. LIGHT BULBS: Simon’s eyes that wink answers. FIG. 1. Simon, the very simple mechanical brain.] For the equipment inside Simon, we could choose either electronic tubes or relays. We choose relays, although they are slower, because it is easier to explain circuits using relays. We can look at a relay circuit laid out on paper and tell how it works, just by seeing whether or not current will flow. Examples will be given below. When we look at a circuit using electronic tubes laid out on paper, we still need to know a good deal in order to calculate just how it will work. How will Simon perceive a number or other information by means of punched tape, or relays, or lights? With punched paper tape having, for example, 2 spaces where holes may be, Simon can be told 4 numbers—00, 01, 10, 11. Here the binary digit 1 means a hole punched; the binary digit 0 means no hole punched. With 2 relays together in a register, Simon can remember any one of the 4 numbers 00, 01, 10, and 11. Here the binary digit 1 means the relay picked up or energized or closed; 0 means the relay not picked up or not energized or open. With 2 lights, Simon can give as an answer any one of the 4 numbers 00, 01, 10, 11. In this case the binary digit 1 means the light glowing; 0 means the light off. (See Fig. 1.) We can say that the two lights by which Simon puts out the answer are his _eyes_ and say that he tells his answer by _winking_. We can say also that the two mechanisms for reading punched paper tape are Simon’s _ears_. One tape, called the _input tape_, takes in numbers or operations. The other tape takes in instructions and is called the _program tape_. SIMON’S MENTALITY—POSSIBLE RANGE OF INFORMATION We can say that Simon has a _mentality_ of 4. We mean not age 4 but just the simple fact that Simon knows only 4 numbers and can do only 4 operations with them. But Simon can keep on doing these operations in all sorts of routines as long as Simon has instructions. We decide that Simon will know just 4 numbers, 0, 1, 2, 3, in order to keep our model mechanical brain very simple. Then, for any register, we need only 2 relays; for any answer, we need only 2 lights. Any calculating machine has a _mentality_, consisting of the whole collection of different ideas that the machine can ever actually express in one way or another. For example, a 10-place desk calculating machine can handle numbers up to 10 decimal digits without additional capacity. It cannot handle bigger numbers. [Illustration: FIG. 2. Four directions.] What are the 4 _operations with numbers_ which Simon can carry out? Let us consider some simple operations that we can perform with just 4 numbers. Suppose that they stood for 4 directions in the order east, north, west, south (see Fig. 2). Or suppose that they stood for a turn counterclockwise through some right angles as follows: 0: Turn through 0°, or no right angles. 1: Turn through 90°, or 1 right angle. 2: Turn through 180°, or 2 right angles. 3: Turn through 270°, or 3 right angles. Then we could have the operations of _addition_ and _negation_, defined as follows: ADDITION NEGATION _c_ = _a_ + _b_ _c_ = -_a_ _b_: 0 1 2 3 _a_|_c_ _a_ +————————— ————+———— 0 | 0 1 2 3 0 | 0 1 | 1 2 3 0 1 | 3 2 | 2 3 0 1 2 | 2 3 | 3 0 1 2 3 | 1 For example, the first table says, “1 plus 3 equals 0.” This means that, if we turn 1 right angle and then turn in the same direction 3 more right angles, we face in exactly the same way as we did at the start. This statement is clearly true. For another example, the second table says, “2 is the negative of 2.” This means that, if we turn to the left 2 right angles, we face in exactly the same way as if we turn to the right 2 right angles, and this statement also is, of course, true. With only these two operations in Simon, we should probably find him a little too dull to tell us much. Let us, therefore, put into Simon two more operations. Let us choose two operations involving both numbers and logic: in particular, (1) finding which of two numbers is greater and (2) selecting. In this way we shall make Simon a little cleverer. It is easy to teach Simon how to find which of two numbers is the greater when all the numbers that Simon has to know are 0, 1, 2, 3. We put all possible cases of two numbers _a_ and _b_ into a table: _b_: 0 1 2 3 _a_+————————— 0 | 1 | 2 | 3 | Then we tell Simon that we shall mark with 1 the cases where _a_ is greater than _b_ and mark with 0 the cases where _a_ is not greater than _b_: GREATER THAN _b_: 0 1 2 3 _a_+————————— 0 | 0 0 0 0 1 | 1 0 0 0 2 | 1 1 0 0 3 | 1 1 1 0 For example, “2 is greater than 3” is false, so we put 0 in the table on the 2 line in the 3 column. We see that, for the 16 possible cases, _a_ is greater than _b_ in 6 cases and _a_ is not greater than _b_ in 10 cases. There is a neat way of saying what we have just said, using the language of _mathematical logic_ (see Chapter 9 and Supplement 2). Suppose that we consider the statement “_a_ is greater than _b_” where _a_ and _b_ may be any of the numbers 0, 1, 2, 3. We can say that the _truth value p_ of a _statement P_ is 1 if the statement is true and that it is 0 if the statement is false: _p_ = 1 if _P_ is true, 0 if _P_ is false The truth value of a statement _P_ is conveniently denoted as _T_(_P_) (see Supplement 2): _p_ = _T_(_P_) Now we can say that the table for the operation _greater than_ shows the truth value of the statement “_a_ is greater than _b_”: _p_ = _T_(_a_ > _b_) Let us turn now to the operation _selection_. By _selecting_ we mean choosing one number _a_ if some statement _P_ is true and choosing another number _b_ if that statement is not true. As before, let _p_ be the truth value of that statement _P_, and let it be equal to 1 if _P_ is true and to 0 if _P_ is false. Then the operation of selection is fully expressed in the following table and logical formula (see Supplement 2): SELECTION _c_ = _a_·_p_ + _b_·(1 - _p_) _p_: 0 0 0 0 1 1 1 1 _b_: 0 1 2 3 0 1 2 3 _a_+—————————————————— 0 | 0 1 2 3 0 0 0 0 1 | 0 1 2 3 1 1 1 1 2 | 0 1 2 3 2 2 2 2 3 | 0 1 2 3 3 3 3 3 For example, suppose that _a_ is 2 and _b_ is 3 and the statement _P_ is the statement “2 is greater than 0.” Since this statement is true, _p_ is 1, and _a_·_p_ + _b_·(1 - _p_) = 2(1) + 3(0) = 2 This result is the same as selecting 2 if 2 is greater than 0 and selecting 3 if 2 is not greater than 0. Thus we have four operations for Simon that do not overstrain his mentality; that is, they do not require him to go to any numbers other than 0, 1, 2, and 3. These four operations are: addition, negation, greater than, selection. We label these operations also with the numbers 00 to 11 as follows: addition, 00; negation, 01; greater than, 10; selection, 11. SIMON’S MEMORY—STORING INFORMATION The _memory_ of a mechanical brain consists of physical equipment in which information can be stored. Usually, each section of the physical equipment which can store one piece of information is called a _register._ Each register in Simon will consist of 2 relays. Each register will hold any of 00, 01, 10, 11. The information stored in a register 00, 01, 10, 11 may express a number or may express an operation. [Illustration: S1-2 Relay energized] [Illustration: S1-1 Relay not energized FIG. 3. Register _S_1 storing 10.] How many registers will we need to put into Simon to store information? We shall need one register to read the input tape and to store the number or operation recorded on it. We shall call this register the _input register I_. We shall need another register to store the number or operation that Simon says is the answer and to give it to the output lights. We shall call this register the _output register O_. We shall need 5 registers for the part of Simon which does the computing, which we shall call the _computer_: we shall need 3 to store numbers put into the computer (_C_1, _C_2, _C_3), 1 to store the operation governing the computer (_C_4), and 1 to store the result (_C_5). Suppose that we decide to have 8 registers for storing information, so as to provide some flexibility for doing problems. We shall call these registers _storage registers_ and name them _S_1, _S_2, _S_3, ··· _S_8. Then Simon will have 15 registers: a memory that at one time can hold 15 pieces of information. How will one of these registers hold information? For example, how will register _S_1 hold the number 2 (see Fig. 3)? The number 2 in machine language is 10. Register _S_1 consists of two relays, _S_1-2 and _S_1-1. 10 stored in register _S_1 means that relay _S_1-2 will be energized and that relay _S_1-1 will not be energized. THE CONTROL OF SIMON So far we have said nothing about the control of Simon. Is he docile? Is he stubborn? We know what his capacity is, but we do not know how to tell him to do anything. How do we connect our desires to his behavior? How do we tell him a problem? How do we get him to solve it and tell us the answer? How do we arrange control over the sequence of his operations? For example, how do we get Simon to add 1 and 2 and tell us the answer 3? On the outside of Simon, we have said, there are two ears: little mechanisms for reading punched paper tape. Also there are two eyes that can wink: light bulbs that by shining or not shining can put out information (see Fig. 1). One of the ears—let us call it the _left ear_—takes in information about a particular problem: numbers and operations. Here the _problem tape_ or _input tape_ is listened to. Each line on the input tape contains space for 2 punched holes. So, the information on the input tape may be 00, 01, 10, or 11—either a number or an operation. The other ear—let us call it the _right ear_—takes in information about the sequence of operations, the program or routine to be followed. Here the _program tape_ or _routine tape_ or _control tape_ is listened to. Each line on the program tape contains space for 4 punched holes. We tell Simon by _instructions_ on the program tape what he is to do with the information that we give him on the input tape. The information on the program tape, therefore, may be 0000, 0001, 0010, ···, 1111, or any number from 0 to 15 expressed in binary notation (see Supplement 2). How is this accomplished? In the first place, Simon is a machine, and he behaves during time. He does different things from time to time. His behavior is organized in _cycles_. He repeats a cycle of behavior every second or so. In each cycle of Simon, he listens to or reads the input tape once and he listens to or reads the program tape twice. Every complete instruction that goes on the program tape tells Simon a register from which information is to be sent and a register in which information is to be received. The first time that he reads the program tape he gets the name of the register that is to receive certain information, the _receiving register_. The second time he reads the program tape he gets the name of the register from which information is to be sent, the _sending register_. He finishes each cycle of behavior by transferring information from the sending register to the receiving register. For example, suppose that we want to get an answer out of Simon’s computer into Simon’s output lights. We put down the instruction Send information from _C_5 into _O_ or, more briefly, _C_5 → _O_ But he does not understand this language. We must translate into machine language, in this case punched holes in the program tape. Naturally, the punched holes in the program tape must be able to specify any sending register and any receiving register. There are 15 registers, and so we give them punched hole _codes_ as follows: REGISTER CODE REGISTER CODE _I_ 0001 _C_1 1010 _S_1 0010 _C_2 1011 _S_2 0011 _C_3 1100 _S_3 0100 _C_4 1101 _S_4 0101 _C_5 1110 _S_5 0110 _O_ 1111 _S_6 0111 _S_7 1000 _S_8 1001 To translate the direction of transfer of information, which we showed as an arrow, we put on the program tape the code for the receiving register first—in this case, output, _O_, 1111—and the code for the sending register second—in this case, _C_5, 1110. The instruction becomes 1111, 1110. The first time in any cycle that Simon listens with his right ear, he knows that what he hears is the name of the receiving register; and the second time that he listens, he knows that what he hears is the name of the sending register. One reason for this sequence is that any person or machine has to be prepared beforehand to absorb or take in any information. Now how do we tell Simon to add 1 and 2? On the input tape, we put: Add 00 1 01 2 10 On the program tape, we need to put: _I_ → _C_4 _I_ → _C_1 _I_ → _C_2 _C_5 → _O_ which becomes: 1101, 0001; 1010, 0001; 1011, 0001; 1111, 1110 THE USEFULNESS OF SIMON Thus we can see that Simon can do such a problem as: Add 0 and 3. Add 2 and the negative of 1. Find which result is greater. Select 3 if this result equals 2; otherwise select 2. To work out the coding for this and like problems would be a good exercise. Simon, in fact, is a rather clever little mechanical brain, even if he has only a mentality of 4. It may seem that a simple model of a mechanical brain like Simon is of no great practical use. On the contrary, Simon has the same use in instruction as a set of simple chemical experiments has: to stimulate thinking and understanding and to produce training and skill. A training course on mechanical brains could very well include the construction of a simple model mechanical brain as an exercise. In this book, the properties of Simon may be a good introduction to the various types of more complicated mechanical brains described in later chapters. The rest of this chapter is devoted to such questions as: How do transfers of information actually take place in Simon? How does the computer in Simon work so that calculation actually occurs? How could Simon actually be constructed? What follows should be skipped unless you are interested in these questions and the burdensome details needed for answering them. SIMON’S THINKING—TRANSFERRING INFORMATION The first basic thinking operation for any mechanical brain is transferring information automatically. Let us see how this is done in Simon. [Illustration: FIG. 4. Scheme of Simon.] Let us first take a look at the scheme of Simon as a mechanical brain (see Fig. 4). We have 1 input, 8 storage, 5 computer, and 1 output registers, which are connected by means of transfer wires or a transfer line along which numbers or operations can travel as electrical impulses. This transfer line is often called the _bus_, perhaps because it is always busy carrying something. In Simon the bus will consist of 2 wires, one for carrying the right-hand digit and one for carrying the left-hand digit of any number 00, 01, 10, 11. Simon also has a number of neat little devices that will do the following: When any number goes into a register, the coils of the relays of the register will be connected with the bus. When any number goes out of a register, the contacts of the relays of the register will be connected with the bus. For example, suppose that in register _C_5 the number 2 is stored. In machine language this is 10. That means the left-hand relay (_C_5-2) is energized and the right-hand relay (_C_5-1) is not energized. Suppose that we want to transfer this number 2 into the output register _O_, which has been cleared. What do we do? Let us take a look at a circuit that will transfer the number (see Fig. 5). First we see two relays in this circuit. They belong to the _C_5 register. The _C_5-2 relay is energized since it holds 1; current is flowing through its coil, the iron core becomes a magnet, and the contact above it is pulled down. The _C_5-1 relay is not energized since it holds 0; its contact is not pulled down. The next thing we see is two _rectifiers_. The sign for these is a triangle. These are some modern electrical equipment that allow electrical current to flow in only one direction. In the diagram, the direction is shown by the pointing of the triangle along the wire. Rectifiers are needed to prevent undesired circuits. Next, we see the bus, consisting of two wires. One carries the impulses for left-hand or 2 relays, and the other carries impulses for the right-hand or 1 relays. Next, we see two relays, called the _entrance relays_ for the _O_ register. Current from Source 1 may flow to these relays, energize them, and close their contacts. When the first line of the program tape is read, specifying the receiving register, the code 1111 causes Source 1 to be energized. This fact is shown schematically by the arrow running from the program tape code 1111 to Source 1. Finally, we see the coils of the two relays for the Output or _O_ register. We thus see that we have a circuit from the contacts of the _C_5 register through the bus to the coils of the _O_ register. [Illustration: FIG. 5. Transfer circuit.] We are now ready to transfer information when the second line of the program tape is read. This line holds 1110 and designates _C_5 as the sending register and causes Source 2 to be energized. This fact is shown schematically by the arrow running from the second line of the program tape to Source 2. When the second line is read, current flows: 1. From Source 2. 2. Through the contacts of the _C_5 register if closed. 3. Through the rectifiers. 4. Through the bus. 5. Through the entrance relay contacts of the _O_ register. 6. Through the coils of the _O_ register relays, energizing such of them as match with the _C_5 closed contacts; and finally 7. Into the ground. Thus relay _O_-2 is energized; it receives current because contact _C_5-2 is closed. And relay _O_-1 is not energized; it receives no current since contact _C_5-1 is open. So we have actually transferred information from the _C_5 register to the _O_ register. The same process in principle applies to all transfers: The pattern of electrical impulses, formed by the positioning of one register, is produced in the positioning of another register. SIMON’S COMPUTING AND REASONING Now so far the computing registers in Simon are a mystery. We have said that _C_1, _C_2, and _C_3 take in numbers 00, 01, 10, 11, that _C_4 takes in an operation 00, 01, 10, 11, and that _C_5 holds the result. What process does Simon use so that he has the correct result in register _C_5? Let us take the simplest computing operation first and see what sort of a circuit using relays will give us the result. The simplest computing operation is _negation_. In negation, a number 00, 01, 10, 11 goes into the _C_1 register, and the operation 01 meaning negation goes into the _C_4 register, and the correct result must be in the _C_5 register. So, first, we note the fact that the _C_4-2 relay must not be energized, since it contains 0, and that the _C_4-1 relay must be energized, since it contains 1. Now the table for negation, with _c_ =-_a_, is: _a_ | _c_ ————+———— 0 | 0 1 | 3 2 | 2 3 | 1 Negation in machine language will be: _a_ | _c_ ————+———— 00 | 00 01 | 11 10 | 10 11 | 01 Now if _a_ is in the _C_1 register and if _c_ is in the _C_5 register, then negation will be: _C_1 | _C_5 —————+————— 00 | 00 01 | 11 10 | 10 11 | 01 But each of these registers _C_1, _C_5 will be made up of two relays, the left-hand or 2 relay and the right-hand or 1 relay. So, in terms of these relays, negation will be: _C_1-2 _C_1-1 | _C_5-2 _C_5-1 ——————————————+—————————————— 0 0 | 0 0 0 1 | 1 1 1 0 | 1 0 1 1 | 0 1 Now, on examining the table, we see that the _C_5-1 relay is energized if and only if the _C_1-1 relay is energized. So, in order to energize the _C_5-1 relay, all we have to do is transfer the information from _C_1-1 to _C_5-1. This we can do by the circuit shown in Fig. 6. (In this and later diagrams, we have taken one more step in streamlining the drawing of relay contacts: the contacts are drawn, but the coils that energize them are represented only by their names.) [Illustration: FIG. 6. Negation—right-hand digit.] [Illustration: FIG. 7. Negation—left-hand digit.] Taking another look at the table, we see also that the _C_5-2 relay must be energized if and only if: _C_1-2 AND _C_1-1 HOLDS: HOLDS: 0 1 1 0 A circuit that will do this is the one shown in Fig. 7. In Fig. 8 is a circuit that will do all the desired things together: give the right information to the _C_5 relay coils if and only if the _C_4 relays hold 01. [Illustration: FIG. 8. Negation circuit.] Let us check this circuit. First, if there is any operation other than 01 stored in the _C_4 relays, then no current will be able to get through the _C_4 contacts shown and into the _C_5 relay coils, and the result is blank. Second, if we have the operation 01 stored in the _C_4 relays, then the _C_4-2 contacts will not be energized—a condition which passes current—and the _C_4-1 contacts will be energized—another condition which passes current—and: IF THE NUMBER AND THE _C_5 RELAYS IN _C_1 IS: THEN _C_1-1: AND _C_1-2: ENERGIZED ARE: 0 does not close does not close neither 1 closes does not close _C_5-2, _C_5-1 2 does not close closes _C_5-2 only 3 closes closes _C_5-1 only Thus we have shown that this circuit is correct. We see that this circuit uses more than one set of contacts for several relays (_C_1-2, _C_4-1, _C_4-2); relays are regularly made with 4, 6, or 12 sets of contacts arranged side by side, all controlled by the same pickup coil. These are called 4-, 6-, or 12-_pole_ relays. [Illustration: FIG. 9. Addition circuit.] [Illustration: FIG. 10. Greater-than circuit.] Circuits for _addition_, _greater than_, and _selection_ can also be determined rather easily (see Figs. 9, 10, 11). (_Note_: By means of the _algebra of logic_, referred to in Chapter 9 and Supplement 2, the conditions for many relay circuits, as well as the circuit itself, may be expressed algebraically, and the two expressions may be checked by a mathematical process.) For example, let us check that the addition circuit in Fig. 9 will enable us to add 1 and 2 and obtain 3. We take a colored pencil and draw closed the contacts for _C_1-1 (since _C_1 holds 01) and for _C_2-2 (since _C_2 holds 10). Then, when we trace through the circuit, remembering that addition is stored as 00 in the _C_4 relays, we find that both the _C_5 relays are energized. Hence _C_5 holds 11, which is 3. Thus Simon can add 1 and 2 and make 3! [Illustration: FIG. 11. Selection Circuit.] PUTTING SIMON TOGETHER In order to put Simon together and make him work, not very much is needed. On the outside of Simon we shall need two small mechanisms for reading punched paper tape. Inside Simon, there will be about 50 relays and perhaps 100 feet of wire for connecting them. In addition to the 15 registers (_I_, _S_1 to _S_8, _C_1 to _C_5, and _O_), we shall need a register of 4 relays, which we shall call the _program register_. This register will store the successive instructions read off the program tape. We can call the 4 relays of this register _P_8, _P_4, _P_2, _P_1. For example, if the _P_8 and _P_2 relays are energized, the register holds 1010, and this is the program instruction that calls for the 8th plus 2nd, or 10th, register, which is _C_1. For connecting receiving registers to the bus, we shall need a relay with 2 poles, one for the 2-line and one for the 1-line, for each register that can receive a number from the bus. For example, for entering the output register, we actually need only one 2-pole relay instead of the two 1-pole relays drawn for simplicity in Fig. 5. There will be 13 2-pole relays for this purpose, since only 13 registers receive numbers from the bus; registers _I_ and _C_5 do not receive numbers from the bus. We call these 13 relays the _entrance relays_ or _E relays_, since _E_ is the initial letter of the word entrance. [Illustration: FIG. 12. Select-Receiving-Register circuit.] The circuit for selecting and energizing the _E_ relays is shown in Fig. 12. We call this circuit the _Select-Receiving-Register_ circuit. For example, suppose that the _P_8 and _P_2 relays are energized. Then this circuit energizes the _E_10 relay. The _E_10 relay closes the contacts between the _C_1 relay coils and the bus; and so it connects the _C_1 register to receive the next number that is sent into the bus. This kind of circuit expresses a classification and is sometimes called a _pyramid circuit_ since it spreads out like a pyramid. A similar pyramid circuit is used to select the sending register. We shall need a relay for moving the input tape a step at a time. We shall call this relay the _MI relay_, for _m_oving _i_nput tape. We also need a relay for moving the program tape a step at a time. We shall call this relay the _MP relay_ for _m_oving _p_rogram tape. Here then is approximately the total number of relays required: RELAYS NAME NUMBER _I_, _S_, _C_, _O_ Input, Storage, Computer, Output 30 _P_ Program 4 _E_ Entrance 13 _MI_ Move Input Tape 1 _MP_ Move Program Tape 1 ———— Total 49 A few more relays may be needed to provide more contacts or poles. For example, a single _P_1 relay will probably not have enough poles to meet all the need for its contacts. [Illustration: FIG. 13. Latch relay.] Each cycle of the machine will be divided into 5 equal _time intervals_ or _times_ 1 to 5. The timing of the machine will be about as follows: TIME ACTION 1 Move program tape. Move input tape if read out of in last cycle. 2 Read program tape, determining the receiving register. Read through the computing circuit setting up the _C_5 register. 3 Move program tape. Energize the _E_ relay belonging to the receiving register. 4 Read program tape again, determining the sending register. 5 Transfer information by reading through the Select-Sending-Register circuit and the Select-Receiving-Register circuit. In order that information may remain in storage until wanted, register relays should hold their information until just before the next information is received. This can be accomplished by keeping current in their coils or in other ways. There is a type of relay called a _latch relay_, which is made with two coils and a latch. This type of relay has the property of staying or latching in either position until the opposite coil is impulsed (see Fig. 13). This type of relay would be especially good for the registers of Simon. If any reader sets to work to construct Simon, and if questions arise, the author will be glad to try to answer them. Chapter 4 COUNTING HOLES: PUNCH-CARD CALCULATING MACHINES When we think of counting, we usually think of saying softly to ourselves “one, two, three, four, ···.” This is a good way to find the total of a small group of objects. But when we have a large group of objects or a great many groups of objects to be counted, a much faster way of counting is needed. A very fast way of sorting and counting is _punch-card calculating machinery_. This is machinery which handles information expressed as holes in cards. _Punch-card machines_ can: Sort, count, file, select, and copy information, Make comparisons, and choose according to instructions, Add, subtract, multiply, and divide, List information, and print totals. For example, in a life insurance company, much routine handling of information about insurance policies is necessary: Writing information on newly issued policies. Setting up policy-history cards. Making out notices of premiums due. Making registers of policies in force, lapsed, died, etc., for purposes of valuation as required by law or good management. Calculating and tabulating premium rates, dividend rates, reserve factors, etc. Computing and tabulating expected and actual death rates; and much more. All these operations can be done almost automatically by punch-card machines. ORIGIN AND DEVELOPMENT When a census of the people of a country is taken, a great quantity of sorting and counting is needed: by village, county, city, and state; by sex; by age; by occupation; etc. In 1886, the census of the people of the United States which had been taken in 1880 was still being sorted and counted. Among the men then studying census problems was a statistician and inventor, Herman Hollerith. He saw that existing methods were so slow that the next census (1890) would not be finished before the following census (1900) would have to be begun. He knew that cards with patterns of holes had been used in weaving patterns in cloth. He realized that the presence or absence of a property, for example employed or unemployed, could be represented by the presence or absence of a hole in a piece of paper. An electrical device could detect the hole, he believed, since it would allow current to flow through, whereas the absence of the hole would stop the current. He experimented with sorting and counting, using punched holes in cards, and with electrical devices to detect the holes and count them. A definite meaning was given to each place in the card where a hole might be punched. Then electrical devices handled the particular information that the punches represented. These devices either counted or added, singly or in various combinations, as might be desired. More than 50 years of development of punch-card calculating machinery have since then taken place. Several large companies have made quantities of punch-card machines. A great degree of development has taken place in the punch-card machines of International Business Machines Corporation (IBM), and for this reason these machines will be the ones described in this chapter. What is said here, however, may also in many ways apply to punch-card machines made by other manufacturers—Remington-Rand, Powers, Control Instrument, etc. GENERAL PRINCIPLES To use punch-card machines, we first convert the original information into patterns of holes in cards. Then we feed the cards into the machines. Electrical impulses read the pattern of holes and convert them into a pattern of timed electrical currents. Actually, the reading of a hole in a column of a punch card is done by a brush of several strands of copper wire pressed against a metal roller (Fig. 1). The machine feeds the card (the bottom edge first, where the 9’s are printed) with very careful timing over the roller; and, when the punched hole is between the brush and the roller, an electrical circuit belonging to that column of the card is completed. The machine responds according to its general design and its wiring for the particular problem: it punches new cards, or it prints new marks, or it puts information into new storage places. Clerks, however, move the cards from one machine to another. They wait on the machines, keep the card feeds full, and empty the card hoppers as they fill up. A human error of putting the wrong block of cards into a machine may from time to time cause a little trouble, especially in sorting. Actually, in a year, billions of punch cards are handled precisely. [Illustration: FIG. 1. Reading of punch cards.] The _punch card_ is a masterpiece of engineering and standardization. Its exact thickness matches the knife-blade edges that feed the cards into slots in the machines, and matches the channels whereby these cards travel through the machines. The standard card is 7⅜ inches long and 3¼ inches wide, and it has a standard thickness of 0.0065 inch and other standard properties with respect to stiffness, finish, etc. [Illustration: FIG. 2. Scheme of standard punch card. (Note: Positions 11 and 12 are not usually marked by printed numbers or letters.)] The standard IBM punch card of today has 80 _columns_ and 12 _positions_ for punching in each column (Fig. 2). A single punched hole in each of the positions known as 0 to 9 stands for each of the digits 0 to 9 respectively. The remaining 2 single punch positions available in any column are usually called the _11 position_ and _12 position_ (though sometimes called the numerical _X position_ and _Y position_). These two positions do not behave arithmetically as 11 and 12. Actually, in the space between one card and the next card as they are fed through the machines, more positions occur. For example, there may be 4 more: a 10 position preceding the 9, and a 13, a 14, and a 15 position following the 12. The 16 positions in total correspond to a full turn, 360°, of the roller under the brush, and to a complete _cycle_ in the machine; and a single position corresponds to ¹/₁₆ of 360°, or 22½°. In some machines, the total number of positions may be 20. A pair of punches stands for each of the letters of the alphabet, according to the scheme shown. A 12-1 J 11-1 Unused 0-1 B 12-2 K 11-2 S 0-2 C 12-3 L 11-3 T 0-3 D 12-4 M 11-4 U 0-4 E 12-5 N 11-5 V 0-5 F 12-6 O 11-6 W 0-6 G 12-7 P 11-7 X 0-7 H 12-8 Q 11-8 Y 0-8 I 12-9 R 11-9 Z 0-9 For example, the word MASON is shown punched in Fig. 3. [Illustration: FIG. 3. Alphabetic punching.] [Illustration: FIG. 4. Single-panel plugboard.] To increase the versatility of the machines and provide them with instructions, many of them have _plugboards_ (Fig. 4). These are standard interchangeable boards filled with prongs on one side and holes or terminals called _hubs_ on the other side. The side with the prongs connects to the ends of electrical circuits in the punch-card machine, which are brought together in one place for the purpose. On the other side of the board, using plugwires, we can connect the hubs to each other in different ways to produce different results. The single-panel plugboard is 10 inches long and 5¾ inches wide. It contains 660 hubs in front and 660 corresponding prongs in the back. A double-panel plugboard or a triple-panel plugboard applies to some machines. In less time than it takes to describe it, we can take one wired-up plugboard out of a machine and put in a new wired-up plugboard and thus change completely the instructions under which the machine operates. Many of the machines have a number of different switches that we must also change, when going from one kind of problem to another. The numbers that are stored or sorted in punch-card machines may be of any size up to 80 digits, one in each column of the punch card. In doing arithmetic (adding, subtracting, multiplying, and dividing), however, the largest number of digits is usually 10. Beyond 10 digits, we can work out tricks in many cases. TYPES OF PUNCH-CARD MACHINES The chief IBM punch-card machines are: the _key punch_, the _verifier_, the _sorter_, the _interpreter_, the _reproducer_, the _collator_, the _multiplying punch_, the _calculating punch_, and the _tabulator_. Of these 9 machines, the last 6 have plugboards and can do many different operations as a result. There is a flow of punch cards through each of these machines. The machines differ from each other in the number and relation of the paths of flow, or _card channels_, and in the number and relation of the momentary stopping places, or _card stations_, at which cards are read, punched, or otherwise acted on. We can get a good idea of what a machine is from a picture of these card channels. Key Punch We use a key punch (Fig. 5) to punch original information into blank cards. In the key punch there is one card channel; it has one entrance, one station, and one exit. At the card station, there are 12 _punching dies_, one for each position in the card column, and each card column is presented one by one for punching. The numeric _keyboard_ (Fig. 6) for the key punch has 14 keys: One key for each of the punches 0 to 9, 11, and 12, A _space key_, which allows a column of the punch card to go by with no punch in it, A _release key_, which ejects the card and feeds another card. [Illustration: FIG. 5. Key punch.] [Illustration: FIG. 6. Keyboard of key punch.] Of course, in using a key punch, we must punch the same kind of information in the same group of columns. For example, if these cards are to contain employees’ social security numbers, we must punch that number always in the same card columns, numbered, say, 15 to 23, or 70 to 78, etc. Verifier The verifier is really the same machine as the key punch, but it has dull punching dies moving gently instead of sharp ones moving with force. It turns on a red light and stops when there is no punched hole in the right spot to match with a pressed key. Sorter The sorter is a machine for sorting cards, one column at a time (Fig. 7). The sorter has a card channel that forks; it has one entrance, one station, and 13 exits. Each exit corresponds to: one of the 12 punch positions 0 to 9, 11, and 12; or _reject_, which applies when the column is nowhere punched. It has one card station where a brush reads a single column of the card. We can turn a handle and move the brush to any column. [Illustration: FIG. 7. Sorter.] Interpreter The interpreter takes in a card, reads its punches, prints on the card the marks indicated by the punches, and stacks the card. We call this process _interpreting_ the card, since it translates the punched holes into printed marks. The interpreter (Fig. 8) has one card channel, with one entrance, 2 card stations, and one exit. What the machine does at the second card station depends on what the machine reads at the first card station and on what we have told the machine by switches and plugboard wiring to do. [Illustration: FIG. 8. Interpreter.] Reproducer The reproducer or reproducing punch can: _Reproduce_, or copy the punches in one group of cards into another group of cards (in the same or different columns). _Compare_, or make sure that the punches in two groups of cards agree (and shine a red light if they do not). _Gang punch_, or copy the punches in a _master card_ into a group of _detail cards_. _Summary punch_, or copy totals or summaries obtained in the tabulator into blank cards in the reproducer. [Illustration: FIG. 9. Reproducer.] The reproducer (Fig. 9) has 2 independent card channels, the cards not mingling in any way, called the _reading channel_ and the _punching channel_. We can run the machine with only the punching channel working; in fact, IBM equips some models only with the punching channel, particularly for “summary punch” operation. The machine is timed so that, when any card is at the middle station in either channel, then the next preceding card is at the latest station, and the next following card is at the earliest station. At 5 stations, the machine reads a card. At the middle station of the punching channel, the machine punches a card. Using a many-wire cable, we can connect the tabulator to the reproducer and so cause the tabulator to give information electrically to the reproducer. This connection makes possible the “summary punch” operation. Here is an instance with punch-card machines where, in order to transfer information from one machine to another, we are not required to move cards physically from one machine to another. Collator The collator is a machine that arranges or _collates_ cards. It is particularly useful in selecting, matching, and merging cards. The collator (Fig. 10) has 2 card channels which join and then fork into 4 channels ending in pockets called _Hoppers_ 1, 2, 3, and 4. The 2 card feeds are called the _Primary Feed_ and the _Secondary Feed_. Cards from the Primary Feed may fall only into the first and second hoppers. Cards from the Secondary Feed may fall only into the second, third, and fourth hoppers. The collator has 3 stations at which cards may be read. [Illustration: No.1--Selected primaries No.2--Merged cards and unselected primaries No.3--Separate secondaries not selected No.4--Selected secondaries FIG. 10. Collator.] IBM can supply additional wiring called the _collator counting device_. With this we can make the collator count cards as well as compare them. For example, we could put 12 blank cards from the Secondary Feed behind each punched-card from the Primary Feed in order to prepare for some other operation. Calculating Punch The calculating punch was introduced in 1946. It is a versatile machine of considerable capacity. It adds, subtracts, multiplies, and divides. It also has a control over a sequence of operations, in some cases up to half a dozen steps. This machine (Fig. 11) has one card channel with 4 stations called, respectively, _control brushes_, _reading brushes_, _punch feed_, and _punching dies_. At station 1, there are 20 brushes; we can set these by hand to read any 20 of the 80 card columns. At station 2 there are 80 regular reading brushes. At station 3 the card waits for a part of a second while the machine calculates, and, when that is done, the card is fed into station 4, where it is punched or verified. The multiplying punch is an earlier model of the calculating punch, without the capacity for division. [Illustration: FIG. 11. Calculating punch.] Tabulator The tabulator can select and list information from cards. Also, it can total information from groups of cards in _counters_ of the tabulator and can print the totals. [Illustration: FIG. 12. Tabulator.] The tabulator (Fig. 12) has one card channel with two stations where cards may be read, called the _Upper Brushes_ and _Lower Brushes_. When the Lower Brush station is reading one card, the Upper Brush station is reading the next card. The tabulator also has another channel, which is for endless paper (and sometimes separate sheets or cards). This channel has one station; here printing takes place. Unlike the typewriter, the tabulator prints a whole row at a time. It can print up to 88 numerals or letters across the sheet in one stroke. The cards flowing through the card channel and the paper flowing through the paper channel do not have to move in step; in fact, we need many different time relations between them, and the number of rows printed on the paper may have almost any relation to the number of punch cards flowing through the card channel. At the station where paper is printed, we can put on the machine a mechanism called the _automatic carriage_. This is like a typewriter carriage, which holds the paper for a typewriter, but we can control the movement of paper through the automatic carriage by plugboard wiring, switch settings, and holes in punch cards. Thus we can arrange for headings, spacing, and feeding of new sheets to be controlled by the information and the instructions, with a great deal of versatility. HANDLING INFORMATION We have now described briefly the chief available punch-card machines as of the middle of 1948. The next question is: How do we actually get something done by means of punch cards? Let us go back to the census example, even though it may not be a very typical example, and see what would be done if we wished to compile a census by punch cards. The first thing we do is plan which columns of the punch card will contain what information about the people being counted. For example, the following might be part of the plan: NO. OF INFORMATION POSSIBILITIES COLUMNS State 60 1- 2 County 1,000 3- 5 Township 10,000 6- 9 City or village 10,000 10-13 Sex 2 14 Age last birthday 100 15-16 Occupation 100,000 17-21 ... ... ... Under the heading state, we know that there are 48 states, the District of Columbia, and several territories and possessions—all told, perhaps 60 possibilities. So, 2 punch-card columns are enough: they will allow 100 different sets of punches from 00 to 99 to be put in them. We then assign the _code_ 00 to Maine, 01 to New Hampshire, 02 to Vermont, etc., or we might assign the code 00 to Alabama, 01 to Arizona, 02 to Arkansas, etc.—whichever would be more useful. Under the other headings, we do the same thing: count the possibilities; assign codes. In this case, it will be reasonable to use numeric codes 0 to 9 in each column in all places because we shall have millions of cards to deal with and numeric codes can be sorted faster than alphabetic codes. Alphabetic codes require 2 punched holes in each column, and sorting any column takes 2 operations. The punch cards are printed with the chosen headings. We set up the codes in charts and give them to clerks. Using key punches and verifiers, they punch up the cards and check them. They work from the original information collected by the census-taker in the field. Since the original information will come in geographically, probably only one geographic code at a time will be needed, and it will be simple to keep track of. As to occupation, however, it may be useful to assign other clerks full-time to examining the original information and specifying the right code for the occupation. Then the clerks who do the punching will have only copying to do. The great bulk of the work with the census will be sorting, counting, and totaling. The original punch cards will be summarized into larger and larger groups. For example, the cards for all males age 23 last birthday living in the state of Massachusetts are sorted together. This group of cards may be put into a tabulator wired to a summary punch. When the tabulator has counted the last card of this group, the summary punch punches one card, showing the total number in this group. Some time later a card like this will be ready for every state. Then the whole group of state cards may be fed into the tabulator wired to the reproducer acting as summary punch. When totaled, the number of males age 23 last birthday in the United States will be punched into a single card. After more compiling, a card like this will be ready for all males in the United States at each age. Then this group of cards may be fed into the tabulator wired to the summary punch. Each card may be listed by the tabulator on the paper flowing through it, showing the age and the number of males living at that age. At the end of the listing, the tabulator will print the total number of all males in the list, and the summary punch will punch a card containing this total. ARITHMETICAL OPERATIONS Punch-card machines can perform the arithmetical operations of counting, adding, subtracting, multiplying, dividing, and rounding off. Counting Counting can be done by the sorter, the tabulator, and the collator. The tabulator can print the total count. The tabulator and summary punch wired together can put the total count automatically into another punch card. The sorter shows the count in dials. Adding and Subtracting Adding and subtracting can be done by the tabulator, the calculating punch, and the multiplying punch. In the calculating and multiplying punches, the sum or difference is usually punched into the same card from which the numbers were first obtained. The tabulator, however, obtains the result first in a counter; from the counter, it can be printed on paper or punched into a blank card with the aid of the summary punch. Numbers are handled as groups of decimal digits, and the machines mirror the properties of digits in the decimal system. Negative numbers are usually handled as _complements_ (see Supplement 2). For example, if we have in the tabulator a counter with a capacity of six digits, the number-000013 is stored in the counter as the complement 999987. We cannot store in the counter the number +999987, since we cannot distinguish it from-000013. In other words, if a counter is to be used for both positive and negative numbers, its capacity is actually one digit less, since in the last decimal place on the left 0 will mean positive and 9 will mean negative. Multiplying and Dividing Multiplying is done in the calculating and multiplying punches. In both cases, the multiplication table is built into the circuits of the machine, and the system of _left-hand components_ and _right-hand components_ is used (see Supplement 2). Dividing is done in the calculating punch and is carried out in that machine much as in ordinary arithmetic. By means of an estimating circuit the calculating punch guesses what multiple of the divisor will go into the dividend. Then it determines that multiple and tries it. Rounding Off Rounding off may be done in 3 punch-card machines, the calculating and multiplying punches, and the tabulator. For example, suppose we have the numbers 49.1476, 68.5327, and we wish to round them off to 2 decimal places. The results will be 49.15 and 68.53. For the first number, we raise the .0076, turning .1476 into .15, since .0076 is more than .005. For the second number, we drop the .0027 since it is less than .005. Each of these punch-card machines provides what is called a _5 impulse_ in each machine cycle. When the number is to be rounded off, the 5 impulse is plugged into the first decimal place that is to be dropped, and it is there added. If the figure in the decimal place to be dropped is 0 to 4, the added 5 makes no difference in the last decimal place that is to be kept. But, if the figure in the decimal place to be dropped is 5 to 9, then the added 5 makes a carry into the last decimal place that is to be kept, increasing it by 1, and this is just what is wanted for rounding off. LOGICAL OPERATIONS Punch-card machines do many operations of reasoning or logic that do not involve addition, subtraction, multiplication, or division. Just as we can write equations for arithmetical operations, so we can write equations for these logical operations using mathematical logic (see Chapter 9 and Supplement 2). If any reader, however, is not interested in these logical equations, he should skip each paragraph that begins with “in the language of logic,” or a similar phrase. Translating Reading and writing are operations perhaps not strictly of reasoning but of _translating_ from one language to another. Basically these operations take in a mark in one language and give out a mark with the same meaning in another language. For example, the interpreter takes in punched holes and gives out printed marks, but the holes and the marks have the same meaning. The major part of sorting is done by a punch-card sorting machine and can be considered an operation of translating. In sorting a card, the machine takes in a mark in the form of a punched hole on a punch card and specifies a place bearing the same mark where the card is put. The remaining part of sorting is done by human beings. This part consists of picking up blocks of cards from the pockets of the sorter and putting the blocks together in the right sequence. Comparing [Illustration: FIG. 13. Comparer.] The first operation of reasoning done by punch-card machines is _comparing_. For an example of comparing in the operation of the tabulator, let us take instructing the machine when to pick up a total and print it. As an illustration, suppose that we are making a table by state, county, and township of the number of persons counted in a census. Suppose that for each township we have one punch card telling the total number of persons. If all the cards are in sequence, then, whenever the county changes, we want a minor total, and, whenever the state changes, we want a major total. What does the machine do? The tabulator has a mechanism that we shall call a _comparer_ (Fig. 13). A comparer has 2 inputs that may be called _Previous_ and _Current_ and one output that may be called _Unequal_. The comparer has the property of giving out an impulse if and only if there is a difference between the 2 inputs. In the language of the algebra of logic (see Supplement 2 and Chapter 9), let the pieces of information coming into the comparer be _a_ and _b_, and let the information coming out of the comparer be _p_. Then the equation of the comparer is: _p_ = _T_(_a_ ≠ _b_) where “_T_ (···)” is “the truth value of ···” and “···” is a statement, and where the truth value is 1 if true and 0 if false. In wiring the tabulator so that it can tell when to total, we use the comparer. We feed into it the county from the current card and the county from the previous card. Out of the comparer we get an impulse if and only if these two pieces of information are different. This is just what happens when the county changes. The impulse from the comparer is then used in further wiring of the tabulator: it makes the counter that is busy totaling the number of persons in the county print its total and then clear. In the same way, another comparer, which watches state instead of county, takes care of major totals when the state changes. Selecting The next operation of reasoning which punch-card machines can do is _selecting_. The tabulator, collator, interpreter, reproducer, and calculating punch all may contain mechanisms that can select information. These mechanisms are called _selectors_. For example, suppose that we are using the tabulator to make a table showing for each city the number of males and the number of females. In the table we shall have three columns: first, city; second, males; third, females. Suppose that each punch card in columns 30 to 36 shows the total of males or females in a city. Suppose that, if and only if the card is for females, it has an X punch (or 11 punch) in column 79. What do we want to have happen? We want the number in columns 30 to 36 to go into the second column of the table if there is no X in column 79, and we want it to go into the third column of the table if there is an X in column 79. This is just another way of saying that we want the number to go into the males column if it is a number of males, and into the females column if it is a number of females. We make this happen by using a selector. A selector (Fig. 14) is a mechanism with 2 inputs and 2 outputs. The 2 inputs are called _X Pickup_ and _Common_. The 2 outputs are called _X_ and _No X_. The X Pickup, as its name implies, watches for X’s. The Common takes in information. What comes out of X is what goes into Common if and only if an X punch is picked up; otherwise nothing comes out. What comes out of No X is what goes into Common if and only if an X punch is not picked up; otherwise nothing comes out. From the point of view of ordering punch-card equipment, we should note that there are two types of selectors: _X selectors_ or _X distributors_, which have a selecting capacity of one column—that is, one decimal digit—and _class selectors_, which ordinarily have a selecting capacity of 10 columns or 10 decimal digits. But we shall disregard this difference here, as we have disregarded most other questions of capacity in multiplication, division, etc. [Illustration: FIG. 14. Selector.] In the language of logic (see Chapter 9 and Supplement 2), if _p_, _a_, _b_, _c_ are the information in X Pickup, Common, X, and No X, respectively, then the equations for a selector are: _b_ = _a_·_p_ _c_ = _a_·(1 - _p_) Returning now to the table we wish to make, we connect columns 30 to 36 of the punch card to Common. We connect column 79 of the punch card to the X Pickup. We connect the output No X to the males column of the table. We connect the output X to the females column of the table. In this way we make the number in the punch card appear in either one of two places in the table according to whether the number counts males or females. We might mention several more properties of selectors. A selector can be used in the reverse way, with X Pickup, X, and No X as inputs and Common as output (Fig. 15). What will come out of Common is (1) what goes into input No X if there is no X punch in the column to which input X Pickup is wired, and (2) what goes into input X if there is an X punch in the column to which input X Pickup is wired. In this case the logical equation for the selector is: _a_ = _bp_ + _c_(1 - _p_) Also, selectors can be used one after another, so that selecting based on 2 or 3 X punches can be made. [Illustration: FIG. 15. Selector.] In the language of logic, if _p_, _q_, _r_ are the truth values of “there is an X punch in column _i_, _j_, _k_,” respectively, then by means of selectors we can get such a function as: _c_ = _apq_ + _b_(1 - _q_)(1 - _r_) Also, a selector may often be energized not only by an X punch but also by a punch 0, 1, 2, ···, 9 and 12. In this case, the selector is equipped with an additional input that can respond to any digit. This input is called the Digit Pickup. Digit Selector Something like an ordinary selector is another mechanism called a _digit selector_ (Fig. 16). This has one input, Common, and 12 outputs, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12. This mechanism is often included in the tabulator and may be included in other punch-card machines. For example, suppose that we want to do something if and only if column 62 of a punch card contains a 3 or a 4 or a 9. Then we connect a brush that reads column 62 of the punch card to the Common input of the digit selector. And we connect out from the digit selector jointly from outputs 3, 4, and 9. [Illustration: FIG. 16. Digit selector.] In the language of logic, if _a_ is the digit going into Common, and if _p_ is the impulse coming out of the digit selector, then the equation of the mechanism in this case is: _p_ = _T_(_a_ = 3, 4, 9) Sequencer A fourth operation of reasoning done by punch-card machines is finding that one number is greater than, or equal to, or less than another. This operation is done in the collator and may be called _sequencing_. For example, suppose that we have a file of punch cards for cities, showing in columns 41 to 48 the number of people. Suppose that we wish to pick out the cards for cities over 125,000 in population. Now the collator has a mechanism that has 2 inputs and 3 outputs (Fig. 17). We may call this mechanism a _sequencer_, since it can tell the sequence of two numbers. What goes into the _Primary_ input is a number: let us call it _a_. What goes into _Secondary_ is another number: let us call it _b_. An impulse comes out of _Low Primary_ if _a_ is less than _b_. An impulse comes out of _Equal_ if _a_ equals _b_. An impulse comes out of _Low Secondary_ if _a_ is greater than _b_. [Illustration: FIG. 17. Sequencer.] In the language of logic, if _p_, _q_, _r_ are the three indications in Low Primary, Equal, and Low Secondary, then: _p_ = _T_(_a_ < _b_) _q_ = _T_(_a_ = _b_) _r_ = _T_(_a_ > _b_) Returning to our example, we punch up a card with 125,000 in columns 43 to 48, and we put this card into the Secondary Feed. We take the punch cards for cities and put them into the Primary Feed. In the plugboard, we connect the hubs of the Secondary Brushes (that read the card in the Secondary Feed), columns 43 to 48, to the Secondary input of the Sequencer. We connect the hubs of the Primary Brushes (that read the card in the Primary Feed), columns 41 to 48, to the Primary input of the Sequencer. Then we connect the Low Primary output of the Sequencer to a device that causes the city card being examined to fall into pocket 1. We connect Equal output and Low Secondary output to a device that causes the city card being examined to fall into pocket 2. Then, when the card for any city comes along, the machine compares the number of people in the city with 125,000. If the number is greater than 125,000, the card will fall into pocket 1; otherwise the card will fall into pocket 2. At the end of the run, we shall find in pocket 1 all the cards we want. NEW DEVELOPMENTS We may expect to see over the next few years major developments in punch-card machinery. It would seem likely that types of punch-card machines like the following might be constructed: A punch-card machine that performs any arithmetical or logical operation at high speed and may perform a dozen such operations in sequence during the time that a punch card passes through the machine. A punch-card machine that uses loops of punched paper tape, which express either a sequence of values in a table that the machine can consult or a sequence of instructions that govern the operations of the machine. Punch-card machinery that uses a larger card than the 80-column card. A punch-card machine that may have a fairly large amount of internal memory, perhaps 30 or 40 registers where numbers or words may be stored and referred to. SPEED The speed of various operations with present IBM punch-card machines is about as shown in the table. MACHINE OPERATION TIME IN SECONDS Key punch Punch 80 columns About 20 to 40 Verifier Check 80 columns About 20 to 40 Sorter Sort 1 card on 1 column 0.15 Interpreter Print 1 line 0.8 Reproducer Reproduce a card, all 80 columns 0.6 Collator Merge 2 cards 0.25 Multiplying punch Multiply by 8 digits 5.6 Calculating punch Add 0.3 Calculating punch Multiply by 8 digits 3.6 Calculating punch Divide, obtaining 8 quotient digits 9.0 Tabulator Print 1 line, numbers only 0.4 Tabulator Print 1 line, letters included 0.75 Tabulator Add numbers from 1 card 0.4 COST Punch-card machines may be either rented or purchased from some manufacturers but only rented from others. If we take the cost of a clerk as $120 to $150 a month, the monthly rent of most punch-card machines ranges from ⅒ of the cost of a clerk for the simplest type of machine, such as a key punch, to 3 times the cost of a clerk for a complicated and versatile type of machine, such as a tabulator with many attachments. The rental basis is naturally convenient for many kinds of jobs. RELIABILITY The reliability of work with punch cards and punch-card machines is often much better than 99 per cent: in 10,000 operations, failures should be less than 2 or 3. This is, of course, much better than with clerical operations. There are a number of causes for machine or card failures. Sometimes cards may be warped and may not feed into the machines properly. Or, the air in the room may be very dry, and static electricity may make the cards stick together. Or, the air may be too humid; the cards may swell slightly and may jam in the machine. A punch may get slightly out of true alignment, and punches in the cards may be slightly off. A relay may get dust on its contact points and, from time to time, fail to perform in the right way. Considerable engineering effort has been put into remedying these and other troubles, with much success. To make sure that we have correct results from human beings working with punch-card machines, we may verify each process. Information that is punched on the key punch may be verified on the verifier. Multiplications done with multiplicand _a_ and multiplier _b_ may be repeated and compared with multiplications done with multiplicand _b_ and multiplier _a_. Cards that are sorted on the sorter may be put through the collator to make sure that their sequence is correct. It is often good to plan every operation so that we have a proof that the result is right. It is standard practice to have the machines inspected regularly in order to keep them operating properly. On the average, for every 50 to 75 machines, there will be one full-time service man maintaining them and taking care of calls for repairs. Of course, as with any machinery, some service calls will be a result of the human element; for example, a problem may have been set up wrongly on a machine. GENERAL USEFULNESS Punch-card calculations are much faster and more accurate than hand calculations. With punch cards, work is organized so that all cases are handled at the same time in the same way. This process is very different from handling each case separately from start to finish. As soon as the number of cases to be handled is more than a hundred and each item of information is to be used five or more times, punch cards are likely to be advantageous, provided other factors are favorable. Vast quantities of information have been handled very successfully by punch-card machines. Over 30 scientific and engineering laboratories in the United States are doing computation by punch cards. Over a billion punch cards, in fact, are used annually in this country. Chapter 5 MEASURING: MASSACHUSETTS INSTITUTE OF TECHNOLOGY’S DIFFERENTIAL ANALYZER NO. 2 In the previous chapter we talked about machines that move information expressed as holes in cards. In this chapter we shall talk about machines that move information expressed as measurements. ANALOGUE MACHINES A simple example of a device that uses a measurement to handle information is a doorpost. Here the height of a child may be marked from year to year as he grows (Fig. 1). Or, suppose that we have a globe of the world and wish to find the shortest path between Chicago and Moscow. We may lay a piece of string on the globe, pull it tight between those points, and then measure the string on a scale to see about what distance it shows (Fig. 2). Machines that handle information as measurements of physical quantities are called _analogue_ machines, because the measurement is _analogous_ to, or like, the information. A common example of analogue machine is the _slide rule_. With this we calculate by noting the positions of ruled lines on strips that slide by each other. These strips are made of fine wood, or of plastic, or of steel, in such fashion that the ruled lines will hold true positions and not warp. If we space the rulings so that 1, 2, 3, 4, 5, 6 ··· are equally spaced, then the slide rule is useful for addition (Fig. 3). But if we space the rulings so that _powers_ (for example, powers of two—1, 2, 4, 8, 16, 32 ···) (Fig. 4) are equally spaced, we can do multiplication. The spacings are then according to the _logarithms_ of numbers (see Supplement 2). Multiplication is more troublesome than addition, and so more slide rules are made for multiplication than for addition. [Illustration: FIG. 1. Measurement by doorpost.] [Illustration: FIG. 2. Measurement by string.] [Illustration: FIG. 3. Slide Rule for adding.] [Illustration: FIG. 4. Slide Rule for multiplying.] During World War II, the aiming and firing of guns against hostile planes was done by machine. After sighting a plane, these machines automatically calculated how to direct fire against it. They were much better and faster than any man. These _fire-control instruments_ were analogue machines with steel and electrical parts built to fine tolerances. With care we can get accuracy of 1 part in 10,000 with analogue machines, but greater accuracy is very hard to get. PHYSICAL QUANTITIES Suppose that we wish to make an analogue machine. We need to represent information by a measurement of something. What should we select? What physical thing to be measured should we choose to put into the machine? Different amounts of this _physical quantity_ will match with different amounts of the measurement being expressed. In the case of the doorpost, the string, and the slide rule, the physical quantity is distance. In many fire-control instruments, the physical quantity is the _amount of turning of a shaft_ (Fig. 5). Many other physical quantities have from time to time been used in analogue machines, such as electrical measurements. The speedometer of an automobile tells distance traveled and speed. It is an analogue machine. It uses the amount of turning of a wheel, and some electrical properties. It handles information by means of measurements. The basic physical quantity that it measures is the amount of turning of a shaft. [Illustration: FIG. 5. Measurement by amount of turning of a shaft.] DIFFERENTIAL ANALYZER The biggest and cleverest mechanical brain of the analogue type which has yet been built is the _differential analyzer_ finished in 1942 at Massachusetts Institute of Technology in Cambridge, Mass. The fundamental physical quantity used in this machine is the amount of turning of a shaft. The name _analyzer_ means an apparatus or machine for analyzing or solving problems. It happens that the word “analyzer” has been used rather more often in connection with analogue machines, and so in many cases the word “analyzer” carries the meaning “analogue” as well. The word “differential” in the phrase “differential analyzer” refers to the main purpose of the machine: it is specially adapted for solving problems involving _differential equations_. Now what is a differential equation? DIFFERENTIAL EQUATIONS In order to explain what a differential equation is, we need to use certain ideas. These ideas are: _equation_; _formula_; _function_; _rate of change_; _interval_; _derivative_; and _integral_. In the next few paragraphs, we shall introduce these ideas briefly, with some explanation and examples. It is entirely possible for anyone to understand these ideas rather easily, by collecting true statements about them; no one should feel that because these ideas may be new they cannot be understood readily. PHYSICAL PROBLEMS In physics, chemistry, mechanics, and other sciences there are many problems in which the behavior of distance, of time, of speed, heat, volume, electrical current, weight, acceleration, pressure, and many other _physical quantities_ are related to each other. Examples of such problems are: [Illustration: FIG. 6. Paths of a shot from a gun, trajectories.] What are the various angles to which a gun should be raised in order that it may shoot various distances? (See Fig. 6.) (The paths of a shot from a gun are called _trajectories_.) If a plane flies in a direction always at the same angle from the north, how much farther will it travel than if it flew along the shortest path? (See Fig. 7.) (A path always at the same angle from the north is called a _loxodrome_, and a shortest path on a globe is called a _great circle_.) How should an engine be designed so that it will have the least vibration when it moves fast? In _physical problems_ like these, the answer is not a single number but a _formula_. What we want to do in any one of these problems is find a formula so that any one of the quantities may be calculated, given the behavior of the others. For example, here is a familiar problem in which the answer is a formula and not a number: [Illustration: FIG. 7. Paths of a flight.] [Illustration: FIG. 8. Room formulas.] How are the floor area of a room, its length, and its width related to each other? (See Fig. 8.) The answer is told in any one of three _equations_: (_floor area_) EQUALS (_length_) TIMES (_width_) (_length_) EQUALS (_floor area_) DIVIDED BY (_width_) (_width_) EQUALS (_floor area_) DIVIDED BY (_length_) The first equation shows that the floor area depends on the length of the room and also on the width of the room. So we say floor area is a _function_ of length and width. This particular function happens to be _product_, the result of multiplication. In other words, floor area is equal to the product of length and width. Now there is another kind of function called a _differential function_ or _derivative_. A _differential function_ or _derivative_ is an _instantaneous rate of change_. An instantaneous rate of change is the result of two steps: (1) finding a rate of change over an _interval_ and then (2) letting the interval become smaller and smaller indefinitely. For example, suppose that we have the problem: How are speed, distance, and time related to each other? One of the answers is: (_speed_) EQUALS THE INSTANTANEOUS RATE OF CHANGE OF (_distance_) WITH RESPECT TO (_time_) Or we can say, and it is just the same thing in other words: (_speed_) EQUALS THE DERIVATIVE OF (_distance_) WITH RESPECT TO (_time_) Now we can tell what a differential equation is. It is simply an equation in which a derivative occurs, such as the last example. Perhaps the commonest kind of equation in physical problems is the differential equation. SOLVING PHYSICAL PROBLEMS Now we were able to change the equation about floor area into other forms, if we wanted to find length or width instead of floor area. When we did this, we ran into the _inverse_ or opposite of multiplication: division. In the same way, we can change the equation about speed into other forms, if we want to find distance or time instead of speed. If we do this, we run into a new idea, the inverse or opposite of the derivative, called _integral_. The two new equations are: (_distance_) EQUALS THE INTEGRAL OF (_speed_) WITH RESPECT TO (_time_) (_time_) EQUALS THE INTEGRAL OF [ONE DIVIDED BY (_speed_)] WITH RESPECT TO (_distance_) These equations may also be called differential equations. An integral is the result of a process called _integrating_. To integrate speed and get distance is the result of three steps: (1) breaking up an interval of time into a large number of small bits, (2) adding up all the small distances that we get by taking each bit of time and multiplying by the speed which applied in that bit of time, and (3) letting the bits of time get smaller and smaller, and letting the number of them get larger and larger, indefinitely. In other words, (_total distance_) EQUALS THE SUM OF ALL THE SMALL (_distances_), EACH EQUAL TO: A BIT OF (_time_) MULTIPLIED BY THE (_speed_) APPLYING TO THAT BIT This is another way of saying as before, (_distance_) EQUALS THE INTEGRAL OF (_speed_) WITH RESPECT TO (_time_) To solve a differential equation, we almost always need to integrate one or more quantities. ORIGIN AND DEVELOPMENT OF THE DIFFERENTIAL ANALYZER For at least two centuries, solving differential equations to answer physical problems has been a main job for mathematicians. Mathematics is supposed to be logical, and perhaps you would think this would be easy. But mathematicians have been unable to solve a great many differential equations; only here and there, as if by accident, could they solve one. So they often wished for better methods in order to make the job easier. A British mathematician and physicist, William Thomson (Lord Kelvin), in 1879 suggested solving differential equations by a machine. He went further: he described mechanisms for integrating and other mathematical processes, and how these mechanisms could be connected together in a machine. No such machine was then built; engineering in those years was not equal to it. In 1923, a machine of this type for solving the differential equations of trajectories was proposed by L. Wainwright. In 1925, at Massachusetts Institute of Technology, the problem of a machine to solve differential equations was again being studied by Dr. Vannevar Bush and his associates. Dr. Bush experimented with mechanisms that would integrate, add, multiply, etc., and methods of connecting them together in a machine. A major part of the success of the machine depended on a device whereby a very small turning force would do a rather large amount of work. He developed a way in which the small turning force, about as small as a puff of breath, could be used to tighten a string around a drum already turning with a considerable force, and thus clutch the drum, bring in that force, and do the work that needed to be done. You may have watched a ship being loaded, seen a man coil a rope around a _winch_, and watched him swing a heavy load into the air by a slight pull on the rope (Fig. 9). If so, you have seen this same principle at work. The turning force (or _torque_) that pulls on the rope is greatly increased (or _amplified_) by such a mechanism, and so we call it a _torque amplifier_. [Illustration: FIG. 9. Increasing turning force; winch, or torque amplifier.] By 1930, Dr. Bush and his group had finished the first differential analyzer. It was entirely mechanical, having no electrical parts except the motors. It was so successful that a number of engineering schools and manufacturing businesses have since then built other machines of the Bush type. Each time, some improvements were made in accuracy and capacity for solving problems. But, if you changed from one problem to another on this type of machine, you had to do a lot of work with screwdrivers and wrenches. You had to undo old mechanical connections between shafts and set up new ones. Accordingly, in 1935, the men at MIT started designing a second differential analyzer. In this one you could make all the connections electrically. MIT finished its second differential analyzer in 1942, but the fact was not published during World War II, for the machine was put to work on important military problems. In fact, a rumor spread and was never denied that the machine was a white elephant and would not work. The machine was officially announced in October 1945. It was the most advanced and efficient differential analyzer ever built. We shall talk chiefly about it for the rest of this chapter. A good technical description of this machine is in a paper, “A New Type of Differential Analyzer,” by Vannevar Bush and Samuel H. Caldwell, published in the _Journal of the Franklin Institute_ for October 1945. GENERAL ORGANIZATION OF MIT DIFFERENTIAL ANALYZER NO. 2 A differential analyzer is basically made up of shafts that turn. When we set up the machine to solve a differential equation, we assign one shaft in the machine to each quantity referred to in the equation. It is the job of that shaft to keep track of that quantity. The total amount of turning of that shaft at any time while the problem is running measures the size of that quantity at that time. If the quantity decreases, the shaft turns in the opposite direction. For example, if we have speed, time, and distance in a differential equation, we label one shaft “speed,” another shaft “time,” and another shaft “distance.” If we wish, we may assign 10 turns of the “time” shaft to mean “one second,” 2 turns of the “distance” shaft to mean “one foot,” and 4 turns of the “speed” shaft to mean “one foot per second.” These are called _scale factors_. We could, however, use any other convenient units that we wished. By just looking at a shaft or a wheel, we can tell what part of a full turn it has made—a half, or a quarter, or some other part—but we cannot tell by looking how many full turns it has made. In the machine, therefore, there are mechanisms that record not only full turns but also tenths of turns. These are called _counters_. We can connect a counter to any shaft. When we want to know some quantity that a shaft and counter are keeping track of, we read the counting mechanism. The second differential analyzer, which MIT finished in 1942, went a step further than any previous one. In this machine, a varying number can be expressed either (1) mechanically as the amount of turning of a shaft, or (2) electrically as the amount of two _voltages_ in a pair of wires. The MIT men did this by means of a mechanism called an _angle-indicator_. Angle indicators have essentially three parts: a _transmitter_, a _receiver_, and switches. The transmitter (Fig. 10) can sense the exact amount that a shaft has turned and give out a voltage in each of two wires which tells exactly how much the shaft has turned (Fig. 11). The receiving device (Fig. 12), which has a motor, can take in the voltages in the two wires and drive a second shaft, making it turn in step with the first shaft. By means of the switchboard (Fig. 13), the two wires from the transmitter of any angle-indicator can lead anywhere in the machine and be connected to the receiver of any other angle indicator. [Illustration: FIG. 10. Scheme of angle-indicator transmitter.] [Illustration: FIG. 11. Indication of angle.] [Illustration: FIG. 12. Scheme of angle-indicator receiver.] In a differential analyzer, we can connect the shafts together in many different ways. For example, suppose that we want one shaft _b_ to turn twice as much as another shaft _a_. For this to happen we must have a mechanism that will connect shaft _a_ to shaft _b_ and make shaft _b_ turn twice as much as shaft _a_. We can draw the scheme of this mechanism in Fig. 14: a box, standing for any kind of simple or complicated mechanism; a line going into it, standing for input of the quantity _a_; a line going out of it, standing for output of the quantity _b_; and a statement saying that _b_ equals 2_a_. [Illustration: FIG. 13. Switchboard.] One mechanism that will make shaft _b_ turn twice as much as shaft _a_ is a _pair of gears_ such that: (1) they mesh together and (2) the gear on shaft _a_ has twice as many teeth as the gear on shaft _b_ (Fig. 15). On the mechanical differential analyzer that MIT finished in 1930, a pair of gears was the mechanism actually used for doubling. To make one shaft turn twice as much as another by this device, we would: go over to the machine with a screwdriver; pick out from a box two gears, one with twice as many teeth as the other; slide them onto the shafts that are to be connected; make the gears mesh together; and screw them tight on their shafts. [Illustration: FIG. 14. Scheme of a doubling mechanism.] [Illustration: FIG. 15. Example of a doubling mechanism.] On the MIT differential analyzer No. 2, however, we are better off. A much more convenient device for doubling is used. We make use of: a _gearbox_ in whichthere are two shafts that may be geared so that one turns twice as much as the other, and two angle-indicator transmitters and receivers. Looking at the drawing (Fig. 16), we can see that: shaft _a_ drives shaft _c_ to turn in step, shaft _c_ drives shaft _d_ to turn twice as much, and shaft _d_ drives shaft _b_ to turn in step. Here we can accomplish doubling by closing the pairs of switches that connect to the gearbox shafts. [Illustration: Angle indicators: T, transmitters, and R, receivers FIG. 16. Another example of a doubling mechanism.] Above, we have talked about a mechanism with gears that would multiply the amount of turning by the _constant ratio_ 2. But, of course, in a calculation, any ratio, say 7.65, 3.142, ···, might be needed, not only 2. In order to handle various constant ratios, gearboxes of two kinds are in differential analyzer No. 2. The first kind is a _one-digit gearbox_. It can be set to give any of 10 ratios, 0.1, 0.2, 0.3, ···, 1.0. The second kind is a _four-digit gearbox_. It can be set to give any one of more than 11 thousand ratios, 0.0000, 0.0001, 0.0002, ···, 1.1109, 1.1110. We can thus multiply by constant ratios. Adders We come now to a new mechanism, whose purpose is to add or subtract the amount of turning of two shafts. It is called an _adder_. The scheme of it is shown in Fig. 17: an input shaft with amount of turning _a_, another input shaft with amount of turning _b_, and an output shaft with amount of turning _a_ + _b_. The adder essentially is another kind of gearbox, called a _differential gear assembly_. This name is confusing: the word “differential” here has nothing to do with the word “differential” in “differential analyzer.” This mechanism is very closely related to the “differential” in the rear axle of a motor car, which distributes a driving thrust from the motor to the two rear wheels of the car. [Illustration: FIG. 17. Scheme of an adder mechanism.] [Illustration: FIG. 18. Example of an adding mechanism (differential gear assembly).] A type of differential gear assembly that will add is shown in Fig. 18. This is a set of 5 gears _A_ to _E_. The 2 gears _A_ and _B_ are input gears. The amount of their turning is _a_ and _b_, respectively. They both mesh with a third gear, _C_, free to turn, but the axis of _C_ is fastened to the inside rim of a fourth, larger gear, _D_. Thus _D_ is driven, and the amount of its turning is (_a_ + _b_)/2. This gear meshes with a gear _E_ with half the number of teeth, and so the amount of turning of _E_ is _a_ + _b_. We can subtract the turning of one shaft from the turning of another simply by turning one of the input shafts in the opposite direction. Integrators Another mechanism in a differential analyzer, and the one that makes it worth while to build the machine, is called an _integrator_. This mechanism carries out the process of integrating, of adding up a very large number of small changing quantities. Figure 19 shows what an integrator is. It has three chief parts: a _disc_, a little _wheel_, and a _screw_. The round disc turns horizontally on its vertical shaft. The wheel rests on the disc and turns vertically on its horizontal shaft. The screw goes through the support of the disc; when the screw turns, it changes the distance between the edge of the wheel and the center of the disc. [Illustration: FIG. 19. Mechanism of integrator.] Now let us watch this mechanism move. If the disc turns a little bit, the wheel pressing on it must turn a little bit. If the screw turns a small amount, the distance between the edge of the wheel and the center of the disc changes. The amount that the wheel turns is doubled if its distance from the center of the disc is doubled, and halved if that distance is halved. So we see that: (_the total amount that the wheel turns_) EQUALS THE SUM OF ALL THE SMALL (_amounts of turning_), EACH EQUAL TO: A BIT OF (_disc turning_) MULTIPLIED BY THE (_distance from the center of the disc to the edge of the wheel_) APPLYING TO THAT BIT If we look back at our discussion of integrating (p. 72), we see that the capital words here are just the same as those used there. Thus we have a mechanism that expresses integration: (_the total amount that the wheel turns_) EQUALS THE INTEGRAL OF (_the distance from the center of the disc to the wheel_) WITH RESPECT TO (_the amount that the disc turns_) The scheme of this mechanism is shown in Fig. 20. For example, suppose that the screw measures the speed at which a car travels and that the disc measures time. The wheel, consequently, will measure distance traveled by the car. The mechanism INTEGRATES speed with respect to time and gives distance. [Illustration: FIG. 20. Scheme of integrator.] This mechanism is the device that Lord Kelvin talked about in 1879 and that Dr. Bush made practical in 1925. The mechanical difficulty is to make the friction between the disc and the wheel turn the wheel with enough force to do other work. In the second differential analyzer, the angle indicator set on the shaft of the wheel solves the problem very neatly. [Illustration: FIG. 21. Graph of air resistance coefficient.] Function Tables The behavior of some physical quantities can be described only by a series of numbers or a graphic curve. For example, the _resistance_ or _drag_ of the air against a passing object is related to the speed of the object in a rather complicated way. Part of the relation is called the _drag coefficient_ or _resistance coefficient_; a rough graph of this is shown in Fig. 21. This graph shows several interesting facts: (1) when the object is still, there is no air resistance; (2) as it travels faster and faster, air resistance rapidly increases; (3) when the object travels with the speed of sound, resistance is very great and increases enormously; (4) but, when the object starts traveling with a speed about 20 per cent faster than sound, the drag coefficient begins to decrease. This drawing or _graph_ shows in part how air resistance depends on speed of object; in other words, it shows the drag coefficient as a _function_ of speed (see Supplement 2). [Illustration: FIG. 22. Pointer following graph.] Now we need a way of putting any function we wish into a differential analyzer. To do this, we use a mechanism called a _function table_. We draw a careful graph of the function according to the scale we wish to use, and we set the graph on the outside of a large drum (Fig. 22). For example, we can put the resistance coefficient graph on the drum; the speed (or _independent variable_) goes around the drum, and the resistance coefficient (or _dependent variable_) goes along the drum. The machine slowly turns the drum, as may be called for by the problem. A girl sits at the function table and watches, turning a handwheel that keeps the sighting circle of a pointer right over the graph. The turning of the handwheel puts the graphed function into the machine. Instead of employing a person, we can make one side of the graph black, leaving the other side white, and put in a _phototube_ (an electronic tube sensitive to amount of light) that will steer from pure black or pure white to half and half (see Fig. 23). We do not need many function tables to put in information, because we can often use integrators in neat combinations to avoid them. We shall say more about this possibility later. We can also use a function table to put out information and to draw a graph. To do so, we disconnect the handwheel; we connect the shaft of the handwheel to the shaft that records the function we are interested in; we take out the pointer and put in a pen; and we put a blank sheet of graph paper around the drum. [Illustration: FIG. 23. Phototube following graph.] We have now described the main parts of the second MIT differential analyzer. They are the parts that handle numbers. We can now tell the capacity of the differential analyzer by telling the number of main parts that it holds: Shafts About 130 One-digit gearboxes 12 Four-digit gearboxes 16 Adders About 16 Integrators 18 Function tables 3 On a simpler level, we can say that the machine holds these physical parts: Miles of wire About 200 Relays About 3000 Motors About 150 Electronic tubes About 2000 INSTRUCTING THE MIT DIFFERENTIAL ANALYZER NO. 2 Besides the function tables for putting information into the machine, there are three mechanisms that read punched paper tape. The three tapes are called the _A tape_, the _B tape_, and the _C tape_. From these tapes the machine is set up to solve a problem. Suppose that we have decided how the machine is to solve a problem. Suppose that we know the number of integrators, adders, gearboxes, etc., that must be used, and know how their inputs and outputs are to be connected. To carry out the solution, we now have to put the instructions and numbers into the machine. The _A_ tape contains instructions for connecting shafts in the machine. Each instruction connects a certain output of one type of mechanism (adder, etc.) to a certain input of another type of mechanism. When the machine reads an instruction on this tape, it connects electrically the transmitting angle-indicator of an output shaft to the receiving angle-indicator of another input shaft. Now the connecting part of the differential analyzer behaves as if it were very intelligent: it assigns an adder or an integrator or a gearbox, etc., to a new problem only if that mechanism is not busy. For example, if a problem tape calls for adder 3 (in the list belonging to the problem), the machine will assign the first adder that is not busy, perhaps adder 14 (in the machine), to do the work. Each time that adder 3 (in the problem list) is called for in the _A_ tape, the machine remembers that adder 14 was chosen and assigns it over again. This ability, of course, is very useful. The _B_ tape contains the ratios at which the gearboxes are to be set. For example, suppose that we want gearbox 4 (in the problem list) to change its input by the ratio of 0.2573. The machine, after reading the _A_ tape, has assigned gearbox 11 (in the machine list). Then, when the machine reads the _B_ tape, it sets the ratio in gearbox 11 to 0.2573. The answer to a differential equation is different for different starting conditions. For example, when we know speed and time and wish to find distance traveled and where we have arrived, we must know the point at which we started. We therefore need to arrange the machine so that we can put in different starting conditions (or different _initial conditions_, as the mathematician calls them). The _C_ tape puts the initial conditions into the machine. For example, reading the _C_ tape for the problem, the machine finds that 3000 should, at the start of the problem, stand in counter 4. The machine then reads the number at which counter 4 actually stands, say 6728.3. It subtracts the two numbers and remembers the difference, -3728.3. And whenever the machine reads that counter later, finding, say, 9468.4 in it, first the 3728.3 is subtracted, and then the answer 5740.1 is printed. ANSWERS Information may come out of the machine in either one of two ways: in printed numbers or in a graph. In fact, the same quantity may come out of the machine in both ways at the same time. To obtain a graph, we change a function table from input to output, put a pen on it, and have it draw the graph. The machine has 3 electric typewriters. The machine will take numerical information out of the counters at high speed even while they are turning, and it will put the information into relays. Then it will read from the relays into the typewriter keys one by one while they type from left to right across the page. HOW THE DIFFERENTIAL ANALYZER CALCULATES Up to this point in this chapter, the author has tried to tell the story of the differential analyzer in plain words. But for reading this section, a little knowledge of calculus is necessary. (See also Supplement 2.) If you wish, skip this section, and go on to the next one. We have described how varying quantities, or _variables_, are operated on in the machine in one way or another: adding, subtracting, multiplying by a constant, referring to a table, and integrating. What do we do if we wish to multiply 2 variables together? A neat trick is to use the formula: _xy_ = ⌠_x dy_ + ⌠_y dx_ ⌡ ⌡ To multiply in this way requires 2 integrators and 1 adder. The connections that are made between them are as follows: Shaft _x_ To Integrator 1, Screw Shaft _x_ To Integrator 2, Disc Shaft _y_ To Integrator 1, Disc Shaft _y_ To Integrator 2, Screw Integrator 1, Wheel To Adder 1, Input 1 Integrator 2, Wheel To Adder 1, Input 2 Adder 1, Output To Shaft expressing _xy_ A product of 2 variables _under the integral sign_ can be obtained a little more easily, because of the curious powers of the differential analyzer. Thus, if it is desired to obtain ∫_xy dt_, we can use the formula: ┌ ┐ ⌠ ⌠ │ ⌠ │ │_xy dt_ = │_x d_│ │ _y dt_ │ ⌡ ⌡ │ ⌡ │ └ ┘ and this operation does not require an adder. The connections are as follows: Shaft _t_ To Integrator 1, Disc Shaft _y_ To Integrator 1, Screw Integrator 1, Wheel To Integrator 2, Disc Shaft _x_ To Integrator 2, Screw Integrator 2, Wheel To Shaft expressing ∫_xy dt_ In order to get the quotient of 2 variables, _x_/_y_, we can use some more tricks. First, the _reciprocal_ 1/_y_ can be obtained by using the two _simultaneous equations_: ⌠ 1 ⌠ 1 │ ———— _dy_ = log _y_, │ - ———— _d_(log _y_) = _y_ ⌡ _y_ ⌡ _y_ The connections are as follows: Shaft _y_ To Integrator 1, Disc AND TO Integrator 2, Wheel Shaft log _y_ To Integrator 1, Wheel AND TO Integrator 2, Disc Shaft 1/_y_ To Integrator 1, Screw, AND NEGATIVELY TO Integrator 2, Screw In order to get _x_/_y_, we can then multiply _x_ by 1/_y_. We see that this setup gives us log _y_ for nothing, that is, without needing more integrators or other equipment. Clearly, other tricks like this will give sin _x_, cos _x_, _eˣ_, _x²_, and other functions that satisfy simple differential equations. An integral of a reciprocal can be obtained even more directly. Suppose that ⌠ 1 _y_ = │ ————— _dt_ ⌡ _x_ 1 Then _Dₜy_ = —————, _D{_y} t_ = _x_, _x_ ⌠ and _t_ = │_x dy_ ⌡ The connections therefore are: Shaft _t_ To Integrator, Wheel Shaft _x_ To Integrator, Screw Shaft _y_ To Integrator, Disc The light wheel then drives the heavy disc. Clearly only the angle-indicator device makes this possible at all. Naturally, the closer the wheel gets to the center of the disc, that is, _x_ approaching zero, the greater the strain on the mechanism, and the more likely the result is to be off. Mathematically, of course, the limit of 1/_x_ as _x_ approaches zero equals infinity, and this gives trouble in the machine. There is no standard mathematical method for solving any differential equation. But the machine provides a standard direct method for solving all differential equations with only one independent variable. First: assign a shaft for each _term_ that appears in the equation. For example, the highest derivative that appears and the independent variable are both assigned shafts. The integral of the highest derivative is easily obtained, and the integral of that integral, etc. Second: connect the shafts so that all the mathematical relations are expressed. Both _explicit_ and _implicit_ equations may be expressed. Third: for any shaft there must be just one _drive_, or source of torque. A shaft may, however, drive more than one other shaft. Fourth: choose _scale factors_ so that the limits of the machine are not exceeded yet at the same time are well used. For example, the most that an integrator or a function table can move is 1 or 2 feet. Also, the number of full turns made by a shaft in representing its variable should be large, often between 1000 and 10,000. Of course, as with all these large machines, anyone would need some months of actual practice before he could put on a problem and get an answer efficiently. AN APPRAISAL OF THE MACHINE The second MIT differential analyzer is probably the best machine ever built for solving most differential equations. It regularly has an accuracy of 1 part in 10,000. This is enough for most engineering problems. If greater accuracy is needed, the second differential analyzer cannot provide it. Once in a while the machine can reach an accuracy of 1 part in 50,000; but, to balance this, it is sometimes less accurate than 1 part in 10,000. The MIT differential analyzer No. 2 can find answers to problems very quickly. The time for setting up a problem to be run on the machine ranges from 5 to 15 minutes. The time for preparing the tapes that set up the problem is, of course, longer; but the punch for preparing the tape is a separate machine and does not delay the differential analyzer. The time for the machine to produce a single solution to a problem ranges usually from 3 minutes to a half-hour. It is easy to put on a problem, run a few solutions, take the problem off, study the results, change a few numbers, and then put the problem back on again. This virtue is a great help in a search in a new field. While the study is going on, time is not wasted, for the machine can be busy with a different problem. Running a problem a second time is a good check on the reliability of an answer. For, when the problem is run the second time, we can arrange that the machine will route the problem to other mechanisms. The machine has a control panel. Here the operator watching the machine can tell what units are doing what parts of what problems. If a unit gives trouble or needs to be inspected, the clerk can throw a “busy” switch. Then the machine cannot choose that unit for work to be done. The machine contains many protecting signals and alarms. It is idle for repairs less than 5 per cent of the time. It is not easy to determine the total cost of the machine, for it was partially financed by several large gifts. Also, much of the labor was done by graduate students in return for the instruction that they gained. The actual out-of-pocket cost was about $125,000. If the machine were to be built by industry, the cost would likely be more than 4 times as much. A simple differential analyzer, however, can be cheap. Small scale differential analyzers have been built for less than $1000; their accuracy has been about 1 part in 100. There are many things that this machine cannot do; it was not built to do them. (1) It cannot choose methods of solution. (2) It cannot perform steps in solving a problem that depend on results as they are found. (3) It cannot solve differential equations containing two or more independent variables. Such equations are called _partial differential equations_; they appear in connection with the flow of heat or air or electricity in 2 or 3 dimensions, and elsewhere. (4) It cannot solve problems requiring 6 or more digits of accuracy. (5) The machine, while running, can store numbers only for an instant, since it operates on the principle of smoothly changing quantities; however, when the machine stops, the number last held by each device is permanently stored. None of these comments, however, are criticisms of the machine. Instead they show avenues of development for future machines. As was said before, for solving most differential equations, this machine has no equal to date. The range of problems which any differential analyzer can do depends mostly on the number of its integrators. The second differential analyzer has 18 and provides for expansion to 30. The machine is constructed, also, so that it can be operated in 3 independent sections, each working to solve a different problem. The differential analyzer can operate unattended. After it has been set up and the first few results examined, it can be left alone to grind out large blocks of answers. An interesting example of the experimental use of a differential analyzer in a commercial business is the following: In Great Britain, R. E. Beard of the Pearl Assurance Company built a differential analyzer with 6 integrators. He applied this machine to compute to 3 figures certain insurance values known as _continuous annuities_ and _continuous contingent insurances_. He has described the machine and the application he made in a paper published in the _Journal of the Institute of Actuaries_, Vol. 71, 1942, pp. 193-227. Chapter 6 ACCURACY TO 23 DIGITS: HARVARD’S IBM AUTOMATIC SEQUENCE-CONTROLLED CALCULATOR One of the first giant brains to be finished was the machine in the Computation Laboratory at Harvard University called the _IBM Automatic Sequence-Controlled Calculator_. This great mechanical brain started work in April 1944 and has been running 24 hours a day almost all the time ever since. It has produced quantities of information for the United States Navy. Although many problems that have been placed on it have been classified by the Navy as confidential, the machine itself is fully public. The way it was working on Sept. 1, 1945, has been thoroughly described in a 540-page book published in 1946, Volume I of the Annals of the Harvard Computation Laboratory, entitled _Manual of Operation of the Automatic Sequence-Controlled Calculator_. Since then the machine has been improved in many ways. This machine does thousands of calculating steps, one after another, according to a scheme fixed ahead of time. This property is what gives the machine its name: _automatic_, since the individual operations are automatic, once the punched tape fixing the chain of operations has been put on the machine, and _sequence-controlled_, since control over the sequence of its operations has been built into the machine. ORIGIN AND DEVELOPMENT More than a hundred years ago, an English mathematician and actuary, Charles Babbage (1792-1871), designed a machine—or _engine_ as he called it—that would carry out the sequences of mathematical operations. In the 1830’s he received a government grant to build an _analytical engine_ whereby long chains of calculations could be performed. But he was unsuccessful, because the refined physical devices necessary for quantities of digital calculation were not yet developed. Only in the 1930’s did these physical devices become sufficiently versatile and reliable for a calculator of hundreds of thousands of parts to be successful. The Automatic Sequence-Controlled Calculator at Harvard was largely the concept of Professor Howard H. Aiken of Harvard. It was built through a partnership of efforts, ideas, and engineering between him and the International Business Machines Corporation, in the years 1937 to 1944. The calculator was a gift from IBM to Harvard University. Some very useful additional control units, named the _Subsidiary Sequence Mechanism_, were built at the Harvard Computation Laboratory in 1947 and joined to the machine. [Illustration: FIG. 1. Scheme of Harvard IBM Automatic Sequence-Controlled Calculator.] GENERAL ORGANIZATION The machine (see Fig. 1) is about 50 feet long, 8 feet high, and about 2 feet wide. It consists of 22 panels; 17 of them are set in a straight line, and the last 5 are at the rear of the machine. In the scheme of the machine shown in Fig. 1, the details you would see in a photograph have been left out. Instead you see the sections of the machine that are important because of what they do: _input_, _memory_, _control_, and _output_. Why do we not see a section labeled “computer”? Because in this mechanical brain the computing part of the machine is closely joined to the memory: every storage register can add and subtract. We shall soon discuss these sections of the machine more fully. PHYSICAL DEVICES Now in order for any brain to work, _physical devices_ must be used. For example, in the human body, a nerve is the physical device that carries information from one part of the body to another. In the Harvard machine, an insulated _wire_ is the physical device that carries information from one part of the machine to another. One side of every panel in the Harvard machine is heavily laden with a great network of wires. Between the panels, you can see in many places cables as thick as your arm and containing hundreds of wires. More than 500 miles of wire are used. The physical devices in the Harvard machine are numerous, as we would expect. It is perhaps not surprising that this machine has more than 760,000 parts. But, curiously enough, there are only 7 main kinds of physical devices in the major part of the machine. They are: wire, _two-position switches_, _two-position relays_ (see Chapter 2), _ten-position switches_, _ten-position relays_, _buttons_, and _cam contacts_ (see below). These are the devices that handle information in the form of electrical impulses. They can be combined by electrical circuits in a great variety of ways. There are, of course, other kinds of physical devices that are important, but they are not numerous, and they have rather simple duties. Looking at the machine, you can see three examples easily. Physical devices of the first kind convert punched holes into electrical impulses: 2 _card feeds_, 4 _tape feeds_. Those of the second kind convert electrical impulses into punched holes: 1 _card punch_, 1 _tape punch_. Those of the third kind convert electrical impulses into printed characters: 2 _electric typewriters_. We can think of a fourth kind of physical device that would be a help, but, at present writing, it does not yet exist: a device that converts printed characters into electrical impulses. The Harvard machine, of course, is complicated. But it is complicated because of the variety of ways in which relatively simple devices have been connected together to make a machine that thinks. Switches A _two-position switch_ (see Fig. 2) turned by hand connects a wire to either one of 2 others. These 2 positions may stand for “yes” and “no,” 0 and 1, etc. There are many two-position switches in the machine. A _ten-position switch_ or _dial switch_ (see Fig. 3) turned by hand connects the wire running into the center of the switch with a wire at any one of ten positions 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 around the edge. There are over 1400 dial switches in the machine. How does turning the pointer on the top of the dial make connection between the center wire and the edge wire? Under the face of the dial is the part that works, a short rod of metal fastened to the pointer (shown with dashes in Fig. 3). When the pointer turns, this rod also turns, making the desired connection. [Illustration: FIG. 2. Two-position switch.] [Illustration: FIG. 3. Dial switch.] Relays _Two-position relays_—more often called just _relays_ (see Chapter 2)—do the automatic routing of the electrical impulses that cause computing to take place. Each relay may take 2 positions, open or closed, and these positions may stand for 0 and 1. There are more than 3000 relays in the Harvard machine. A magnet pulling one way and a spring pulling the other way are sufficient in an ordinary relay to give 2 positions, “on” and “off,” “yes” and “no,” 0 and 1. But how do we make a relay that can hold any one of 10 positions? Figure 4 shows one scheme for a _ten-position relay_. The _arm_ can take any one of 10 positions, connecting the contact _Common_ to any one of the contacts O, 1, 2, 3, 4, 5, 6, 7, 8, and 9 so that current can flow. The _gear_ turns all the time. When an impulse comes in on the _Pickup_ line, the _clutch_ connects the arm to the gear. When an impulse comes in on the _Drop-out_ line, the clutch disconnects the arm from the gear. For example, suppose that the ten-position relay is stopped at contact 2, as shown. Suppose that we now pick up the relay, hold it just long enough to turn 3 steps, and then drop it out. The relay will now rest at contact 5. [Illustration: FIG. 4. Scheme of a ten-position relay, or counter position.] [Illustration: FIG. 5. Scheme of a counter wheel.] In the Harvard machine, the ten-position relays, much like the scheme shown, do the same work as _counter wheels_ (Fig. 5) in an ordinary desk calculating machine, and so they are often spoken of as _counter positions_ in the Harvard machine. They are very useful in the machine not only because they express the 10 decimal digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 but also because adding and subtracting numbers is accomplished by turning them through the proper number of steps. In fact, an additional impulse is provided when the counter position turns from 9 to 0, for purposes of carry. A group of 24 counter positions makes up each _storage counter_—or _storage register_—in the machine. There are 2200 of these counter positions. Each is connected to a continuously running gear on a small shaft (Fig. 6). All these shafts are connected by other gears and shafts to a main drive shaft, and they are driven by a 5-horsepower motor at the back of the machine. When a counter position is supposed to step, a clutch connects the drive to the running gear, and the counter position steps. When the counter position is supposed to stay unchanged, the clutch is disconnected and the driving gear runs free. In fact, when you first approach the Harvard machine, about the first thing you are aware of is the running of these gears and the intermittent whirring and clicking of the counter positions as they step. The machine gives a fine impression of being busy! [Illustration: FIG. 6. Scheme of counter 16.] Timing Contacts A _button_ (see Fig. 7) is a device for closing an electric circuit when and only when you push it. A simple example is the button for ringing a bell: you push the button, a circuit is closed, and something happens. When you let go, the circuit is opened. The Harvard machine has a button for starting, a button for stopping, and many others. [Illustration: FIG. 7. Button.] [Illustration: FIG. 8. Cam, with 5 lobes and contact.] A _cam contact_ (see Fig. 8) is an automatic device for closing an electric circuit for just a short interval of time. When the lobes on the cam strike the contact, it closes and current flows. When the lobes have gone by, the spring pushes open the contact, and no current flows. Just as a two-position relay is the automatic equivalent of a two-position switch, and a ten-position relay is the automatic equivalent of a ten-position switch, so a cam contact is the automatic equivalent of a button. All the cams in the machine have 20 pockets where small round metal lobes may or may not be inserted. Each cam makes a full turn once in ³/₁₀ of a second and is in time with all the others. Thus we can time all the electrical circuits in the machine in units of ³/₂₀₀ of a second. NUMBERS Numbers in the machine regularly consist of 23 decimal digits. The 24th numerical position at the left in any register contains only 0 for a positive number and only 9 for a negative number. _Nines complements_ (see Supplement 2) are used for negative numbers. For example,-00284 is represented as 999715, supposing that we had 5-digit numbers instead of 23-digit numbers. The sum of two nines complements is automatically corrected so that it is still a correct nines complement. The device that accomplishes this is called _end-around-carry_ (see Supplement 2). The decimal point is fixed for each problem; in other words, in any problem, the decimal point is consistently kept in one place, usually between the 15th and 16th decimal columns from the right. HOW INFORMATION GOES INTO THE MACHINE Numerical information may go into the machine in any one of 3 ways: (1) by regular IBM punch cards, using standard IBM card feeds (panel 16); (2) by hand-set dial switches (panels 1, 2); and (3) by long loops of punched tape placed on the value tape feeds (panels 12 to 14). Three sets of 24 columns each punched on a regular IBM punch card can be used to send 3 numbers and their signs into the machine in one machine cycle. This is the fastest way for giving numbers to the machine, but the most limited; for the cards must be referred to in order and can be referred to automatically only once. Also, there is the risk that they may be out of order. A card may be passed through the machine without reading; this saves some sorting in preparing cards for the machine. Machines for preparing the cards are regular IBM key punches, and machines for sorting them after preparation are regular IBM card sorters. In panels 1 and 2 there are 60 registers by which unchanging numbers like 1, or 3.14159265···, or 7.65 may be put into the machine. These are called the _constant registers_. Each constant register consists of 24 dial switches and contains 23 digits and a sign, 0 if positive and 9 if negative. Whenever the mathematician says a certain constant is needed for a problem, the operator of the machine walks over to these panels, and, while the machine is turned off, sets the dial switches for the number, one by one, by hand. If we need 40 constants of 10 digits each for a problem, then the operator sets 400 dial switches by hand and makes certain that the remaining 14 switches in each of the 40 constant registers used are either at 0 or 9, depending on the sign of the number. Only then can he return to start the machine. [Illustration: FIG. 9. Value tape code.] The third means by which numerical information can be put into the machine is the _value tape feeds_, in panels 12, 13, and 14. Here the machine can consult tables of numbers. The numbers are punched on paper tape 24 holes wide, made of punch-card stock. Tapes for the value tape feeds may be prepared by hand or by the machine itself using punch cards or machine calculation. The tapes use equally spaced _arguments_ (see Supplement 2). The tape punch changes the decimal digits in its keyboard into the following punching code (see Fig. 9): 0 0000 5 1100 1 1000 6 1010 2 0100 7 1001 3 0010 8 0110 4 0001 9 0101 Here the 1 denotes a punched hole and 0 no punched hole, and the 4 columns from left to right of the code correspond to 4 rows of the paper tape from bottom to top. To make sure the value tape is correct, the machine itself can read the value tape and check it mathematically or compare it with punch-card values. HOW INFORMATION COMES OUT OF THE MACHINE Information comes out of the machine in any one of three ways: (1) by punching on IBM cards with a regular IBM card punch that is built into the machine (panel 17), (2) by typing on paper sheets with electric typewriters (panels 16 and 17), and (3) by punching paper tape 24 holes wide of the same kind as is fed into the machine. Usually, one of the electric typewriters is used to print a result for a visual check and to print it before the machine makes a specified check of the value. Then, about 10 seconds later, after the result has been checked as specified in the machine, the checked result is printed by the second typewriter. In the second typewriter, a special one-use carbon ribbon of paper is used to produce copy for publication by a photographic process. The card punch writes a number more rapidly than an electric typewriter. This extra speed is sometimes very useful. However, the punch’s chief purpose is to record intermediate results on punch cards. Then, if there is a machine failure, and if the problem has been well organized, the problem may be run over from these intermediate results, instead of requiring a return to the original starting information. The tape punch used for preparing tape by hand can also be operated by cable from the machine. HOW INFORMATION IS HANDLED IN THE MACHINE The machine is a mechanical brain. So, between taking in information and putting out information, the machine does some “thinking.” It does this thinking according to instructions. The instructions go into the machine as: (1) the setting of switches, or (2) the pressing of buttons, or (3) the wiring of plugboards, or (4) feeding in tape punched with holes. The instructions are remembered in the machine in these 4 ways, and we can call these sets of devices the control of the machine. To illustrate: One of the buttons pressed for every problem is the Start Key: when you press it, the machine starts to work on the problem. One of the switches with which you give instructions is a switch that turns electric typewriter 1 on or off. One of the plugboards contains some hubs by which you can tell the machine how many figures to choose in the quotient when dividing, for clearly you do not need a quotient of 23 figures every time the machine divides. You can have 5 choices in any one problem; you can specify them by plugging, and you can call for any one of 5 choices of quotient size from time to time during the problem. In many cases, when we wish the machine to do the same thing for all of a single problem and do it whenever the occasion arises, we can put the instruction into the wiring of a plugboard. We use plugboard wiring, for example, in fixing the decimal point in multiplication, so that the product will read out properly, and in guiding the operation of the typewriters, so that printing will take place in the columns where we want it. Sequence of Steps The most important part of the control of the machine is the _sequence-tape feed_ and its _sequence-control tape_. These tell the machine a great part of what operations are to be performed. [Illustration: FIG. 10. Sequence-control tape code.] At the end of the room where the machine is, there is the special tape punch mentioned above. It holds a big spool of card stock that is thin, flexible, smooth, and tough. With one keyboard we may prepare value tape. With another keyboard we prepare the sequence-control tape. The tape (see Fig. 10) contains places for 24 round punched holes in each row. Some and only some of these holes are punched. Each row of punched holes is equivalent to an instruction to the machine and is called a _line of coding_ or _coding line_. In general, the instruction has the form: Take a number out of Register _A_; put the number into Register _B_; and perform operation _C_. The first group of 8 holes at the left is called the _A field_ or the _out-field_. Here we tell the machine where a number is to be taken from. The middle group of 8 holes is called the _B field_ or the _in-field_. Here we tell the machine where a number is to be put. The last group of 8 holes is called the _C field_ or the _miscellaneous field_. Here we tell the machine part or all of the operation that is to be performed. To illustrate (see Fig. 10), we have holes 3, 2, 1 punched in the _A_ field, holes 3, 2 punched in the _B_ field, and hole 7 punched in the _C_ field. Now 321 is the _code_—or machine language, or machine call number—for storage counter 7; 32 is the code for storage counter 6; and 7 in the _C_ field is the code (in this case, and generally) for “Add, and read the next line of coding.” So, if we punch out this line of coding and put the tape on the machine, we tell the machine to read the number in counter 7, add it into counter 6, and proceed to the next line of coding and read that. The holes in each group of 8 holes from left to right are numbered: 8, 7, 6, 5, 4, 3, 2, 1. The code 631, for example, means that holes 6, 3, 1 are punched and that no holes are punched at 8, 7, 5, 4, 2. Since it is more natural, the code is read from left to right, or 631, instead of from right to left in the sequence 136. The devices in the machine have _in-codes_, used in the in-field, and _out-codes_, used in the out-field. For each of the 72 regular storage counters, the in-code and the out-code are the same. The first 8 storage counters have the codes 1, 2, 21, 3, 31, 32, 321, 4, 41; the last 2 storage counters, the 71st and the 72nd, have the codes 7321, 74. The constant registers—often called _constant switches_, or just _switches_—naturally have only out-codes, since numbers can be entered into the constant registers only by setting dial switches by hand. The first 8 constant registers have the out-codes 741, 742, 7421, 743, 7431, 7432, 74321, 75, and the 59th and 60th constant registers have the out-codes 821, 83. Transferring, Adding, and Clearing Each storage counter has the property that any number transferred into it is added into it. For example, the instruction Take the number in switch 741; transfer it into storage register 321 is coded: 741, 321, 7 The 7 in the third column is an instruction to the sequence-tape feed to turn up to the next coding line and read it. If any number is already stored in register 321, the content of 741 will be added to it, and the total will then be stored in 321. Resetting or clearing a regular storage register is accomplished by a coding that is a departure from the usual scheme of “out” and “in.” The instruction Clear register 321; read the next coding line is coded: 321, 321, 7 Similarly, you can clear any other regular storage register if you repeat its code in the out-and in-fields. However, a few of the storage registers in the machine have special reset codes, and these may occur in any of the three fields _A_, _B_, _C_. As the result of a recent modification of the machine, you can easily double the number in any storage register. For example, the instruction Double the number in register 321; read the next coding line is coded: 321, 321, 743 Subtracting If the number in switch 741 is to be subtracted from the number in storage counter 321, the instruction is changed into: Take the negative of the number in switch 741; transfer it into storage register 321; read the next line of coding The coding line becomes: 741, 321, 732 By putting 32 in the _C_ field, we cause the number in switch 741 to be subtracted from whatever number is in register 321. We have 2 more choices in adding and subtracting. The value of the number without regard to sign—in other words, its _absolute value_ (see Supplement 2)—may be added or subtracted. The instruction Add the absolute value of is expressed by a _C_ field code 2, and the instruction Add the negative of the absolute value of is expressed by a _C_ field code 1. Multiplying When we wish to multiply one number by another and get a product, we have 3 numbers. We tell the machine about each of these numbers on a separate line of coding. Multiplication is signaled by sending a number into the _multiplicand counter_. The multiplicand counter has an in-code 761. If the multiplicand is in 321, the instruction is: Take the number in 321; enter it as multiplicand; read the next coding line The coding is: 321, 761, 7 On the third following coding line, the multiplier is sent into the _multiplier counter_. If the multiplier is in switch 741, the instruction is: Take the number in 741; enter it as multiplier; read the next coding line The coding is: 741, ——, 7 We do not punch anything in the middle field: the machine is “educated” and “knows” that it has started a multiplication and needs a multiplier, and it expects this multiplier in the third coding line. To have no code for the multiplier counter is, of course, a departure from the general rule, but it saves some punching and permits the use of this space for certain other codes, thus saving some operating time. We need not confuse the 761 in-code for the multiplicand counter with the 761 out-code, which happens to be the out-code of the 25th constant register, because neither can occur in the other’s field. We may, of course, use other registers besides 321 and 741 for supplying the multiplicand and multiplier. To get the product and put it into any storage counter _D_, we use two lines of coding one right after the other: —— —— 6421 8761 _D_ —— The _product counter_ has the out-code 8761. When the product is desired, it is called for, transferred into counter _D_, and the multiplication unit is automatically cleared. It takes time, however, for the machine to perform a multiplication. That is the reason for the preceding coding line and the 6421 in the _C_ field. While the multiplication is going on, we can instruct the machine to do other things that we want done. We can insert or _interpose_ coding lines in between the multiplier line and the product line. For example, if we have a multiplier of 10 digits, we can insert 8 coding lines and maybe more. The 6421 code essentially tells the machine to finish both the multiplication and the interposed instructions, and, as soon as the later one of these two tasks is finished, to transfer out the product to counter _D_. Up to the middle of 1946, the wiring of the machine was a little different and less convenient. When the product was obtained by the multiplication unit, it had to be accepted and transferred at once into one of the 72 storage registers. Dividing Division is called for by first sending the divisor into the _divisor counter_, and this has a code 76 in the _B_ field. If the divisor is in counter 321, the instruction may be: Take the number in 321; enter it as divisor; read the next coding line The coding will then be: 321, 76, 7 Three coding lines later, the dividend is called for, and the coding, if the dividend is in switch 7431, is: 7431, ——, 7 We can send the quotient, when ready, into any desired counter _Q_ by the following two lines of coding: —— —— 642 876 _Q_ —— In the same way as with multiplication, we can insert a number of coding lines in between the dividend line and the first quotient line. Both multiplication and division are carried out in the same unit of the machine, the _multiply-divide unit_. The machine first constructs a table of the multiples of the multiplicand or divisor: 1 times, 2 times, 3 times, ···, 9 times. In multiplication this table is then used by selecting multiples according to the digits of the multiplier one after another. In division the table is used by comparing multiples of the divisor against the dividend and successive remainders, finding which will go and which will not. Since the numbers in the machine are normally of 15 to 23 digits, any particular multiple will be used, on the average, several times, and so this process is relatively efficient. Actually the multiplicand and the divisor go into the same counter. Division, however, has the code 76 and multiplication the code 761, and so the difference is essentially an operation code not in the third or _C_ field. Consulting a Table When we desire the machine to consult a table of values (i.e., a _function_—see Supplement 2), we punch the table with its arguments and function values on a tape, and we put the tape on a value tape feed mechanism. The instruction to the machine may be: Take the number in register _A_; find the value of the function for this number, and enter it in register _B_. The coding is: —— —— 73 _A_ 7654 61 —— —— 762 —— —— 543 —— —— 75431 841 7654 —— _A_ 763 6421 8762 _B_ 73 —— 8763 7 Without explaining this coding line by line, we can say that this is what happens: The machine reads the argument in register _A_. The machine reads the argument in the table at which the value tape feed is resting. It subtracts them, and thereby determines how far away the desired argument is. The machine then turns the tape that required distance. It checks that the new argument is the wanted argument. It reads the value of the function entered at that point on the function tape. Selecting There is a storage counter in the machine that is called the _selection counter_. The selection counter is counter 70 and has the code 732. It has all the properties of an ordinary storage counter and, in addition, one extra property: depending on the sign of the number stored in the selection counter, it is possible to select whether some other number shall be treated positively or negatively. In other words, addition of a number anywhere in the machine may take place either positively or negatively, if the number stored in the selection counter is positive or negative, respectively. For example, suppose that _x_ is the number in the selection counter. Suppose that _y_ is the number in some other counter _A_. Suppose that _z_ is the number in counter _B_. Suppose that we use the coding: _A_, _B_, 7432 What we get in _B_, because of the 7432 in the third or _C_ field, is _z_ plus _y_ if _x_ is positive or zero, and _z_ minus _y_ if _x_ is negative. In the language of the algebra of logic (see Chapter 9 and Supplement 2), where _T_( ...) is “the truth value of ...,” the number in _b_ equals: _z_ + _y_·_T_(_x_ ≥ 0) - _y_·_T_(_x_ < 0) (The nines complement of 0, namely 999···9 to 24 digits, is treated by the machine as negative.) Why do we need an operation like this in a mechanical brain? Among other reasons, what we want to do with a number, in mathematics, often depends on its sign. It may happen that a table is, for negative arguments, the negative of what it is for positive arguments; in other words, _F_(-_x_) =-_F_(_x_). This is true, for instance, for a table of _cubes_ {_F_(_x_) = _x_³} or for a table of _trigonometric tangents_ (see Supplement 2). If so, we certainly do not want to take the time and trouble to list the whole table. We put down only half the table and then, if _x_ is negative, use the negative of the value in the table. In order to apply such a time-saving rule when using the machine, we need the selection counter or its equivalent. Checking There is another special counter in the machine that is called the _check counter_. It also has all the properties of an ordinary storage counter and, in addition, one extra property: If the sign of the number stored in the check counter on a certain coding line is negative, then on the next coding line the machine may be stopped. In other words, suppose that the check counter stores a certain tolerance _t_. Suppose, under the instructions we give the machine, that it calculates a positive number _x_ that ought to be less than this tolerance. Suppose that something may go wrong and that _x_ actually may be greater than _t_. Then we put a check into our instructions. We tell the machine: When you have found _x_, subtract it from _t_. If the result is positive, go ahead. If the result is negative or zero, _stop_! Here is the coding. Suppose that the tolerance _t_ is in switch 751. Suppose that the number _x_ to be checked is in counter 4321. Then the instructions and coding are: Clear the check counter — — 7 Put in the tolerance, from switch 751 751 74 7 Subtract the absolute value of the number to be checked 4321 74 71 Stop, O Mechanical Brain, if your result be negative! — — 64 An operation like this is very useful in a mechanical brain. It enables the calculation to be interrupted if something has gone wrong. Of course, other operations of checking besides this one are used—for example, inspecting for reasonableness the results printed on typewriter 1. Other Operations There are other operations in the machine. There are two pairs of storage registers that can be _coupled_ together so that we can handle problems requiring numbers of 46 digits instead of 23. Registers 64 and 65 can be coupled, and registers 68 and 69 can be coupled. There is another storage counter, No. 71, that has an extra property. We can read out the number it holds times 1, or times 10¹², or times 10⁻¹², as may be called for. As a result of this counter, we can do problems requiring 144 registers storing numbers of 11 digits each, instead of 72 registers storing 23 digits each. Bigger statistical problems can be handled, for example. There are some minor sequences of operations, or _subroutines_, that can be called for by a single code. The subroutine may be a whole set of additions, subtractions, multiplications, divisions, and choices, having a single purpose: to compute some number by a _process of rapid approximation_ (see Supplement 2). There are built-in subroutines for some special mathematical functions: the _logarithm_ of a number to the base 10, the _exponential_ of a number to the base 10, and the _sine_ of a number. (See Supplement 2.) There are also 10 changeable subroutines, each of 22 coding lines, which can be called in, when wanted, by the main sequence-control tape or by each other. These subroutines constitute the Subsidiary Sequence Mechanism, and are extremely useful. They have _A_, _B_, and _C_ fields just like the main sequence-control, but they are given information by plugging with short lengths of wire instead of by feeding punched paper tape. RAPID APPROXIMATION FOR A LOGARITHM Up to this point in this chapter the author has tried to tell the facts about the Harvard machine in plain words. But for reading this section, a little knowledge of calculus is necessary. (See also Supplement 2.) If you wish, skip this section and go on to the next one. What is the process that the machine uses to compute any desired logarithm to 23 digits? Suppose that we take for an example the process by which the machine computes log_{10} 49.3724. We choose a 6-digit number for simplicity; the machine would handle a 23-digit number in the same way. The process uses 2 fundamental equations involving the logarithm: the sum relation log (_a_·_b_·_c_···) = log _a_ + log _b_ + log _c_··· and the series relation _h_² _h_³ _h_⁴ logₑ(1 + _h_) = _h_ - ———— + ———— - ———— + ···, │_h_│ < 1 2 3 4 The error in this series is less than the first neglected term. Now, the machine stores the base 10 logarithms (to 23 decimal places) of the following 36 numbers: 1 1.1 1.01 1.001 2 1.2 1.02 1.002 ... ... ... ... 9 1.9 1.09 1.009 First, the number 49.3724 is examined in a counter called the _Logarithm-In-Out counter_, and the position of the decimal point is determined, giving the _characteristic_ of the logarithm. The number 49.3724 has the characteristic 1. Next, 4 successive divisions are performed, in which the 4 divisors are (1) the first digit of the number, (2) the first 2 digits of the quotient, (3) the first 3 digits of the next quotient, and (4) the first 4 digits of the subsequent quotient; thus, 4.93724/4 = 1.23431 1.23431/1.2 = 1.02860 1.02860/1.02 = 1.00843 1.00843/1.008 = 1.00043 For simplicity we have kept only 6 digits, although the machine, of course, would keep 23. It is interesting to note that the machine is able to sense digits and thus determine the 4 divisors; this is an arithmetical and numerical process and one that cannot be done in ordinary algebra. We now have: log₁₀ 49.3724 = 1 + log₁₀ 4 + log₁₀ 1.2 + log₁₀ 1.02 + log₁₀ 1.008 + log₁₀ 1.00043 To compute log₁₀ 1.00043 to 21 decimals we use ( _h_² _h_³ _h_⁴ _h_⁵ _h_⁶ ) log₁₀_e_ · (_h_ - ————— + ————— - ———— + ————— - —————) ( 2 3 4 5 6 ) with _h_ = 0.00043. Only 6 terms of the series relation are needed. For, the error is less than _h_⁷/7, which is less than 10⁻²¹/7, since _h_ < ¹/₁₀₀₀. The machine uses the series relation in the form log₁₀ (1 + _h_) = {([{(_c_₆_h_ + _c_₅)_h_ + _c_₄}_h_ + _c_₃]_h_ + _c_₂)_h_ + _c_₁}_h_ where _c_₁ = _M_, _c_₂ = -_M_/2, _c_₃ = _M_/3, ···, and _M_ = log₁₀__e_= 0.434294···. The 6 values of the _c_’s are also stored in the machine. When any logarithm is to be computed, the sum of the characteristic, of the 4 logarithms of the successive divisors, and of the first 6 terms of the series relation gives the logarithm. The maximum time required is 90 seconds. AN APPRAISAL OF THE CALCULATOR The IBM Automatic Sequence-Controlled Calculator at Harvard is a landmark in the development of machines that think. Its capacity for many problems for which it is suited is far beyond the capacity of a hundred human computers. Speed The time required in the machine for adding, subtracting, transferring, or clearing numbers is ³/₁₀ of a second. This is the time of one machine cycle or of reading one coding line. Multiplication takes at the most 6 seconds, and an average of 4 seconds. Division takes at the most 16 seconds, and an average of 11 seconds. Each, however, requires only 3 lines of coding, or ⁹/₁₀ of a second’s attention from the sequence mechanism; interposed operations fill the rest of the time. To calculate a logarithm, an exponential, or a sine to the full number of digits obtainable by means of the automatic subroutine takes at the most 90, 66, and 60 seconds, respectively. To get three 24-digit numbers from feeding a punch card takes ⅓ second. To punch a number takes from ½ second up to 3 seconds. To print a number takes from 1½ seconds up to 7 seconds. Cost and Value The cost of the machine was somewhere near 3 or 4 hundred thousand dollars, if we leave out some of the cost of research and development, which would have been done whether or not this particular machine had ever been built. A staff of 10 men, consisting of 4 mathematicians, 4 operators, and 2 maintenance men, are needed to keep the machine running 24 hours a day. This might represent, if capitalized, another 1 or 2 hundred thousand dollars. If a capital value of $500,000 is taken as equivalent to $50,000 a year, then the cost of the machine in operation 24 hours a day is in the neighborhood of $150 a day or $6 an hour. The value of the machine, however, is very much greater. If 100 human beings with desk calculators were set to work 8 hours a day at $1.50 an hour, the cost would be $1200 a day, or 8 times as much. Yet it is very doubtful that the work they could produce would equal that turned out by the machine, either in quality or quantity, when the machine is well suited to the problem. Reliability By reliability we mean the extent to which the results produced by the machine can be relied on to be right. The machine contains no built-in device for making its operations reliable. So, if we wish to check a multiplication, for example, we can do the multiplication a second time, interchanging the multiplier and the multiplicand. But if, say, digit 16 of the product were not transferring correctly, we would get the same wrong result both ways and we would not have a sufficient check. Thus, when we set up a problem for the machine to do, one of the big tasks we have is checking. We have to work out ways of making sure that the result, when we get it, is right and ways of instructing the machine to make the tests we want. This is not a new task. Whenever you or I set out to solve a problem, we have to make sure—usually by doing the problem twice, and preferably by doing it a different way the second time—that our answer, when we get it, is correct. One of the chief tasks for the mathematician, in making a sequence-control tape for the machine, is to put into it sufficient checks to make sure that the results are correct. We can use a number of different kinds of partial checks: the check counter; _differences_, and _smoothness_ (see Supplement 2); watching the results printed on typewriter 1; mathematical checks; comparison with known specific values; etc. In actual experience on the machine, human failures, such as failure to state the problem exactly or failure to put it on the machine correctly, have given about as much trouble as mechanical failures. The machine operates without mechanical failure about 90 to 95 per cent of the time. The balance of the time the machine is idle while being serviced or repaired. The machine is serviced by mechanics trained and supervised at Harvard. Often when we change the machine from one problem to another problem, we find some kind of trouble. Consequently, we need to work out in detail the first part of any calculation placed on the machine. We then compare the results step by step with the results produced by the machine. Any mathematician working with the machine needs considerable training in order to diagnose trouble quickly and guide the maintenance men to the place where repair or replacement is needed. Once you find the trouble, you can fix it easily. Without disturbing the soldered connections, you can easily pull out from its socket a relay that is misbehaving and plug in a new relay. With a screwdriver you can change a counter position—detach it from its socket and replace it by another one that is working correctly. One “bug” that will long be remembered around the Laboratory was a case involving a 5 that would incorrectly come in to a number every now and then. It did not happen often—only once in a while. After a week of search the bug was finally located: the insulation on a wire that carried a 5 had worn through in one spot, and once in a while this wire would shake against a post that could carry current and took in the 5! Efficiency In many respects, this machine is efficient and well-balanced. Its reading and writing speed is close to its calculating speed. We can punch or print a result on the average for every 10 additions or 1½ multiplications. The memory of 72 numbers in the machine is extremely useful; a smaller memory is a serious limitation on the achievements of a computing machine. The machine can do many kinds of arithmetic and logic. It is well educated and can compute automatically some rather complicated mathematical functions, like logarithm or sine. It has done difficult and important problems. It has computed and tabulated (see Supplement 2) _Bessel functions_, _definite integrals_, etc. It can solve _differential equations_ (see Chapter 5) and many other problems in mathematics, physics, and engineering. On the other hand, no calculator will ever again be built just like this one, useful though it is. Electronic computing is easily 100 times as fast as relay computing; nearly every future calculator will do its computing electronically. Many other improvements will be made. For example, in this calculator, there are 72 addition-subtraction mechanisms, yet only one of these can be used at a time. Also, the machine has only one combined multiply-divide unit. So we have to organize any computation with few multiplications, and with still fewer divisions, for they take longer still. Until 1947, we had to organize any computation in this calculator into one single fixed sequence of operations. In other words, there was no way to move from one subroutine to another subroutine depending on some indication that turned up in our computation. Recently, the Harvard Computation Laboratory decided to remedy this condition and provided the Subsidiary Sequence Mechanism equivalent to 10 subroutines of 22 lines of coding each. These are on relays and plug wires and may be called for by the sequence-control tape or by each other. This provision has added greatly to the efficiency of the calculator. Whatever else can be said about the Harvard IBM Automatic Sequence-Controlled Calculator, it must be said that this was the first general-purpose mechanical brain using numbers in digit form and able to do arithmetic and logic in hundreds of thousands of steps one after another. And great credit must go to Professor Howard H. Aiken of Harvard and the men of International Business Machines Corporation who made this great mechanical brain come into existence. Chapter 7 SPEED—5000 ADDITIONS A SECOND: MOORE SCHOOL’S ENIAC (ELECTRONIC NUMERICAL INTEGRATOR AND CALCULATOR) Another of the giant brains that has begun to work is named _ENIAC_. This name comes from the initial letters of the full name, _Electronic Numerical Integrator and Calculator_. Eniac was born in 1942 at the Moore School of Electrical Engineering, of the University of Pennsylvania, in Philadelphia. Eniac’s father was the Ordnance Department of the U. S. Army, which provided the funds to feed and rear the prodigy. In the short space of four years, Eniac grew to maturity, and in February 1946 he began to earn his own living by electronic thinking. Eniac promptly set several world’s records. He was the first giant brain to use electronic tubes for calculating. He was the first one to reach the speed of 5000 additions a second. He was the first piece of electronic apparatus containing as many as 18,000 electronic tubes all functioning together successfully. As soon as Eniac started thinking, he promptly made relay calculators obsolete from the scientific point of view, for they have a top speed of perhaps 10 additions a second. At the age of 5, he moved to Maryland at a cost of about $90,000, and his permanent home is now the Ballistic Research Laboratories at the U. S. Army’s Proving Ground at Aberdeen, Md. ORIGIN AND DEVELOPMENT In the Department of Terrestrial Magnetism in the Carnegie Institution of Washington, a great deal of information about the earth is studied. Many kinds of physical observations are there gathered and analyzed: electricity in the atmosphere, magnetism in the earth, and the weather, for example. In 1941, a physicist, Dr. John W. Mauchly, was thinking about the great mass of numerical information they had to handle. He became convinced that much swifter ways of handling these numbers were needed. He was certain electronic devices could be used for computing at very high speeds, yet he found no one busy applying electronics in this field. With hopes of finding some way of developing electronic computing, he joined the staff of the Moore School of Electrical Engineering in the autumn of 1941. The Moore School in 1934 and 1935 had built a differential analyzer; and, from that time on, the school had made a number of improvements in it. In 1941, with war imminent, the differential analyzer was put hard at work calculating tables for the Army’s Ballistic Research Laboratories. These tables were mostly firing tables, tables of the paths along which projectiles travel when fired—_trajectories_; obviously, you cannot fire a gun usefully, unless you know how to aim it. The amount of calculation of trajectories was so huge that Dr. Mauchly suggested that a machine using electronic tubes be constructed to calculate them. A good deal of discussion took place between men at the Moore School, men at the Ballistic Research Laboratories, and men from the Ordnance Department in Washington. A contract for research into an electronic trajectory computer was concluded with the Ordnance Department of the U. S. Army. Mauchly and one of the young electronics engineers studying at Moore School, J. Presper Eckert, Jr., set to work on the design. Gradually the design of a machine took form, and the crucial experiments on equipment were completed. In 1943, the design was settled as a special-purpose machine to calculate trajectories. Later on, the group modified the plans here and there to enable the machine to calculate a very wide class of problems. A group of Moore School electronics engineers and technicians during 1944 and 1945 built the machine, using as much as possible standard radio tubes and parts. Here, again, in spite of the successful progress of the electronic machine, the rumor that it was a “white elephant” was allowed to spread in order to protect the work from prying enemy ears. GENERAL ORGANIZATION The main part of Eniac consists of 42 _panels_, which are placed along the sides of a square U. Each of these panels is 9 feet high, 2 feet wide, and 1 foot thick. They are of sheet steel, painted black, with switches, lights, etc., mounted on them. At the tops of all the panels are air ducts for drawing off the hot air around the tubes. Large motors and fans above the machine suck the heated air away through the ducts. There are also 5 pieces of equipment which can be rolled from place to place and are called _portable_, but there is no choice as to where they can be plugged in. We shall call this equipment panels 43 to 47. Panels Now what are these panels, and what do they do? Each panel is an assembly of some equipment. The names of the panels are shown in the accompanying table. The arrangement of Eniac at the Ballistic Research Laboratories as shown in the table is slightly different from the arrangement of Eniac at Moore School. NAMES OF PANELS OF ENIAC PANEL NO. NAME (AND ADDITIONAL NAMES IN SOME CASES) 1 Initiating Unit 2 Cycling Unit 3, 4 Master Programmer, panels 1, 2 5 Accumulator 1 6 Accumulator 2 7 Accumulator 3 8 Accumulator 4 (Quotient) 9 Divider-Square-Rooter 10 Accumulator 5 (Numerator I) 11 Accumulator 6 (Numerator II) 12 Accumulator 7 (Denominator—Square Root I) 13 Accumulator 8 (Denominator—Square Root II) 14 Accumulator 9 (Shift I) 15 Accumulator 10 (Shift II) 16 Blank panel for new unit (Converter) 17 Accumulator 11 (Multiplier) 18 Accumulator 12 (Multiplicand) 19-21 Multiplier, panels 1, 2, 3 22 Accumulator 13 (Left-Hand Partial Products I) 23 Accumulator 14 (Left-Hand Partial Products II) 24 Accumulator 15 (Right-Hand Products I) 25 Accumulator 16 (Right-Hand Products II) 26 Blank panel for new unit (100 Registers) 27 Accumulator 17 28 Accumulator 18 29 Accumulator 19 30 Accumulator 20 31, 32 Function Table 1, panels 1, 2 33, 34 Function Table 2, panels 1, 2 35, 36 Function Table 3, panels 1, 2 37-39 Constant Transmitter, panels 1, 2, 3 40-42 Printer, panels 1, 2, 3 43-45 Portable Function Tables _A_, _B_, and _C_ 46 IBM Card Reader 47 IBM Summary Punch _Note_: The accumulators from which a number can be sent to the printer are now accumulators 1, 2, and 15 to 20. In reading over the table, we find a number of words that need explaining. Some of the explanation we can give in the summary of the units of Eniac: SUMMARY OF UNITS OF ENIAC QUANTITY DEVICE SIGNIFICANCE 20 Accumulators Store, add, and subtract numbers 1 Multiplier Multiplies 1 Divider-Square-Rooter Divides, and obtains twice the _square root_ of a number (see Supplement 2) 3 Function Tables Part of the memory, for referring to tables of numbers 1 Constant Transmitter Stores numbers from the card reader and from hand-set switches 1 Printer Punches machine results into cards 1 Cycling Unit Controls the timing of the various parts of the machine 1 Initiating Unit Has controls for starting a calculation, for clearing, etc. 1 Master Programmer Holds the chief controls for coordinating the various parts of the machine An _accumulator_ is a storage counter. It can hold a number; it can clear a number; it can transmit a number either positively or negatively; and it can receive a number by adding the number in and thus holding the sum of what it held before and the number received. Eniac when first built had only 20 accumulators, and so it could remember only 20 numbers at one time (except for constant numbers set in switches). This small memory was the most serious drawback of Eniac; panel 26 was designed, therefore, to provide a great additional memory capacity. The _divider-square-rooter_, as its name tells, is a mechanism that can divide and that can find twice the square root of a number. Eniac is one of the several giant brains that have had square root capacity built into them, particularly since square root is needed for solving trajectories. Many panels of Eniac have double duty and some have triple duty. For example, panel 24 is an accumulator, but it also (1) stores the right-hand partial products (see Supplement 2) of the multiplier and (2) was a register, when Eniac was at Moore School, from which information to be punched in the printer could be obtained. Clearly, if we have a multiplication to do, we cannot also use this accumulator for storing a number that is to remain unchanged during the multiplication. Parts The total number of parts in Eniac is near half a million, even if we count electronic tubes as single parts. There are over 18,800 electronic tubes in the machine. It is interesting to note that only 10 kinds of electronic tubes are used in the calculating circuits and only about 60 kinds of _resistors_ and 30 kinds of _capacitors_. A resistor is a device that opposes the steady flow of electric current through it to a certain extent (called _resistance_ and measured in _ohms_). A capacitor is a device that can store electrical energy up to a certain extent (called _capacitance_ and measured in _farads_). All these tubes and parts are standard parts in radios. All types are identified by the color labels established in standard radio manufacturing. It is the combinations of these parts, like the combinations of pieces in a chess game, that give rise to the marvelous powers of Eniac. The combinations of parts at the first level are called _plug-in units_. A plug-in unit is a standard box or tray or chassis made of sheet steel containing a standard assembly of tubes, wires, and other parts. It can be pushed in or pulled out of a standard socket with many connections. An example of a plug-in unit is a _decade_, or, more exactly, an _accumulator decade_. This is just a counter wheel or decimal position expressed in Eniac language: it can express successively all the digits from 0 to 9 and then pass from 9 to 0, giving rise to a carry impulse. It is striking that a mechanical counter to hold 10 digits can be made up of 10 little wheels, ¼ inch wide and an inch high. But an accumulator in Eniac, to hold 10 digits, is a set of 10 decades each 2 inches wide and 2½ feet high. There are only about 20 kinds of plug-in units altogether. Each plug-in unit is interchangeable with any other of the same kind. So, if a decade, for example, shows trouble, you can pull it out of its socket and plug in a spare decade instead. Numbers Numbers in Eniac are of 10 decimal digits with a sign that may be plus or minus. The decimal point is fixed. However, when you are connecting one accumulator with another, you can shift the decimal point if you want to. Also, 2 accumulators may be coupled together so as to handle numbers of 20 digits. HOW INFORMATION GOES INTO THE MACHINE There are three ways by which information—numbers or instructions—can go into the Eniac. Numbers can be put into the machine by means of punch cards fed into the Card Reader, panel 46, or switches on the Constant Transmitter, panels 37 to 39. Numbers or instructions can also go into the machine by means of the Function Tables, panels 43 to 45. Here there are dial switches, which are set by hand. Instructions can also go into the machine by setting the switches, plugging the inputs and outputs, etc., of the wires or lines along which numbers and instructions travel. HOW INFORMATION COMES OUT OF THE MACHINE There are two ways by which numerical information can come out of the machine. Numbers can come out of the machine punched on cards by the Summary Punch, panel 47. They are then printed in another room by means of a separate IBM tabulator. Also, numbers can be read out of the machine by means of the lights in the _neon bulbs_ mounted on each accumulator. You can read in the lights of a panel the number held by the accumulator, if the panel is not computing. HOW INFORMATION IS MANIPULATED IN THE MACHINE Eniac handles information rather differently from any other of the big brains. Instead of having only one bus or “railroad line” along which numbers can be sent, Eniac has more than 10 such lines. They are called _digit trays_ and labeled A, B, C, ···. Each contains 11 _digit trunk lines_ or _digit trunks_—10 to carry the digits of a number, and the 11th to carry the sign. Instead of having only one telegraph line along which instructions can be sent, Eniac has more than 100 such lines. They are called _program trunk lines_ or _program trunks_ and labeled A1, A2, ···, A11, B1, B2, ···, B11, ···, etc. They are assembled in groups of 11 to a tray; the _program trays_, in fact, look just like the digit trays, except for their connectors and their purpose, which are different. Below, we shall make clear how the program trays carry control information. Now, actually, Eniac has many more trunk lines than we have just stated, for each of the lines we have mentioned can be divided into numerous separate sections by the removal of plug connections. How we choose to do this depends on the needs of the problem, the space between the panels, the time when the line is used, etc. Transferring Numbers, Adding, and Subtracting Basically, a number is represented in Eniac by an arrangement of on and off electronic tube elements in pairs, called _flip-flops_. There is one flip-flop enclosed in a single tube (type 6SN7) for each value 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 for each of the 10 digits stored in an accumulator. So we have at least 100 flip-flops for each accumulator, and thus at least 100 electronic tubes are required to store 10 digits. Actually, an accumulator needs 550 electronic tubes. So we see that there is not very much of a future in this type of arrangement. The newer electronic brains use different devices for storage of numbers. In order to show what number is stored in an accumulator, there are 100 little neon bulbs mounted on the face of each accumulator panel. Each bulb glows when the flip-flop that belongs to it is on. For example, suppose that the 4th decade in Accumulator 11 holds the digit 7. Then the 7th flip-flop in that decade will be on, and all the others will be off. The 7th neon bulb for that decade will glow. Now suppose that the number 7 is in the 4th decade in Accumulator 11 and is to be added into, say, the 4th decade in Accumulator 13. And suppose that it is to be subtracted from the 4th decade in Accumulator 16. What do we do, and what will Eniac do? First, we pick out 2 digit trays, say B and D. Accumulator 11 has 2 outputs, called the _add output_ and the _subtract output_. We plug B into the add output and D into the subtract output. Then we go over to Accumulators 13 and 16. They have 5 inputs, that is, 5 ways of being plugged to receive numbers from digit trunks. These inputs are named with _Greek letters_, α, β, γ, δ, ε. We choose one input, say γ, for Accumulator 13, and we plug B into that input. We choose one input, say ε, for Accumulator 16, and we plug D into that input. Now we have the “railroad” switching for numbers accomplished. We have set up a channel whereby the number in Accumulator 11 will be routed positively into Accumulator 13 and negatively into Accumulator 16. Now let us suppose that, at some definite time fixed by the control, Accumulator 11 is stimulated to transmit and Accumulators 13 and 16 are conditioned to receive. When this happens, a group of 10 _pulses_ comes along a direct trunk from the cycling unit, and a group of 9 pulses comes along another trunk. We can think of each pulse as a little surge of electricity lasting about 2 millionths of a second. The _ten-pulses_, as the first group is called, are 10 millionths of a second apart. The _nine-pulses_, as the second group is called, are also 10 millionths of a second apart but are sandwiched between the ten-pulses. When the 1st ten-pulse comes along, the 7th flip-flop in Accumulator 11 goes off, the 8th flip-flop goes on, the following nine-pulse goes through and goes out on the subtract line to Accumulator 16. Then the 2nd ten-pulse comes along, the 8th flip-flop goes off, the 9th flip-flop goes on, and the next nine-pulse goes out on the subtract line to Accumulator 16. Now the decade sits at 9, and for this reason the next ten-pulse changes an electronic switch (actually another flip-flop) so that all later nine-pulses will go out on the add line. This ten-pulse also turns off the 9th flip-flop and turns on the 0th flip-flop without causing any carry. Now the 4th of the ten-pulses comes along, turns the 0th flip-flop off, and turns the 1st flip-flop on, and the next nine-pulse goes out on the add line to Accumulator 13. The next 6 of the ten-pulses then come along and change Accumulator 11 back to the digit 7 as before, and the next 6 of the nine-pulses go out to Accumulator 13. Thus Eniac has added 7 into Accumulator 13, has added 2, the _nines complement_ of 7 (see Supplement 2), into Accumulator 16, and has left Accumulator 11 holding the same number as before. This is just the result that we wanted. In this way, the nines complement of any digit in a decade is transferred out along the subtract line, and the digit unchanged is transmitted out along the add line. As the pulses arrive at any other accumulator, they add into that accumulator. Multiplying and Dividing Eniac performs multiplication by a built-in table of the products in the 10-by-10 multiplication table, using the method of _left-hand components_ and _right-hand components_ (see Supplement 2). For example, suppose that the 3rd digit of the multiplier is 7 and that the 5th digit of the multiplicand is 6. Then, when Eniac attends to the 3rd digit of the multiplier, the right-hand digit of the 42 = 6 × 7 is gathered in one accumulator, and the left-hand digit 4 is gathered in another accumulator. After Eniac has attended to all the digits of the multiplier, then Eniac performs one more addition and transfers the sum of the left-hand digits into the right-hand digits accumulator. Eniac does division in rather a novel way. First, the divisor is subtracted over and over until the result becomes negative or 0. Then the machine shifts to the next column and adds the divisor until the result becomes positive or 0. It continues this process, alternating from column to column. For example, suppose that we divide 3 into 84 in this way. We have: ______ _ 3 ) 84 ( 32 -3 —— +54 -3 —— +24 -3 —— -6 +3 —— -3 +3 —— 0 After we subtract 3 the third time, the result becomes negative,-6; in the next column, after we add 3 twice, the result becomes 0. The quotient is _ 32, which is the same as 30 - 2, or 28; and 3 × 28 is 84. Thus the process checks. Consulting a Table Eniac has three Function Tables. Here you can store numbers or instructions for the machine to refer to. Each Function Table has 104 _arguments_ (see Supplement 2). For each argument, you can store 12 digits and 2 signs that may be plus or minus. This capacity can be devoted to one 12-digit number with a sign, or to two 6-digit numbers each with a sign, or to six 2-digit instructions. The three Function Tables are panels 43, 44, and 45. To put in the numbers or instructions, you have to go over to these panels and set the numbers or instructions, digit by digit, turning dial switches by hand. It is slow and hard to do this right, but once it is done, Eniac can refer to any number or instruction in any table in ¹/₁₀₀₀ of a second. This is much faster than the table reference time in any other of the giant brains built up to 1948. Programming We said above that Eniac has over 100 control lines or program trunks along which instructions can be sent. These instructions are expressed as pulses called _program pulses_. Now how do we make these pulses do what we want them to do? For example, how can we instruct Accumulator 11 to add what it holds into Accumulator 13? On each unit of Eniac there are plug hubs or sockets (called _program-pulse input terminals_) to which a program trunk may be connected. A program pulse received here can make the unit act in some desired way. On each accumulator of Eniac, we find 12 program-pulse input hubs. Corresponding to each of these hubs, there is a nine-way switch, called a _program-control switch_. The setting of this switch determines what the accumulator will do when the program-pulse input hub belonging to the switch receives a program pulse. For instance, there are switch settings for: receive input on the α line, receive input on the β line, etc.; and transmit output on the add line, etc. There is even a switch setting that instructs the accumulator to do nothing, and this instruction may be both useful and important. Now, in order that Accumulator 11 may transfer a number to Accumulator 13, we need: (1) a digit tray, say B, for the number to travel along; (2) a program trunk line, say G3, to tell Accumulator 11 when to send the number and Accumulator 13 when to receive it; and (3) certain plugging as follows: 1. We plug from program trunk G3 into a program-pulse input hub, say No. 5, of Accumulator 11; 2. We plug from the same program trunk G3 into a program-pulse input hub, say No. 7, of Accumulator 13; 3. We set program-control switch No. 5 of Accumulator 11 to “add”; 4. We set program-control switch No. 7 of Accumulator 13 to some input, say γ. 5. We plug from digit tray B into the add output of Accumulator 11. 6. We plug from digit tray B into the γ input of Accumulator 13. Now, when the program pulse comes along line G3, it makes Accumulator 13 transmit additively along digit tray B into Accumulator 13. And that is the result that we wanted. As each mechanism of Eniac finishes what it is instructed to do, it may or may not put out a program pulse. This pulse in turn may be plugged into any other program trunk line and may stimulate another mechanism to act. Then, when this mechanism finishes, it too may or may not put out a program pulse, and so on. In general, there are two different ways to instruct Eniac to do a problem. One way is to set all the switches, plug all the connections, etc., for the specific problem. This is a long and hard task. Very often, even with great care, it is done not quite correctly, and then the settings must be carefully checked all over again. A second method (called the _von Neumann programming method_) is to store all the instructions for a problem in one or two function tables of Eniac and then tell Eniac to read the function tables in sequence and to do what they say. The rest of the machine is then wired up in a standard fashion. This method of instructing Eniac was proposed by Dr. John von Neumann of the Institute of Advanced Study at Princeton, N. J. Eniac has been modified to the slight extent needed so that this method can be used when desired. In this method, each instruction is a selected one of 60 different standard instructions or orders—one of them, for example, being “multiplication.” Each standard order is expressed by 2 decimal digits. The 60 standard orders are sufficient so that Eniac can do any mathematical problem that does not overstrain its capacity. Since each of the 3 Function Tables can hold 600 2-digit instructions, the machine can hold a program of 1800 instructions under the von Neumann programming method. AN APPRAISAL OF ENIAC AS A COMPUTER As a general-purpose calculating machine, Eniac suffers from unbalance. That is to say, Eniac operates rapidly and successfully in some respects, and slowly and troublesomely in other respects. This is altogether to be expected, however, in a calculator as novel as Eniac and made to so large an extent out of standard radio parts. It was certainly better to finish a calculator like this one and then start on a new one, as the Moore School of Electrical Engineering did, than to prolong design and construction indefinitely in order to make improvements. Speed Eniac adds or subtracts very swiftly at the rate of 5000 a second. Eniac multiplies at the rate of 360 to 500 a second. Division, however, is slow, relatively; the rate is about 50 a second. Reading numbers from punched cards, 12 a second for 10-digit numbers, is even slower. As a result of these rates, you find, when you put a problem on Eniac, that one division delays you as long as 100 additions or 8 multiplications. Division might have been speeded somewhat by (1) _rapidly convergent approximation_ (see Supplement 2) to the _reciprocal_ of the divisor and (2) multiplying by the dividend; this might have taken 5 or 6 multiplication times instead of 8. Also, the use of a standard IBM punch-card feed and card punch slows the machine greatly. One way to overcome this drawback might be to install one or two additional sets of such equipment, which might increase input and output speed. Ease of Programming Eniac has a very rapid and flexible automatic control over the programming of operations. Eniac has more than 10 channels along which numbers can be transferred and more than 100 channels along which program-control pulses can be transferred. There are many ways for providing subroutines. Eniac has the additional advantage that there is no delay in giving the machine successive instructions: all the instructions the machine may need at any time are ready at the start of the problem, and indications occurring in the calculation can change the routine completely. All these advantages, however, are paid for rather heavily by the slow methods for changing programming. You have to plug large numbers of program trunk lines and digit trunk lines, or you have to set large numbers of switches, or both. Also, when you wish to return to a previous problem, you must do all the plugging and switch setting over again. Many delays in the operation of the machine are due to human errors in setting the machine for a new problem. Here again, we must remember that Eniac was originally designed as a special-purpose machine for solving trajectories. To calculate a large family of trajectories very little changing of wires and switches would be needed. Memory The most severe limitation on the usefulness of Eniac was, at the outset, the fact that it had only 20 registers for storing numbers. There are large numbers of problems that cannot be simply handled with so small an internal memory. Even the Harvard IBM calculator (see Chapter 6) is often strained during a problem because of the number of intermediate results that must be stored for a time before combining. The Ballistic Research Laboratories, however, contracted for extensions to Eniac to provide more memory and easier changing of instructions. Reliability Checking results with Eniac is not easy. There is no built-in guarantee that Eniac’s results are correct. A large calculator can and does make both constant and intermittent errors. Ways for checking with Eniac are: Mathematical, if and when available, and this will be seldom. Running the problem a second time, and this will, at most, prove consistency. Deliberate testing of small parts of the problem, which is very useful and is standard practice but leads only to a probability that the final result is correct. You can operate Eniac one addition at a time, and even one pulse at a time, and see what the machine shows in its little neon bulbs. This is a very useful partial check. Cost The cost of Eniac is higher than that of some of the other large mechanical brains—over half a million dollars. Because some of the work was done at the Moore School by students, the cost was probably less than it otherwise would have been. The largest part of the cost was the designing of the machine and the construction of the panels; the tubes were only a small portion of the cost. The tubes used in the calculating circuits cost only 20 to 90 cents. However, no later electronic calculator need cost as much, for many improvements can now be seen. The power required for Eniac is about 150 kilowatts or about 200 horsepower, most of which is used for the heaters of the electronic tubes. The largest number of electronic tubes mentioned for future electronic calculators is about 3000, so we can see that they are likely to use less than a quarter of the power needed for Eniac. Eniac will doubtless give a number of years of successful operation and be extremely useful for problems that employ its assets and are not excluded by its limitations. In fact, at the Ballistic Research Laboratories, for a typical week of actual work, Eniac has already proved to be equal to 500 human computers working 40 hours with desk calculating machines, and it appears that soon two or three times as much work may be obtained from Eniac. Chapter 8 RELIABILITY—NO WRONG RESULTS: BELL LABORATORIES’ GENERAL-PURPOSE RELAY CALCULATOR In 1946, Bell Telephone Laboratories in New York finished two _general-purpose relay calculators_—mechanical brains. They were twins. One was shipped in July 1946 to the National Advisory Committee for Aeronautics at Langley Field, Virginia. The other, after some months of trial operation, was shipped in February 1947 to the Ballistic Research Laboratories at the U. S. Army’s Proving Ground, Aberdeen, Md. Each machine is remarkably reliable and versatile. It can do a wide variety of calculations in a great many different ways. Yet the machine never takes a new step without a check that the old step was correctly performed. There is, therefore, a chance of better than 99.999,999,999 per cent that the machine will not let a wrong result come out. The automatic checking, of course, does not prevent (1) human mistakes—for example, instructing the machine incorrectly—or (2) mechanical failures, in which the machine stops dead in its tracks, letting no result at all come out. ORIGIN AND DEVELOPMENT In Bell Telephone Laboratories the telephone system of the country is continually studied. Their research produced the common type of dial telephone system: a masterly machine for selecting information. Now when a telephone engineer studies an electric circuit, he often finds it very convenient to use numbers in pairs: like 2, 5 or-4,-1. Here the comma is a separation sign to keep the two numbers in the pair separate and in sequence. Mathematicians call numbers of this kind, for no very good reason, _complex numbers_; of course, they are far less complex than why the sun shines or why plants grow. When Bell Laboratories test the design of new circuits, girl computers do arithmetic with complex numbers. Addition and subtraction are easy: each means two operations of addition or subtraction of ordinary numbers. For example, 2, 5, plus-4,-1 equals 2-4, 5-1, which equals-2, 4. And 2, 5 minus-4,-1 is the same as 2, 5 plus 4, 1; and this equals 2 + 4, 5 + 1, which equals 6, 6. Multiplication of two complex numbers, however, is more work. If _a_, _b_ and _c_, _d_ are two complex numbers, then the formula for their product is (_a_ × _c_)-(_b_ × _d_), (_a_ × _d_) + (_b_ × _c_). To get the answer, we need 4 multiplications, 1 subtraction, and 1 addition. Division of two complex numbers requires even more work. If _a_, _b_ and _c_, _d_ are two complex numbers, the formula for the quotient of _a_, _b_ divided by _c_, _d_ is: [(_a_ × _c_) + (_b_ × _d_)] ÷ [(_c_ × _c_) + (_d_ × _d_)], [(_b_ × _c_) - (_a_ × _d_)] ÷ [(_c_ × _c_) + (_d_ × _d_)] For example, (2, 5) ÷ (-4, -1) = [(2 × -4 = -8) + (5 × -1 = -5)] ÷ [(-4 × -4 = 16) + (-1 × -1 = 1)], [(5 × -4 = -20) - (2 × -1 = -2)] ÷ [16 + 1] = -(¹³/₁₇), -(¹⁸/₁₇) Thus, division of one complex number by another needs 6 multiplications, 2 additions, 1 subtraction, and 2 divisions of ordinary numbers—and always in the same pattern or sequence. The Complex Computer About 1939, an engineer at Bell Telephone Laboratories in New York, Dr. George R. Stibitz, noticed the great volume of this pattern arithmetic. He began to wonder why telephone switching equipment could not be used to do the multiplications and divisions automatically. He decided it could. All that was necessary was that the _relays_ (see Chapter 2) used in regular telephone equipment should have a way of remembering and calculating with numbers. Regular telephone equipment would take care of the proper sequence of operations. Regular equipment known as _teletypewriters_ would print the numbers of the answer when it was obtained. A teletypewriter consists essentially of a typewriter that may be operated by electrical impulses. It has a keyboard that may produce electrical impulses in sets corresponding to letters; and it can receive or transmit over wires. Dr. Stibitz _coded_ the numbers: each decimal digit was matched up with a group of four relays in sequence, and each of these relays could be open or closed. If 0 means open and 1 means closed, here is the pattern or code that he used: DECIMAL DIGIT RELAY CODE 0 0 0 1 1 1 0 1 0 0 2 0 1 0 1 3 0 1 1 0 4 0 1 1 1 5 1 0 0 0 6 1 0 0 1 7 1 0 1 0 8 1 0 1 1 9 1 1 0 0 With regular telephone relays and regular telephone company techniques, Dr. Stibitz and Bell Telephone Laboratories designed and constructed the machine. It was called the _Complex Computer_ and was built just for multiplying and dividing complex numbers. Six or eight panels of relays and wires were in one room. Two floors away, some of the girl computers sat in another room, where one of the teletypewriters of the machine was located. When they wished, they could type into the machine’s teletypewriter the numbers to be multiplied or divided. In a few seconds back would come the answer. In fact, there were two more computing rooms where teletypewriters of the machine were stationed. To prevent conflicts between stations, the machine had a circuit like the busy signal from a telephone. In 1940, a demonstration of the Complex Computer took place: the computing panels remained in New York, but the teletypewriter input-output station was set up at Dartmouth College in Hanover, N. H. Mathematicians gave problems to the machine in Dartmouth, it solved them in New York, and it reported the answers in Dartmouth. Special-Purpose Computers With this as a beginning, Bell Laboratories developed another machine for a wide variety of mathematical processes called _interpolating_ (see Supplement 2). Then, during World War II, Bell Laboratories made more special-purpose computing machines. They were used in military laboratories charged with testing the accuracy of instruments for controlling the fire of guns. These computers took in a set of gun-aiming directions put out by the _fire-control instrument_ in some test. They also took in the set of observations that went into the fire-control instrument on that test. Then they computed the differences between the gun-aiming produced by the fire-control instrument and the gun-aiming really required by the observations. Using these differences, the fire-control instrument could be adjusted and corrected. These special-purpose computers were also useful in checking the design of new fire-control instruments and in checking changes due to new types of guns or explosives. Regularly, after each of these special-purpose computers was finished, people began to put other problems on it. It seemed to be fated that, as soon as you had made a machine for one purpose, you wanted to use it for something else. Accordingly, in 1944, two agencies of the U. S. Government together made a contract with Bell Telephone Laboratories for two general-purpose relay computers. These two machines were finished in 1946 and are twins. ORGANIZATION OF THE GENERAL-PURPOSE COMPUTER When a man sits down at a desk to work on a computation, he has six things on his desk to work with: a work sheet; a desk calculator, to add, subtract, multiply, and divide; some rules to be followed; the tables of numbers he will need; the data for the problem; and an answer sheet. In his head, he has the capacity to make decisions and to do his work in a certain sequence of steps. These seven subdivisions of calculation are all found in the Bell Laboratories’ general-purpose relay computer. The general-purpose computer is a computing system, in fact, more than it is a single machine. The part of the system which does the actual calculating is called, in the following paragraphs, the _computer_, or else, since it is in two halves, _Computer 1_ and _Computer 2_. Physical Units The computing system delivered to the Ballistic Research Laboratories fills a room about 30 by 40 feet and consists of the following: 2 _computers_: panels of relays, wiring, etc., which add, subtract, multiply, divide, select, decide, control, etc. 4 _problem positions_: tables each holding 12 mechanisms for feeding paper tape, which read numbers and instructions punched on tape and convert them into electrical impulses. 2 _hand perforators_: keyboard devices for punching instructions and numbers on paper tape. 1 _processor_: a table holding mechanisms for feeding 2 paper tapes and punching a third paper tape, used for checking numbers and instructions punched on tape. 2 _recorders_: each a table holding a teletypewriter, a tape punch, and a tape feed, used for recording answers and, if necessary, consulting them again. The 2 computers correspond to the work sheet, the desk calculator, and the man’s capacity to make decisions and to carry out a sequence of steps. The 4 problem positions correspond to the problem data, the rules, and the tables of numbers. The 2 recorders correspond to the answer sheet. The 2 hand perforators and the processor are auxiliary machines: they translate the ordinary language of arithmetic into the machine language of punched holes in paper tape. This is the computing system as organized for the Ballistic Research Laboratories at Aberdeen. The one for the National Advisory Committee for Aeronautics has only 3 problem positions. The computer system may, in fact, be organized with 1 to 10 computers and with 1 to 20 problem positions. The great bulk of this computing system, like the mechanical brains described in previous chapters, is made up of large numbers of identical parts of only a few kinds. These are: standard telephone relays; wire; and standard _teletype transmitters_, mechanisms that read punched paper tape and produce electrical impulses. Numbers The numbers that the Bell machine contains range from 0.1000000 to 0.9999999 times a _power_ of 10 varying from 10,000,000,000,000,000,000 to 0.000,000,000,000,000,000,1, or, in other words, from 10¹⁹ to 10⁻¹⁹. The machine also contains zero and _infinity_: zero arises when the number is smaller than 10⁻¹⁹, and infinity arises when the number is equal to or greater than 9,999,999,000,000,000,000. (See Supplement 2.) The system used in the machine to represent numbers on relays is called _biquinary_—the _bi_-, because it is partly twofold like the hands, and the -_quinary_ because it is partly fivefold like the fingers. This system is used in the abacus (see Chapter 2 and Supplement 2). In the machine, for each decimal digit, 7 relays are used. These relays are called the 00 and 5 relays, and the 0, 1, 2, 3, and 4 relays. If, as before, 0 indicates a relay that is not energized and 1 indicates a relay that is energized, then each decimal digit is represented by the positioning of the 7 relays as follows: DECIMAL DIGIT RELAYS 00 5 0 1 2 3 4 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 2 1 0 0 0 1 0 0 3 1 0 0 0 0 1 0 4 1 0 0 0 0 0 1 5 0 1 1 0 0 0 0 6 0 1 0 1 0 0 0 7 0 1 0 0 1 0 0 8 0 1 0 0 0 1 0 9 0 1 0 0 0 0 1 Then, for any decimal digit, one and only one of the 00 and 5 relays is energized, and one and only one of the 0, 1, 2, 3, and 4 relays is energized. If more or less than exactly one relay in each set is energized, then the machine knows that it has made a mistake, and it stops dead in its tracks. Thus any accidental failure of a relay is at once caught, and the chance of two compensating failures occurring at the same time is extremely small. HOW INFORMATION GOES INTO THE MACHINE In order to put a problem into this machine—just as with the other machines—first a mathematician who knows how the problem is to be solved, and who knows how to organize it for the machine, lays out the scheme of calculation. Then, a girl goes to one of the hand perforators. Sitting at the keyboard, she presses keys and punches out feet or yards of paper tape expressing the instructions and numbers for the calculation. Each character punched—digit, letter, or sign—has one or more of a maximum of 6 holes across the tape. Another girl, using the other hand perforator, also punches out the instructions and numbers for the calculation. If she wishes to erase a wrong character, she can press an _erase key_ that punches all 6 holes, and then the machine will pass by this row as if it were not there. Three kinds of tapes are produced for the machine: _Problem tapes_, which contain information belonging to the particular problem. _Table tapes_, which contain tables of numbers to be referred to from time to time. _Routine tapes_, which contain the program, or routine, or sequence of steps that the machine is to carry out. In each of these tapes one character takes up ⅒ of an inch along the tape. In the case of a table tape, however, an ordinary 1-digit number requires 4 characters on the tape, and a 7-digit number requires 11 characters on the tape. On a table tape there will be on the average about 1 inch of tape per number. The Processor The two paper tapes prepared on the perforator should agree. But whether or not they agree, a girl takes them over to the processor and puts them both in. The processor has two tape feeds, and she puts one tape on each and starts the machine. The processor compares them row by row, making sure that they agree, and punches a new tape row by row. If the two input tapes disagree, the processor stops. You can look to see which tape is right, and then you can put the correct punch into the new tape with a keyboard mounted on the processor. As the processor compares the two input tapes, it also converts any number written in the usual way into machine language. For example, the processor will automatically translate 23,188 into +.231 8800 × 10⁺⁵. The processor also puts in certain safeguards. If you want it to, the processor will also make a printed record of a tape. Also, when a tape becomes worn from use in the machine, you can put it into the processor and make a fresh copy. The Problem Positions Next, the girl takes the punched tape made by the processor over to a problem position that is idle. Two of the problem positions are always busy guiding the two computers. The other two problem positions stand by, ready to be loaded with problems. A problem position looks like a large covered-over table. Under the covers are 12 tape feeds, or _tape transmitters_. All these transmitters look exactly alike except for their labels and consist of regular teletype transmitters. Six-hole paper tape can be fed into any transmitter. Six metal fingers sense the holes in the paper tape and give out electrical impulses at proper times. At the front of the problem position is a small group of switches that provide complete control over the problem while it is on the machine. These are switches for starting, disconnecting, momentary stop, etc. One tape transmitter is the problem tape transmitter. It takes in all the data for the problem such as the starting numbers. The first thing it does at the start of a problem is to check (by comparing tape numbers) that the right tapes are in the right feeds. Five transmitters are routine tape transmitters. Each of these takes in the sequence of computing steps. The routine tapes also contain information for referring to table tapes and instructions for printing and punching tape. The machine can choose according to instructions between the five routine tapes and can choose between many different sections on each tape. Therefore, we can use a large number of different routines in a calculation, and this capacity makes the machine versatile and powerful. Six transmitters are table tape transmitters. They read tables of numbers when directed to. A table tape can be as long as 100 feet and will hold numbers at the rate of 1 inch per number, so that about 1200 numbers of seven decimal digits can be stored on a table tape. When we look up a number in a table, such as the following, 2½ 3 3½ ··· +———————————————————————————— 1 |1.02500 1.03000 1.03500 2 |1.05063 1.06090 1.07123 3 |1.07689 1.09273 ··· 4 |1.10381 ··· ··· 5 |1.13141 ··· 6 |1.15969 7 | ··· 8 | ··· 9 | ··· 10 | ···| ··· we look along the top and down the side until we find the column and row of the number we are looking for. These are called the _arguments_ of the _tabular value_ that we are looking for (see Supplement 2). Now when we put this table on a tape to go into the Bell Laboratories machine, we write it all on one line, one figure after another, and we punch it as follows: 2-½ 1-5 1.02500 1.05063 1.07689 1.10381 1.13141 6-10 1.15969 ··· 11-15 ··· ··· ··· 3 1-5 1.03000 1.06090 ··· ··· 3½ 1-5 1.03500 ··· You will notice that the column labels 2½, 3, 3½ have been put on the tape, each in front of the group of numbers they apply to. The row labels 1 to 5, 6 to 10, ··· have also been put on the tape, each in front of the group of numbers they apply to. The appropriate column and row numbers, or arguments, must be put often on every table tape, so that it is easy for the machine to tell what part of the table tape it is reading. In the Bell Laboratories machine, we do not need to put equal _blocks_ of arguments like 1-5, 6-10 ··· on the table tape. Instead we can put individual arguments like 1, 2, 3, 4 ···, or, if we wish, we can use blocks of different sizes, like 1-3, 4-15, 16-30···. For some tables, such as income tax tables, it is very useful to have varying-sized blocks of arguments. The machine, when hunting for a certain value in the table, makes a comparison at each block of arguments. The machine needs about 6 seconds to search a foot of tape. If we want to set up a table economically, therefore, we need to consider the average length of time needed for searching. [Illustration: FIG. 1. Scheme of a recorder.] HOW INFORMATION COMES OUT OF THE MACHINE At either one of the two recorders (Fig. 1), information comes out of the machine, either in the form of printed characters or as punched tape. The recorder consists of a _printer_, a _reperforator_, and a tape transmitter. One recorder table belongs to each computer and records the results it computes. The printer is a regular teletypewriter connected to the machine. It translates information produced by the machine as electrical impulses and prints the information in letters and digits on paper. The reperforator is an automatic tape punch. It translates information produced by the machine in the form of electrical impulses and punches the information on paper tape. Next to the tape punch is a tape transmitter. After the tape comes through the punch, it is fed into the transmitter. Here the machine can hunt for a previous result punched in the tape, read that result, and use it again. HOW INFORMATION IS MANIPULATED IN THE MACHINE The main part of the computing system consists of 27 large frames loaded with relays and wiring, called the _computer_, or _Computer 1_ and _Computer 2_. In this “telephone central station,” all the “phone calls” from one number to another are attended to. There are 8 types of these frames in the computer: FRAMES NUMBER Storing register frames 6 Printer frames 2 Problem frames 2 Position frames 2 Calculator frames 6 Control frames 2 Routine frames 4 BTL (Block-Trig-Log) frames 2 Permanent table frames 1 —— Total 27 In most but not quite all respects, the two halves, _Computer 1_ and _Computer 2_, can compute independently. The _storing register frames_ hold enough relays to store 30 numbers. The registers for these numbers are named _A, B, C, D_, ···, _M, N, O_ in two groups of 15 each. One group belongs to Computer 1 and the other to Computer 2. In each Computer, the _calculator frames_ hold enough relays for storing two numbers (held in the _X_ and _Y_ registers) and for performing addition, subtraction, multiplication, division, and square root. In each Computer, the _problem frame_ stores the numbers that are read off the problem tape and the table tapes, and the _printer frame_ stores the numbers that are read into the printer. The printer frame also stores indications, for example, the signs of numbers, plus or minus, for purposes of combining them. These frames also hold the relays that control the printer, the problem tape, and the table tapes. Jointly for both Computers, the _position frames_ connect a problem in some problem position to a Computer that becomes idle. For example, one problem may finish in the middle of the night; the machine automatically and unattended switches to another problem position and proceeds with the instructions there contained. A backlog of computing on hand can be stored in two of the problem positions, while the other two control the two Computers. In each Computer, the _routine frames_ hold the relays that make the Computer follow the routine instructions. Jointly for both Computers, the remaining frames—the _control frames_, the _BTL frames_, and the _permanent table frames_—hold the relays that control: the alarms and lights for indicating failures; some circuits called the BTL controls; the tape processor; and the mathematical tables that are permanently wired into the machine. The permanent table frames hold the following mathematical functions (see Supplement 2): _sine_, _cosine_, _antitangent_, _logarithm_, and _antilogarithm_. Storing Numbers can be stored in the machine in the 30 regular storing registers of both Computers together. They can also be stored, at the cost of tying up some machine capacity, in the other registers: the 4 calculator registers, the 2 problem registers, the 2 table registers, and the 2 printer registers. Numbers can also be punched out on tape, in either of the two printers, and later read again from the tape. Labels identifying the numbers can also be punched and read again from the tape. Each register in the machine stores a number in the biquinary notation, as explained above. In programming the machine, after mentioning a register it is necessary—as a part of the scheme for checking—to tell the machine specifically whether to hold the number in the register or to clear it. Addition and Subtraction The calculator frames can add two numbers together, if so instructed in the routine tape. Suppose that the two numbers are in the registers _B_ and _D_ and that we wish to put the sum in register _F_. Suppose that we wish to clear the _D_ number but hold the _B_ number after using them. The code on the routine tape is _B H_ + _D C_ = _F_. _H_ and _C_ coming right after the names of the registers always designate “hold” and “clear,” respectively. The calculator frames can, likewise, subtract a number. The routine instruction _B H_-_D C_ = _F_ means: Take the number in register _B_ (hold it); subtract the number in _D_ (clear it); put the result in _F_ Multiplication and Division The calculator frames perform multiplication by storing the digits of the multiplier, adding the multiplicand over and over, and shifting, until the product is obtained. However, if the multiplier is 1989, for example, the calculator treats it as 2000-11. This short-cut applies to digits 6, 7, 8, 9 and cuts the time required for multiplying. The routine instruction is _B H_ × _D C_ = _F_. The calculator performs division by repeated subtraction. The routine instruction is _B H_ ÷ _D C_ = _F_. The operation signs +,-, ×, ÷ actually appear on the keyboard of the perforator and on the printed tape produced by the printer. Discrimination _Discrimination_ is the term used in the Bell Laboratories computer for what we have previously called selection, or comparison, or sequencing. The _discriminator_ is a part of the calculator that compares or selects or decides—“discriminates.” The discriminator can decide whether a number is zero or not zero. In the language of the _algebra of logic_ (see Chapter 9 and Supplement 2), if _a_ is a number, the discriminator can find _T_(_a_ = 0). The discriminator can also decide whether a number is positive or negative. In the language of logic, it can find _T_(_a_ > 0) or _T_(_a_ < 0). The actions that a discriminator can cause to be taken are: Stop the machine. Stop the problem, and proceed to another problem. Stop the routine going on, and proceed with a new routine. Permit printing, or prevent printing; etc. In this way the discriminator can: Distinguish between right and wrong results. Tell that a certain result is impossible. Recognize a certain result to be the answer. Control the number of repetitions of a formula. Change from one formula to another formula. Check a number against a tolerance; etc. PROBLEMS Among the problems that have been placed on the machine successfully are: solving the _differential equation_ of a _trajectory_ (see Chapter 5) and solving 32 _linear simultaneous equations_ in 32 _unknowns_ (see Supplement 2). In the second case, the routine tapes were designed to apply equally well to 11 to 100 linear equations in 11 to 100 unknowns. However, the machine can do a very broad class of problems, including, for example, computing a personal income tax. This calculation with all its complexity of choices cannot be placed on any of the mechanical brains described in previous chapters. The machine can, of course, be used to calculate any tables that we may wish to refer to. AN APPRAISAL OF THE CALCULATOR The Bell Telephone Laboratories general-purpose relay computer is probably the best mechanical brain made up to the end of 1947, in regard to the two important factors of reliability and versatility. Reliability The machine produces results that are practically 100 per cent reliable, for the machine checks each step before taking the next one. The checking principle is that exactly a certain number of relays must be energized. For example, as we said before, for each decimal digit there are 7 relays. Exactly 2 of these relays must be energized—no more, no less. If this does not happen, the machine stops at once without losing any numbers. Lights shine for many circuits in the control panel, and, if you compare what they ought to show with what they do show, you can usually find at once the location of the mistake. The trouble may be a speck of dirt between two contact points on a relay, and, when it is brushed away, the machine can go right ahead from where it stopped. According to a statement by Franz L. Alt, director of the computing laboratory at the Ballistic Research Laboratories, in December 1947, “the Bell machine had not given a single wrong result in eight months of operation, except when operators interfered with its normal running.” To guard against the risk of putting tapes in the wrong transmitters, the machine will check by the instructions contained in the tapes that the right tapes are in the right places. Time Required The time required to do problems on this mechanical brain is perhaps longer than on the others. The numbers are handled digit by digit on the input tapes, and the typewriter in the recorder moves space by space in order to get to the proper writing point. These are slow procedures. The speeds of numerical operation are: addition, ³/₁₀ second; multiplication, 1 second on the average; division, 2.7 seconds on the average; square root, 4.5 seconds on the average; logarithm, about 15 seconds. Staff In order to operate the machine, the staff required is: one maintenance man; one mathematical engineer; about six girls for punching tape, etc., depending on the number of problems to be handled at the rate of about one problem per week per girl. Unlike any of the other mechanical brains built by the end of 1947, this machine will run unattended. Maintenance The relays in the machine will operate for years with no failure; they have the experience of standard telephone techniques built into them. Under laboratory conditions this type of relay had by 1946 operated successfully much more than 100 million times. The tape feeding and reading equipment in the machine may be maintained by periodic inspection and service. The total number of teletype transmitters in the machine is 38. If one fails, it is easy to plug in a spare. The total power required for the machine is about 28 horsepower. Batteries are furnished so that, if the power supply should be interrupted, the machine can still operate for as long as a half-hour. Cost The cost of production of this machine in the size of 4 problem positions and 2 computers has been roughly estimated as half a million dollars. This cost includes material, manufacture, installation, and testing. No development cost is included in this figure. Instead, the cost of development has been reckoned as squaring with patents and other contributions of the work to the telephone switching art. It is unlikely that the general-purpose relay computer will be manufactured generally. The pressure of orders for telephones, the need to catch up with the backlog of demand, and the development of electronic computers—all indicate that the Bell system will hardly go further with this type of computer. In an emergency, however, the Bell system would probably construct such machines for the government, if requested. In the meantime, many principles first used in the general-purpose relay computer are likely to find applications in telephone system work. In fact, a present major development being pursued in the telephone sections of Bell Laboratories is the application of the computer principles to the automatic computation of telephone bills. Chapter 9 REASONING: THE KALIN-BURKHART LOGICAL-TRUTH CALCULATOR So far we have talked about mechanical brains that are mathematicians. They are fond of numbers; their main work is with numbers; and the other kinds of thinking they do are secondary. We now come to a mechanical brain that is a logician. It is fond of reasoning—logic; its main work is with what is logically true and what is logically false; and it does not handle numbers. This mechanical brain was finished in June 1947. It is called the _Kalin-Burkhart Logical-Truth Calculator_. As its name tells, it calculates _logical truth_. Now what do we mean by that? TRUTH To be true or false is a property of a statement. Usually we say that a statement is true when it expresses a fact. For example, take the statement “Salt dissolves in water.” We consider this statement to be true because it expresses a fact. Actually, in this case we can roughly prove the fact ourselves. We take a bowl, put some water in it, and put in a little salt. After a while we look into the water and notice that no salt whatever is to be seen. Of course, this statement, like many another, occurs in a _context_ where certain things are understood. One of the understandings here, for example, is “a small amount of salt in a much larger amount of water.” For if we put a whole bag full of salt in just a little water, not all the salt will dissolve. Nearly every statement occurs in a context that we must know if we are to decide whether the statement is true or false. LOGICAL TRUTH Logical truth is different from ordinary truth. With logical truth we appeal not to facts but to suppositions. Usually we say that a statement is logically true when it follows logically from certain suppositions. In other words, we play a game that has useful, even wonderful, results. The game starts with “if” or “suppose” or “let us assume.” While the game lasts, any statement is logically true if it follows logically from the suppositions. For example, let us take five statements: 1. “The earth is flat like a sheet of paper.” 2. “The earth is round like a ball.” 3. “John Doe travels as fast as he can, without turning to left or to right, for many days.” 4. “John Doe will fall off the earth.” 5. “John Doe will arrive back at his starting point.” Let us also take a certain context in which: We know what we mean by such words as “earth,” “flat,” “falling,” etc.; we have other statements and understandings such as “if John Doe walks off the edge of a cliff, he will fall,” “a flat sheet of paper has an edge,” etc. In this context, if statements 1 and 3 are supposed, then statement 4 is logically true. On the other hand, if statements 2 and 3 are supposed, then statement 5 is logically true. Of course, for many centuries, nearly all men believed statement 1; and the importance of the years 1492 to 1521 (Columbus to Magellan) is linked with the final proof that statement 2 expresses a fact. So, depending on the game, or the context, whichever we wish to call it, almost any statement can be logically true. What we become interested in, therefore, is the connections between statements which make them _follow logically_. LOGICAL PATTERNS Perhaps the most familiar example of “following logically” is a pattern of words like the following: 1. All igs are ows. 2. All ows are umphs. 3. Therefore, all igs are umphs. If statements 1 and 2 are supposed, then statement 3 is logically true. In other words, statement 3 logically follows from statements 1 and 2. This word pattern is logically true, no matter what substitutions we make for igs, ows, and umphs. For example, we can replace igs by men, ows by animals, and umphs by mortals, and obtain: 4. All men are animals. 5. All animals are mortals. 6. Therefore, all men are mortals. The invented words “igs,” “ows,” “umphs” mark places in the _logical pattern_ where we can insert any names we are interested in. The words “all,” “are,” “therefore” and the ending s mark the logical pattern. Of course, instead of using invented words like “igs,” “ows,” “umphs” we would usually put _A_’s, _B_’s, _C_’s. This logical pattern is called a _syllogism_ and is one of the most familiar. But there are even simpler logical patterns that are also familiar. THE SIMPLEST LOGICAL PATTERNS Many simple logical patterns are so familiar that we often use them without being conscious of doing so. The simple logical patterns are marked by words like “and,” “or,” “else,” “not,” “if,” “then,” “only.” In the same way, simple arithmetical patterns are marked by words like “plus,” “minus,” “times,” “divided by.” Let us see what some of these simple logical patterns are. Suppose that we take two statements about which we have no factual information that might interfere with logical supposing: 1. John Doe is eligible for insurance. 2. John Doe requires a medical examination. In practice, we might be concerned with such statements when writing the rules governing a plan of insurance for a group of employees. Here, we shall play a game: (1) We shall make up some new statements from statements 1 and 2, using the words “and,” “or,” “else,” “not,” “if,” “then,” “only.” (2) We shall examine the logical patterns that we can make. (3) We shall see what we can find out about their logical truth. Suppose we make up the following statements: 3. John Doe is not eligible for insurance. 4. John Doe does not require a medical examination. 5. John Doe is eligible for insurance and requires a medical examination. 6. John Doe is eligible for insurance, and John Doe is eligible for insurance. 7. John Doe is eligible for insurance, or John Doe requires a medical examination. 8. If John Doe is eligible for insurance, then he requires a medical examination. 9. John Doe requires a medical examination if and only if he is eligible for insurance. 10. John Doe is eligible for insurance or else he requires a medical examination. Now clearly it is troublesome to repeat quantities of words when we are interested only in the way that “and,” “or,” “else,” “not,” “if,” “then,” “only” occur. So, let us use just 1 and 2 for the two original statements, remembering that “1 AND 2” means here “statement 1 AND statement 2” and does not mean 1 plus 2. Then we have: 3: NOT-1 4: NOT-2 5: 1 AND 2 6: 1 AND 1 7: 1 OR 2 8: IF 1, THEN 2 9: 1 IF AND ONLY IF 2 10: 1 OR ELSE 2 Here then are some simple logical patterns that we can make. CALCULATION OF LOGICAL TRUTH Now what can we find out about the logical truth of statements 3 to 10? If we know something about the truth or falsity of statements 1 and 2, what will logically follow about the truth or falsity of statements 3 to 10? In other words, how can we calculate the logical truth of statements 3 to 10, given the truth or falsity of statements 1 and 2? For example, 3 is NOT-1; that is, statement 3 is the negative or the _denial_ of statement 1. It follows logically that, if 1 is true, 3 is false; if 1 is false, 3 is true. Suppose that we use _T_ for logically true and _F_ for logically false. Then we can show our calculation of the logical truth of statement 3 in Table 1. Table 1 Table 2 1 | NOT-1 = 3 2 | NOT-2 = 4 | | _T_ | _F_ _T_ | _F_ _F_ | _T_ _F_ | _T_ Our rule for calculation is: For _T_ put _F_; for _F_ put _T_. Of course, exactly the same rule applies to statements 2 and 4 (see Table 2). The _T_ and _F_ are called _truth values_. Any meaningful statement can have truth values. This type of table is called a _truth table_. For any logical pattern, we can make up a truth table. Let us take another example, “AND.” Statement 5 is the same as statement 1 AND statement 2. How can we calculate the logical truth of statement 5? We can make up the same sort of a table as before. On the left-hand side of this table, there will be 4 cases: 1. Statement 1 true, statement 2 true. 2. Statement 1 false, statement 2 true. 3. Statement 1 true, statement 2 false. 4. Statement 1 false, statement 2 false. On the right-hand side of this table, we shall put down the truth value of statement 5. Statement 5 is true if both statements 1 and 2 are true; statement 5 is false in the other cases. We know this from our common everyday experience with the meaning of “AND” between statements. So we can set up the truth table, and our rule for calculation of logical truth, in the case of AND, is shown on Table 3. Table 3 1 2 | 1 AND 2 = 5 | _T_ _T_ | _T_ _F_ _T_ | _F_ _T_ _F_ | _F_ _F_ _F_ | _F_ “AND” and the other words and phrases joining together the original two statements to make new statements are called _connectives_, or _logical connectives_. The connectives that we have illustrated in statements 7 to 10 are: OR, IF ··· THEN, IF AND ONLY IF, OR ELSE. Table 4 shows the truth table that applies to statements 7, 8, 9, and 10. This truth table expresses the calculation of the logical truth or falsity of these statements. Table 4 1 IF AND 1 OR 2 IF 1, THEN 2 ONLY IF 2 1 OR ELSE 2 1 2 | = 7 = 8 = 9 = 10 | _T_ _T_ | _T_ _T_ _T_ _F_ _F_ _T_ | _T_ _T_ _F_ _T_ _T_ _F_ | _T_ _F_ _F_ _T_ _F_ _F_ | _F_ _T_ _T_ _F_ The “OR” (as in statement 7) that is defined in the truth table is often called the _inclusive “or”_ and means “AND/OR.” Statement 7, “1 OR 2,” is considered to be the same as “1 OR 2 OR BOTH.” There is another “OR” in common use, often called the _exclusive “or,”_ meaning “OR ELSE” (as in statement 10). Statement 10, “1 OR ELSE 2,” is the same as “1 OR 2 BUT NOT BOTH” or “EITHER 1 OR 2.” In ordinary English, there is some confusion over these two “OR’s.” Usually we rely on the context to tell which one is intended. Of course, such reliance is not safe. Sometimes we rely on a necessary conflict between the two statements connected by “OR” which prevents the “both” case from being possible. In Latin the two kinds of “OR” were distinguished by different words, _vel_ meaning “AND/OR,” and _aut_ meaning “OR ELSE.” The “IF ··· THEN” that is defined in the truth table agrees with our usual understanding that (1) when the “IF clause” is true, the “THEN clause” must be true; and (2) when the “IF clause” is false, the “THEN clause” may be either true or false. The “IF AND ONLY IF” that is defined in the truth table agrees with our usual understanding that (1) if either clause is true, the other is true; and (2) if either clause is false, the other is false. In statement 6, there are only two possible cases, and the truth table is shown in Table 5. Table 5 1 | 1 AND 1 = 6 | _T_ | _T_ _F_ | _F_ We know that 6 is true if and only if 1 is true. In other words, the statement “1 AND 1 IF AND ONLY IF 1” is true, no matter what statement 1 may refer to. It is because of this fact that we never use a statement in the form “1 and 1”: it can always be replaced by the plain statement “1.” LOGICAL-TRUTH CALCULATION BY EXAMINING CASES AND REASONING Now you may say that this is all very well, but what good is it? Almost anybody can use these connectives correctly and certainly has had a great deal of practice using them. Why do we need to go into truth values and truth tables? When we draft a contract or a set of rules, we often have to consider several conditions that give rise to a number of cases. We must avoid: 1. All _conflicts_, in which two statements that disagree apply to the same case. 2. All _loopholes_, in which there is a case not covered by any statement. If we have one statement or condition only, we have to consider 2 possible cases: the condition satisfied or the statement true; the condition not satisfied or the statement false. If we have 2 conditions, we have to consider 4 possible cases: true, true; false, true; true, false; false, false. If we have 3 conditions, we have to consider 8 possible cases one after the other (see Table 6). Table 6 CASE 1ST CONDITION 2ND CONDITION 3RD CONDITION 1 _T_ _T_ _T_ 2 _F_ _T_ _T_ 3 _T_ _F_ _T_ 4 _F_ _F_ _T_ 5 _T_ _T_ _F_ 6 _F_ _T_ _F_ 7 _T_ _F_ _F_ 8 _F_ _F_ _F_ Instead of _T_’s and _F_’s, we would ordinarily use _check-marks_ (✓) and _crosses_ (✕), which, of course, have the same meaning. We may consider and study each case individually. In any event, we must make sure that the proposed contract or set of rules covers all the cases without conflicts or loopholes. The number of possible cases that we have to consider doubles whenever one more condition is added. Clearly, it soon becomes too much work to consider each case individually, and so we must turn to a second method, thoughtful classifying and reasoning about classes of cases. Now suppose that the number of conditions increases: 4 conditions give rise to 16 possible cases; 5, 6, 7, 8, 9, 10, ··· conditions give rise to 32, 64, 128, 256, 512, 1024, ··· cases respectively. Because of the large number of cases, we soon begin to make mistakes while reasoning about classes of cases. We need a more efficient way of knowing whether all cases are covered properly. LOGICAL-TRUTH CALCULATION BY ALGEBRA One of the more efficient ways of reasoning is often called the _algebra of logic_. This algebra is a part of a new science called _mathematical logic_. Mathematical logic is a science that has the following characteristics: It studies chiefly nonnumerical reasoning. It seeks accurate meanings and necessary consequences. Its chief instruments are efficient symbols. Mathematical logic studies especially the logical relations expressed in such words as “or,” “and,” “not,” “else,” “if,” “then,” “only,” “the,” “of,” “is,” “every,” “all,” “none,” “some,” “same,” “different,” etc. The algebra of logic studies especially only the first seven of these words. The great thinkers of ancient Greece first studied the problems of logical reasoning as these problems turned up in philosophy, psychology, and debate. Aristotle originated what was called _formal logic_. This was devoted mainly to variations of the logical pattern shown above called the syllogism. In the last 150 years, the fine symbolic techniques developed by mathematicians were applied to the problems of the calculation of logical truth, and the result was mathematical logic, much broader and much more powerful than formal logic. A milestone in the development of mathematical logic was _The Laws of Thought_, written by George Boole, a great English mathematician, and published in 1854. Boole introduced the branch of mathematical logic called the algebra of logic, also called _Boolean algebra_. In late years, all the branches of mathematical logic have been improved and made easier to use. We can give a simple numerical example of Boolean algebra and how it can calculate logical truth. Suppose that we take the truth value of a statement as 1 if it is true and 0 if it is false. Now we have numbers 1 and 0 instead of letters _T_ and _F_. Since they are numbers, we can add them, subtract them, and multiply them. We can also make up simple numerical formulas that will let us calculate logical truth. If _P_ and _Q_ are statements, and if _p_ and _q_ are their truth values, respectively, we have Table 7. Table 7 STATEMENT TRUTH VALUE NOT-_P_ 1 - _p_ _P_ AND _Q_ _pq_ _P_ OR _Q_ _p_ + _q_ - _pq_ IF _P_, THEN _Q_ 1 - _p_ + _pq_ _P_ IF AND ONLY IF _Q_ 1 - _p_ - _q_ + 2_pq_ _P_ OR ELSE _Q_ _p_ + _q_ - 2_pq_ For example, suppose that we have two statements _P_ and _Q_: _P_: John Doe is eligible for insurance. _Q_: John Doe requires a medical examination. To test that the truth value of “_P_ OR _Q_” is _p_ + _q_-_pq_, let us put down the four cases, and calculate the result (see Table 8). Table 8 _p_ _q_ | _p_ + _q_ - _pq_ | 1 1 | 1 + 1 - 1 = 1 0 1 | 0 + 1 - 0 = 1 1 0 | 1 + 0 - 0 = 1 0 0 | 0 + 0 - 0 = 0 Now we know that _P_ or _Q_ is true if and only if either one or both of _P_ and _Q_ are true, and thus we see that the calculation is correct. The algebra of logic (see also Supplement 2) is a more efficient way of calculating logical truth. But it is still a good deal of work to use the algebra. For example, if we have 10 conditions, we shall have 10 letters like _p_, _q_ to handle in calculations. Thus we need a still more efficient way. CALCULATION OF CIRCUITS BY THE ALGEBRA OF LOGIC In 1937 a research assistant at Massachusetts Institute of Technology, Claude E. Shannon, was studying for his degree of master of science. He was enrolled in the Department of Electrical Engineering. He was interested in automatic switching circuits and wondered why an algebra should not apply to them. He wrote his thesis on the answer to this question and showed that: (1) There is an algebra that applies to switching circuits. (2) It is the algebra of logic. A paper, based on his thesis, was published in 1938 in the _Transactions of the American Institute of Electrical Engineers_ with the title “A Symbolic Analysis of Relay and Switching Circuits.” [Illustration: FIG. 1. Switches in series.] For a simple example of what Shannon found out, suppose that we have two switches, 1, 2, in series (see Fig. 1). When do we get current flowing from the source to the sink? There are 4 possible cases and results (see Table 9). Table 9 SWITCH 1 IS CLOSED SWITCH 2 IS CLOSED CURRENT FLOWS Yes Yes Yes No Yes No Yes No No No No No Now what does this table remind us of? It is precisely the truth table for “AND.” It is just what we would have if we wrote down the truth table of the statement “Switch 1 is closed AND switch 2 is closed.” [Illustration: FIG. 2. Switches in parallel.] [Illustration: FIG. 3. Switch open—current flowing.] Suppose that we have two switches 1, 2 in parallel (see Fig. 2). When do we get current flowing from the source to the sink? Answer: when either one or both of the switches are closed. Therefore, this circuit is an exact representation of the statement “Switch 1 is closed or switch 2 is closed.” Suppose that we have a switch that has two positions, and at any time must be at one and only one of these two positions (see Fig. 3). Suppose that current flows only when the switch is open. There are two possible cases and results (see Table 10). Table 10 SWITCH 1 IS CLOSED CURRENT FLOWS Yes No No Yes This is like the truth table for “NOT”; and this circuit is an exact representation of the statement “Switch 1 is NOT closed.” (_Note_: These examples are in substantial agreement with Shannon’s paper, although Shannon uses different conventions.) We see, therefore, that there is a very neat correspondence between the algebra of logic and automatic switching circuits. Thus it happens that: 1. The algebra of logic can be used in the calculation of some electrical circuits. 2. Some electrical circuits can be used in the calculations of the algebra of logic. This fact is what led to the next step. LOGICAL-TRUTH CALCULATION BY MACHINE In 1946 two undergraduates at Harvard University, Theodore A. Kalin and William Burkhart, were taking a course in mathematical logic. They noticed that there were a large number of truth tables to be worked out. To work them out took time and effort and yet was a rather tiresome automatic process not requiring much thinking. They had had some experience with electrical circuits. Knowing of Shannon’s work, they said to each other, “Why not build an electrical machine to calculate truth tables?” They took about two months to decide on the essential design of the machine: 1. The machine would have dial switches in which logical connectives would be entered. 2. It would have dial switches in which the numbers of statements like 1, 2, 3 ··· would be entered. 3. It would scan the proper truth table line by line by sending electrical pulses through the dial switches. 4. It would compute the truth or falsehood of the whole expression. CONSTRUCTION AND COMPLETION OF THE KALIN-BURKHART LOGICAL-TRUTH CALCULATOR With the designs in mind, Kalin and Burkhart bought some war surplus materials, including relays, switches, wires, lights, and a metal box about 30 inches long by 16 inches tall, and 13 inches deep. From March to June, 1947, they constructed a machine in their spare time, assembling and mounting the parts inside the box. The total cost of materials was about $150. In June the machine was demonstrated in Cambridge, Mass., before several logicians and engineers, and in August it was moved for some months to the office of a life insurance company. There some study was made of the possible application of the machine in drafting contracts and rules. GENERAL ORGANIZATION OF THE MACHINE The logical-truth calculator built by Kalin and Burkhart is not giant in size, although giant in capacity. Like other mechanical brains, the machine is made up of many pieces of a rather small number of different kinds of parts. The machine contains about 45 dial switches, 23 snap switches (or two-position switches), 85 relays, 6 push buttons, less than a mile of wire, etc. The lid of the metal box is the front, vertical panel of the machine. UNITS OF THE MACHINE The machine contains 16 units. These units are listed in Table 11, in approximately the order in which they appear on the front panel of the machine—row by row from top to bottom, and from left to right in each row. Table 11 UNITS, THEIR NAMES, AND SIGNIFICANCE UNIT ROW PART NO. MARK NAME SIGNIFICANCE 1 1 Small red 12 — _Statement truth-_ Output: glows if lights _value lights_ statement is assumed true in the case 2 1 2-position 12 ~ _Statement denial_ Input: if up, snap switches _switches_ statement is denied 3 2 14-position 12 _V_ _Statement_ Input of dial switches _switches_ statements 4 3 4-position 11 _k_ _Connective_ Input of dial switches _switches_ connectives: ∧ (and), ∨ (or), ▲ (if-then), ▼ (if and only if) 5 4 11-position 11 _A_ _Antecedent_ Input of dial switches _switches_ antecedents 6 5 11-position 11 _C_ _Consequent_ Input of dial switches _switches_ consequents 7 6 2-position 11 _S_ _Stop switches_ Input: if up, snap switches associates connective to main truth-value light 8 6 2-position 11 ~ _Connective denial_ Input: if up, snap switches _switches_ statement produced by connective is denied 9 7 Red light and 1 Start _Automatic start_ Input: causes the large button calc. to start down a truth table automatically 10 7 Red light and 1 Start _Power switch_ Input: turns the 2 buttons Stop power on or off 11 7 2-position 1 Stop “_Stop-on-true-or-_ Input: causes the snap switch _false_” _switch_ calc.to stop and red either on true button cases or on false cases 12 7 Yellow light 1 — _Main truth-value_ Output: glows if _light_ the statement produced by the main connective is true for the case 13 7 Large button 1 Man. _Manual pulse_ Input: causes the Pulse _button_ calc. to go to the next line of a truth table 14 7 11-position 1 _kⱼ_ _Connective check_ Output: glows when dial switch _switch and light_ any specified connective is true 15 7 13-position 1 TT “_Truth-table-row-_ Input: causes the dial switch Row _stop_” _switch_ calc. to stop on Stop last row of the the truth table 16 Be- Continuous 1 — _Timing control_ Input: controls the tween dial knob _knob_ speed at which 6 & 7 and button the calculator scans rows of the truth table Some of the words appearing in this table need to be defined. _Connective_ here means “AND,” “OR,” “IF ··· THEN,” “IF AND ONLY IF.” Only these four connectives appear on the machine; others when needed can be constructed from these. The symbols used for these connectives in mathematical logic are ∧, ∨, ▲, ▼. These signs serve as labels for the connective switch points. In this machine, when there is a connective between two statements, the statement that comes before is called the _antecedent_ and the statement that comes after is called the _consequent_. HOW INFORMATION GOES INTO THE MACHINE Of the 16 units 13 are input units. They control the setup of the machine so that it can solve a problem. Of the 13 input units, those that have the most to do with taking in the problem are shown in Table 12. Table 12 Name of KIND OF UNIT SWITCHES MARK SWITCH SWITCH SETTINGS 3 Statement _V_₁ to Dial Statements 1 to 12 or constant _V_₁₂ _T_ or _F_ 2 Statement ~ Snap Affirmative (down) or negative denial (up) 4 Connective _k_₁ to Dial ∧ (AND), _k_₁₁ ∨ (OR), ▲ (IF-THEN), ▼ (IF AND ONLY IF) 8 Connective ~ Snap Affirmative (down) or negative denial (up) 5 Antecedent _A_₁ to Dial _V_ or various _k_’s _A_₁₁ 6 Consequent _C_₁ to Dial _V_ or various _k_’s _C_₁₁ 7 Stop _S_₁ to Snap Not connected (down) or _S_₁₁ connected (up) The first step in putting a problem on the machine is to express the whole problem as a single compound statement that we want to know the truth or falsity of. We express the single compound statement in a form such as the following: _V k V k V k V k V k V k V k V k V k V k V k V_ where each _V_ represents a statement, each _k_ represents a connective, and we know the grouping, or in other words, we know the antecedent and consequent of each connective. For example, let us choose a problem with an obvious answer: PROBLEM. Given: statement 1 is true; and if statement 1 is true, then statement 2 is true; and if statement 2 is true, then statement 3 is true; and if statement 3 is true, then statement 4 is true. Is statement 4 true? How do we express this whole problem in a form that will go on the machine? We express the whole problem as a single compound statement that we want to know the truth or falsity of: If [1 and (if 1 then 2) and (if 2 then 3) and (if 3 then 4)], then 4 The 8 statements occurring in this problem are, respectively: 1 1 2 2 3 3 4 4. These are the values at which the _V_ switches (the statement dial switches, Unit 2) from _V_₁ to _V_₈ are set. The 7 connectives occurring in this problem are, respectively: AND, IF-THEN, AND, IF-THEN, AND, IF-THEN, IF-THEN. These are the values at which the _k_ switches (the connective dial switches, Unit 4) from _k_₁ to _k_₇ are set. A grouping (one of several possible groupings) that specifies the antecedent and consequent of each connective is the following: 1 AND 1 IF-THEN 2 AND 2 IF-THEN 3 AND 3 IF-THEN 4 IF-THEN 4 | | | | | | +—————————+ +—————————+ +—————————+ _k_₂ _k_₄ _k_₆ | | | | +———————————————+ +—————————————————————————+ _k_₁ _k_₅ | | +———————————————————————————————————————————————+ _k_₃ | | +—————————————————————————————————————————————————————————+ _k_₇ The grouping has here been expressed graphically with lines but may be expressed in the normal mathematical way with parentheses and brackets as follows: {[1 AND (1 IF-THEN 2)] AND [(2 IF-THEN 3) AND (3 IF-THEN 4)]} IF-THEN 4. So the values at which the antecedent and consequent dial switches are set are as shown in Table 13. Table 13 ANTECEDENT CONSEQUENT CONNECTIVE SWITCH SET AT SWITCH SET AT _k_₁ _A_₁ _V_ _C_₁ _k_₂ _k_₂ _A_₂ _V_ _C_₂ _V_ _k_₃ _A_₃ _k_₁ _C_₃ _k_₅ _k_₄ _A_₄ _V_ _C_₄ _V_ _k_₅ _A_₅ _k_₄ _C_₅ _k_₆ _k_₆ _A_₆ _V_ _C_₆ _V_ _k_₇ _A_₇ _k_₃ _C_₇ _V_ In any problem, statements that are different are numbered one after another 1, 2, 3, 4 ···. A statement that is repeated bears always the same number. In nearly all cases that are interesting, there will be repetitions of the statements. If any statement appeared with a “NOT” in it, we would turn up the denial switch for that statement (Unit 2). The different connectives available on the machine are “AND,” “OR,” “IF ··· THEN,” “IF AND ONLY IF.” If a “NOT” affected the compound statement produced by any connective, we would turn up the denial switch for that connective (Unit 8). The last step in putting the problem on the machine is to connect the main connective of the whole compound statement to the yellow light output (Unit 12). In this problem the last “IF-THEN,” _k_₇, is the main connective, the one that produces the whole compound statement. So we turn Stop Switch 7 (in Unit 7) that belongs to _k_₇ into the up position. There are a few more things to do, naturally, but the essential part of putting the information of the problem into the machine has now been described. HOW INFORMATION COMES OUT OF THE MACHINE Of the 16 units listed in Table 11, 3 are output units, and only 2 of these are really important, as shown in Table 14. Table 14 UNIT NAME OF LIGHT MARK KIND OF LIGHT 1 Statement truth value _V_₁ to _V_₁₂ Small, red 13 Main truth value Large, yellow The answer to a problem is shown by a pattern of the lights of Units 1 and 13. The pattern of lights is equivalent to a row of the truth table. Each little red light (Unit 1) glows when its statement is assumed to be true, and it is dark when its statement is assumed to be false. The yellow light (Unit 13) glows when the whole compound statement is calculated to be logically true, and it is dark when the whole compound statement is calculated to be logically false. The machine turns its “attention” automatically to each line of the truth table one after the other, and pulses are fed in according to the pattern of assumed true statements. We can set the machine to stop on true cases or on false cases or on every case, so as to give us time to copy down whichever kind of results we are interested in. When we have noted the case, we can press a button and the machine will then go ahead searching for more cases. A COMPLETE AND CONCRETE EXAMPLE The reader may still be wondering when he will see a complete and concrete example of the application of the logical-truth calculator. So far we have given only pieces of examples in order to illustrate some explanation. Therefore, let us consider now the following problem: PROBLEM. The A. A. Adams Co., Inc., has about 1000 employees. About 600 of them are insured under a contract for group insurance with the I. I. Insurance Co. Mr. Adams decides that more of his employees ought to be insured. As a part of his study of the change, he asks his manager in charge of the group insurance plan, “What are the possible statuses of my employees who are not insured?” The manager replies, “I can tell you the names of the men who are not insured, and all the data you may want to know about them.” Mr. Adams says, “No, John, that won’t be enough, for I need to know whether there are any groups or classes that for some basic reason I should exclude from the change I am considering.” So the manager goes to work with the following 5 statuses and the following 5 rules, and he produces the following answer. Our question is, “Is he right, or has he made a mistake?” _Statuses._ A status for any employee is a report about that employee, answering all the following 5 questions with “yes” or “no.” 1. Is the employee eligible for insurance? 2. Has the employee applied for insurance? 3. Has the employee’s application for insurance been approved? 4. Does the employee require a medical examination for insurance? 5. Is the employee insured? _Rules._ The rules applying to employees are: _A._ Any employee, to be insured, must be eligible for insurance, must make application for insurance, and must have such application for insurance approved. _B._ Only eligible employees may apply for insurance. _C._ The application of any person eligible for insurance without medical examination is automatically approved. _D._ (Naturally) an application can be approved only if the application is made. _E._ (Naturally) a medical examination will not be required from any person not eligible for insurance. _Answer by the Manager._ There are 5 possible combinations of statuses for employees who are not insured, as shown in Table 15. Table 15 POSSIBLE STATUS 3, STATUS 4, COMBINATION STATUS 1, STATUS 2, APPLICATION EXAMINATION STATUS 5, OF STATUSES ELIGIBLE APPLIED APPROVED REQUIRED INSURED 1 Yes Yes Yes Yes No 2 Yes Yes Yes No No 3 Yes Yes No Yes No 4 Yes No Yes No No 5 No No No No No The question may be asked why employees who are eligible, who have applied for insurance, who have had their applications approved, and who require no medical examination (combination 2) are yet not insured. The answer is that the rules given do not logically lead to this conclusion. As a matter of fact, there might be additional rules, such as: any sick employee must first return to work; or any period from date of approval of application to the first of the following month must first pass. The first step in putting this problem on the Kalin-Burkhart Logical-Truth Calculator is to rephrase the rules, using the language of the connectives that we have on the machine. The rules rephrased are: _A._ If an employee is insured, then he is eligible, he has applied for insurance, and his application has been approved. IF 5, THEN 1 AND 2 AND 3 _B._ If an employee has applied (under these rules) for insurance, then he is eligible. IF 2, THEN 1 _C._ If an employee is eligible for insurance, has applied, and requires no medical examination, his application is automatically approved. IF 1 AND 2 AND NOT-4, THEN 3 _D._ If an employee’s application has been approved, then he has applied. IF 3, THEN 2 _E._ If an employee is not eligible, then he does not require a medical examination (under these rules). IF NOT-1, THEN NOT-4 To get the answer we seek, we must add one more rule _for this answer only_: _F._ The employee is not insured. NOT-5 We now have a total of 4 + 2 + 4 + 2 + 2 + 1 occurrences of statements, or 15 occurrences. This is beyond the capacity of the existing machine. But fortunately Rule _F_ and Rule _A_ cancel each other; they may both be omitted; and this gives us 10 occurrences instead of 15. In other words, all the possible statuses under “Rule _B_ AND Rule _C_ AND Rule _D_ AND Rule _E_” will give us the answer we seek. The rephrasing and reasoning we have done here is perhaps not easy. For example, going from the logical pattern Only igs may be ows to the logical pattern If it is an ow, then it is an ig as we did in rephrasing Rule _B_, deserves rather more thought and discussion than we can give to the subject here. A person who is responsible for preparing problems for the Logical-Truth Calculator should know the algebra of logic. Choosing an appropriate grouping, we now set on the machine: {(IF 2, THEN 1) AND [IF (1 AND 2) AND NOT-4, THEN 3]} AND [(IF 3, THEN 2) AND (IF NOT-1, THEN NOT-4)] The setting is as shown in Table 16. After this setting, the machine is turned on and set to stop on the “true” cases. The Table 16 SETTING OF THE PROBLEM ON THE LOGICAL-TRUTH CALCULATOR UNIT 3 Statement Dial No. _V_₁ _V_₂ _V_₃ _V_₄ _V_₅ _V_₆ 3 Statement Dial Setting 2 1 1 2 4 3 2 Statement Denial Switch Setting — — — — up — 4 Connective Dial No. _k_₁ _k_₂ _k_₃ _k_₄ _k_₅ _k_₆ 4 Connective Dial Setting ▲ ∧ ∧ ∧ ▲ ∧ 8 Connective Denial Switch Setting — — — — — — 5 Antecedent Dial No. _A_₁ _A_₂ _A_₃ _A_₄ _A_₅ _A_₆ 5 Antecedent Dial Setting _V_ _k_₁ _V_ _k_₃ _k_₄ _k_₂ 6 Consequent Dial No. _C_₁ _C_₂ _C_₃ _C_₄ _C_₅ _C_₆ 6 Consequent Dial Setting _V_ _k_₅ _V_ _V_ _V_ _k_₈ 7 Stop Switches, associating connective to Main Truth-Value Light — — — — — up ----------------------------------------------------------------- 3 Statement Dial No. _V_₇ _V_₈ _V_₉ _V_₁₀ _V_₁₁ _V_₁₂ 3 Statement Dial Setting 3 2 1 4 _F_ _F_ 2 Statement Denial Switch Setting — — up up — — 4 Connective Dial No. _k_₇ _k_₈ _k_₉ _k_₁₀ _k_₁₁ 4 Connective Dial Setting ▲ ∧ ▲ off off 8 Connective Denial Switch Setting — — — — — 5 Antecedent Dial No. _A_₇ _A_₈ _A_₉ _A_₁₀ _A_₁₁ 5 Antecedent Dial Setting _V_ _k_₇ _V_ off off 6 Consequent Dial No. _C_₇ _C_₈ _C_₉ _C_₁₀ _C_₁₁ 6 Consequent Dial Setting _V_ _k_₉ _V_ off off 7 Stop Switches, associating connective to Main Truth-Value Light — — — — — possible statuses of employees who are not insured are shown in Table 17. As we look down the last column in Table 17, we observe 6 occurrences of _T_, instead of 5 as the manager determined (see Table 15). Thus, when we compare the manager’s result with the machine result, we find an additional possible combination to be reported to Mr. Adams, combination 7: Employee eligible, employee has not applied, employee’s application not approved, employee requires a medical examination, employee not insured. Table 17 SOLUTION OF THE PROBLEM BY THE CALCULATOR LEGEND: {A} THE EMPLOYEE IS ELIGIBLE FOR INSURANCE {B} THE EMPLOYEE HAS APPLIED FOR INSURANCE {C} THE EMPLOYEE’S APPLICATION FOR INSURANCE HAS BEEN APPROVED {D} THE EMPLOYEE REQUIRES A MEDICAL EXAMINATION {E} THE EMPLOYEE IS INSURED {F} CASE, OR COMBINATION NO. {G} THE COMBINATION DOES NOT CONTRADICT THE RULES, I.E., THE YELLOW LIGHT IS ON {A} {B} {C} {D} {E} {F} {G} _Status_: 1 2 3 4 5 _T_ _T_ _T_ _T_ _F_ 1 _T_ _F_ _T_ _T_ _T_ _F_ 2 _F_ _T_ _F_ _T_ _T_ _F_ 3 _F_ _F_ _F_ _T_ _T_ _F_ 4 _F_ _T_ _T_ _F_ _T_ _F_ 5 _T_ _F_ _T_ _F_ _T_ _F_ 6 _F_ _T_ _F_ _F_ _T_ _F_ 7 _T_ _F_ _F_ _F_ _T_ _F_ 8 _F_ _T_ _T_ _T_ _F_ _F_ 9 _T_ _F_ _T_ _T_ _F_ _F_ 10 _F_ _T_ _F_ _T_ _F_ _F_ 11 _F_ _F_ _F_ _T_ _F_ _F_ 12 _F_ _T_ _T_ _F_ _F_ _F_ 13 _F_ _F_ _T_ _F_ _F_ _F_ 14 _F_ _T_ _F_ _F_ _F_ _F_ 15 _T_ _F_ _F_ _F_ _F_ _F_ 16 _T_ Because of the medical examination, this additional class of employee would need to be considered rather carefully in any change of the group insurance plan. AN APPRAISAL OF THE CALCULATOR In appraising the Kalin-Burkhart Logical-Truth Calculator, we must remember that this is a first model. It was the only machine of its kind up to the end of 1948; and it worked. The cost of the machine, as stated before, was about $150 of parts and perhaps $1000 of labor. This is less than ¹/₁₀₀ of the cost of the other giant brains described in previous chapters. Yet we can properly call this machine a mechanical brain because it transfers information automatically from one part to another of the machine, has automatic control over the sequence of operations, and does certain kinds of reasoning. The machine is swift. It can check up to a 100 cases against a set of rules in less than 1 minute. It can check: 128 cases for 7 conditions in 1¼ minutes, 256 cases for 8 conditions in 2½ minutes, and 4096 cases for 12 conditions in 38 minutes. That is the limit of the present machine. Of course, setting up the machine to do a problem takes some more time. The programming of this machine to do a problem is less complicated than the programming of most of the big machines previously described. Of course, in order to prepare a problem for the machine, the preparer needs to know a fair amount of the algebra of logic. This, however, is not very hard. As to reliability, the machine has in practice been out of order less than 2 per cent of operating time. The big barrier to wide use of the machine, of course, is lack of understanding of the field of problems in which it can be applied. Even in this modern world of ours, we are in rather a primitive stage in regard to recognizing problems in logical truth and knowing how to calculate it. Here, however, is an electrical instrument for logical reasoning, and it seems likely that its applications will multiply. Chapter 10 AN EXCURSION: THE FUTURE DESIGN OF MACHINES THAT THINK In the previous chapters we have described four giant mechanical brains finished by the end of 1946: Massachusetts Institute of Technology’s Differential Analyzer No. 2, Harvard’s IBM Automatic Sequence-Controlled Calculator, Moore School of Electrical Engineering’s Electronic Numerical Integrator and Calculator (Eniac), and Bell Telephone Laboratories’ General-Purpose Relay Computer. All these brains have actually worked long enough to have demonstrated thoroughly some facts of great importance. WHAT EXISTING MACHINES HAVE PROVED The existing mechanical brains have proved that information can be automatically transferred between any two registers of a machine. No human being is needed to pick up a physical piece of information produced in one part of the machine, personally move it to another part of the machine, and there put it in again. We can think of a mechanical brain as something like a battery of desk calculators or punch-card machines all cabled together and communicating automatically. The existing mechanical brains have also proved that flexible, automatic control over long sequences of operations is possible. We can lay out the whole routine to solve a problem, translate it into machine language, and put it into the machine. Then we press the “start” button; the machine starts whirring and prints out the answers as it obtains them. Mechanical brains have removed the limits on complexity of routine: the machine can carry out a complicated routine as easily as a simple one. The existing giant brains have shown that a machine with hundreds of thousands of parts will work successfully. It will operate accurately, it will run unattended, and it will have remarkably few mechanical troubles. These machines have shown that enormous speeds can be realized: 5000 additions a second is Eniac’s record. High speed is needed for many problems in science, government, and business. In fact, there are economic and statistical problems, now settled by armchair methods, for which high-speed mechanical brains may make it possible to compute answers rather than guess them. Also, these machines have been shown to be reasonable in cost. The cost of each of the large calculators is in the neighborhood of $250,000 to $500,000. If we assume a ten-year life, which is conservative, the cost is about $3 to $6 an hour for 24-hour operation. Since each mechanical brain can, for problems for which it is suited, do the work of a hundred human computers, such a machine can save its cost half a dozen times. And these machines are only engineers’ models, built without the advantages of production-line assembly. The cost of giant mechanical brains under design in 1947 and 1948 is in the neighborhood of $100,000 to $200,000. The main reason for the reduction from the previous cost is the use of cheaper automatic memory. As designs improve and charges for research and development are paid off, the cost should continue to go down. NEW DEVICES FOR HANDLING INFORMATION In the laboratories working on new mechanical and electronic brains, scientists are doing a lot of thinking about new devices for handling information. Research into devices for storing information shows that _magnetic wire_ as used in sound recording is a rather good storage medium. Magnetic Wire For example, on a hundredth of an inch of fine steel wire we can “write” a _magnetized spot_ by means of a small “writing” _electromagnet_. The electromagnet is simply some copper wire coiled around some soft iron shaped in a U. When current flows through the coil, the iron becomes a magnet, and the tips of the U magnetize the little section of the wire between them. The magnetized spot can be of two kinds, say north-south or south-north, depending on which way the current flows. We can “read” this difference by means of another small “reading” electromagnet. We can erase the spot by means of a stronger “erasing” magnet that produces a uniform magnetic state throughout the wire. The difference between north-south and south-north corresponds to the difference between 1 and 0, or “yes” and “no,” etc., and is a _unit of information_ (see Chapter 2). Many other variations are possible. For example, the presence or absence of a magnetized spot may be the unit of information, or the “writing,” “reading,” and “erasing” electromagnets all may be the same. Magnetic wire sound recordings made in the 1890’s are still good. This fact shows that magnetic wire may be a more permanent medium for storing information than is paper. Stray magnetic forces are likely to have no harmful effect on information stored on magnetic wire, for these forces would not be strong enough or detailed enough to change greatly the difference between the magnetized spot and its neighboring neutral area. A reel of magnetic wire a mile long and ³/₁₀₀₀ of an inch thick costs about $5. At 80 magnetized spots to the inch, a mile of wire can store about 5 million units of information. Hence, the cost of storing one unit of information is about ¹/₁₀₀₀₀ of a cent. The time needed for changing a magnetized spot from 1 to 0 or from 0 to 1 is about ¹/₁₀₀₀₀ of a second. Magnetic Tape There is, however, a storage device that may be even more useful, and this is _magnetic tape_ (see Fig. 1). The usual size of such tape is ¼ inch wide and 2 or 3 thousandths of an inch thick. Magnetic tape may be made of plastic with magnetic powder all through it, or it may be of paper coated with magnetic powder, or it may be of stainless steel or a magnetic alloy, or it may be of brass or a nonmagnetic alloy coated with a magnetic plating. Magnetic tape has the added advantage that from 4 to 20 channels across the tape can be filled with magnetized spots, and the cost then becomes about ¹/₁₀₀₀₀₀ of a cent per spot. It seems possible that 1000 units of information can be stored in a quarter of a square inch of magnetic tape. This means that more than 1 million units of information can be stored in a cubic inch of space filled with magnetic tape, and about 2 billion units of information in a cubic foot, except that some of the space should be allotted to the reels and other equipment that hold the tape (see Fig. 2). This is closer packing than printed information in the telephone book, and yet with magnetic tape we can get to the information automatically. [Illustration: FIG. 1. Magnetic tape.] [Illustration: FIG. 2. Tape reels.] Think of the enormous files in libraries, government, and business. Think of the problems of space and cost and access which these files imply. We can then see that this new development may well be of extraordinary importance. Mercury Tanks [Illustration: FIG. 3. Mercury tank.] Scientists are investigating other storage devices having still more remarkable properties, but these have the disadvantage that, when the power goes off, the information vanishes. One of these new storage devices is called a _mercury tank_ (see Fig. 3). It consists mainly of a section of iron or steel pipe filled with mercury. At each end of this pipe, touching the mercury, is a thin slab of a crystal of _quartz_. Quartz, which is a common stone, and which nearly all sand is made of, changes its shape when pulsed with electricity. We put a pattern of electrical pulses into the quartz slab at one end of the mercury tank; for example, we could have the pattern 1101 meaning “pulse, pulse, no pulse, pulse.” The electrical pulses going into the quartz slab make the quartz vibrate. Thus ripples are produced in the mercury, and waves in the pattern 1101 meaning “wave, wave, no wave, wave” travel down the tank and strike the quartz slab at the far end. The quartz slab there changes its shape in the rhythm 1101, and it converts the waves back into electrical pulses in the same pattern. Then we take the pulses out of the far end along a wire, make them stronger again with an amplifier, give them the right form again, and feed them back into the front end of the mercury tank. The mercury tank is a clever use of the principle of an _echo_, as when you call across a valley and the rocks answer you back. We can store a pattern of 400 pulses (each a unit of information, a 1 or a 0, and each a millionth of a second in duration), in a mercury tank about 20 inches long. A mercury tank and an echo are examples of _delay lines_—“lines” along which waves are “delayed.” Electrostatic Storage Tube Another of the memory devices being developed is called an _electrostatic storage tube_ (see Fig. 4). This is a big electronic tube with a _screen_ across one end. The screen may be of two layers: one of copper, which conducts electricity, and one of _mica_, a material that does not. In the other end of the tube is a _beam_ of electrons, which we can turn on and off and shoot at any of 2 or 3 thousand specific points or _spots_ on the screen. [Illustration: FIG. 4. Electrostatic storage tube.] There are two sizes of _electric charge_ or quantity of electrons; we can call these 1 and 0. In about a millionth of a second, we can put either size of charge on one of the spots of the screen. With other circuits we can keep it there as long as we want, if the power does not flicker off. We can “remember” perhaps 2 or 3 thousand units of information in one of these electronic tubes. We can read, write, or erase any unit of information in a few millionths of a second. Neither the mercury tank nor the electrostatic storage tube had, by the end of 1947, been put into a working mechanical brain. But there is good reason to believe that they will be successful devices and will open up a new era of speed in storing and referring to information. In fact, several laboratories are developing electronic calculating circuits using these devices which will perform up to 100,000 additions a second or 10,000 multiplications a second. Our minds certainly stagger at the thought of such speeds. NEW OPERATIONS Many kinds of combining operations have already been built into one or more mechanical brains. The operations may be arithmetical: addition, subtraction, multiplication, division, looking up numbers in tables, etc. Or the operations may be logical: comparing, selecting, checking, etc. Additional logical operations will be built into some of the mechanical brains now being constructed: sorting, collating, matching, merging, etc. NEW IDEAS IN PROGRAMMING _Programming_—the way to give instructions to machines—is also being studied in the laboratories. Several new ideas of importance have developed as a result. One idea is that the machine should be able to store its instructions or _program_ or _routine_ in its memory in just the same physical ways as it stores numbers. There is basically no reason why numbers only should be stored in some registers, and instructions only stored in other registers. Another idea is that the machine should have in its permanent memory any subroutine it may need. For example, a subroutine should always be available in the machine for finding _square root_. At any time when a square root was needed, we would only have to call on the machine for the subroutine of square root. The machine would then consult the right part of its memory and carry out the subroutine for square root. A third idea, and one of the most interesting, is that the machine should be able to compute its own instructions. For example, consider a program for finding the product of two _matrices_ (see Supplement 2), each of 100 terms in an array of 10 columns and 10 rows, resulting in a new _matrix_ of 100 terms. The whole program can be made to consist of about 50 orders. Only one of them is “multiply,” and only one of them is “add”; the other orders consist of how to choose expressions to be multiplied or added, etc. Such problems as these are often fascinating to mathematicians, who love to play with the intricate ideas needed. NEW IDEAS IN RELIABILITY Reliability has a number of aspects: 1. No wrong results allowed out of the machine. 2. Few failures. 3. Rapid location of failures. 4. Quick repair or replacement of parts that fail. 5. Easy maintenance. 6. Unattended operation overnight. For example, Bell Laboratories proved that mechanical brains can be built so that no wrong results are allowed to come out. In other words, the machine checks itself all the time as it goes along and stops at once if the check shows that something is wrong. This is likely to be a standard feature of new automatic thinking machinery. The frequency of failures in the machinery being designed in the laboratories may be of the order of one or two mechanical failures a week. For any type of failure an alarm circuit and trouble lights will show what part of the machine needs attention. Plug-in parts for replacement are already in use in at least two of the four mechanical brains described and should be available in all the new machines. It is possible to build a machine that will automatically change from failing equipment to properly functioning equipment. For some years though, this may be too expensive to be reasonable. The use of magnetic tape for storage reduces greatly the number of parts and so increases reliability. For example, instead of 18,000 electronic tubes in an electronic brain, there may be less than 3000. A final degree of reliability is gained when most of the time the machine operates unattended. Then, there is no human operator standing by who may fail to do the correct thing at the moment when the machine needs some attention. In fact, the motto for the room housing a mechanical brain should become, “Don’t think; let the machine do it for you.” Unattended operation from the end of one working day to the beginning of the next, with the machine changing itself from one problem to another problem, has already been proved possible on the Bell Laboratories machine. AUXILIARY DEVICES In order to use a mechanical brain, we have to give it and take from it language that it understands, _machine language_. A mechanical brain that can do 10,000 additions a second can very easily finish almost all its work at once. How can we, slow as we are, keep our friend, the giant brain, busy? We have found so far several answers to this question, none of them yet very good. Devices for preparing input will be very important. For each brain, we shall need a great many of these devices. For, at best, we type at a rate, say, of 4 characters a second, selecting any one of some 38 keys, each of which is equivalent to about 6 units of information. This is about 800 units of information per second. The machine, however, is likely to be able to gulp information from its input mechanism at the amazing rate of 60,000 units of information per second, equal to 75 people typing with no mistakes and no resting. Fortunately, at least some of the time the machine will be busy computing! For an input-preparation device, we may get something that can be fastened to an ordinary typewriter and that will produce magnetic tape agreeing with what is printed by the typewriter. Since the input information must be carefully verified, we shall need a second magnetic tape device such as exists for paper tape on the Bell Laboratories machine: the _processor_. The processor takes two hand-prepared tapes, compares them, reports any differences, and produces a third tape. The third tape copies the two original tapes if they agree, and it receives corrected information as furnished by a girl at a keyboard if the two original tapes disagree. For information already on punch cards, we need an input device that will read punch cards and write on magnetic tape. Where information is on punched paper tape, we need a machine that will read punched paper tape and write on magnetic tape. Problem data, tables of numbers, and routine instructions will go into the mechanical brain. They will all be prepared on regular input devices. The machine will accept information in the form in which it is most convenient for you and me to prepare it. Then, the machine will be instructed to change the information into the form with which it is most convenient for the machine to operate. Many output devices will also be needed, since the machine will be able to produce information very swiftly. These output devices might be cabled to the machine. A kind of traffic control system would govern them. Each will have a magnetic tape that will be loaded up swiftly with information. Then the output device will unload its information more slowly, in any form that we may desire: printing, graphs, film, punch cards, or punched paper tape. The machine is likely to be able to put out information on magnetic tape at the same high speed of 60,000 units of information per second or 10,000 characters per second. But the best printing speed of an electric typewriter is about 10 or 12 characters a second. Card-punching speed is about 130 characters a second. Punch-card tabulator speed can reach a maximum of about 200 characters a second. Thus we see that here, too, we may be snowed under with the information that the giant brain puts out, if we fail to ask the giant only for what we really want. MECHANICAL BRAINS UNDER CONSTRUCTION This chapter would not be complete without mention of the great mechanical brains that were actually under construction at the end of 1947. In power they are intermediate between the machinery now being designed, described in this chapter, and the earlier machines described in the previous chapters of this book. The mechanical brains under construction on December 31, 1947, were: Harvard’s Sequence-Controlled Relay Calculator _Mark II_, constructed at the Harvard Computation Laboratory, tested there July 1947 to January 1948, and delivered to the Naval Proving Ground, Dahlgren, Va., in 1948. The _IBM Selective-Sequence Electronic Calculator_, constructed in the IBM laboratories, Endicott, N. Y., and installed in 1947 at the office of International Business Machines, 590 Madison Ave., New York, N. Y. Moore School of Electrical Engineering’s _EDVAC_ (Electronic Digital Variable Automatic Computer) being constructed partly at Moore School and partly elsewhere, and to be delivered to the Ballistic Research Laboratories, Aberdeen, Md. Harvard’s Sequence-Controlled Electronic Calculator _Mark III_, being constructed at the Harvard Computation Laboratory, and to be delivered to the Naval Proving Ground, Dahlgren, Va. We shall cover briefly (and perhaps a little technically) some of the main features of the first two of these machines; for, during 1948, they began to do problems. The other two had not been finished by the end of 1948 and so would be difficult to describe correctly, for mechanical brains _grow_, and design changes go on until they are finished—and even afterwards. Some information about these machines can be obtained from the organizations referred to above and from reports that should appear from time to time in some of the journals mentioned in Supplement 3. There is also a regular section entitled “Automatic Computing Machinery” in the quarterly _Mathematical Tables and Other Aids to Computation_, where it is likely that current information may be found. Harvard’s Mark II The Harvard Sequence-Controlled Calculator Mark II began to do problems under test during July 1947. This machine is at least twelve times as powerful as Mark I (see Chapter 6) and was constructed entirely by the Harvard Computation Laboratory. The machine contains about 13,000 relays of a new type that will operate reliably within ¹/₁₀₀ of a second. Numbers in the machine are regularly of 10 decimal digits between 1.000,000,000 and 9.999,999,999, inclusive, multiplied by a power of 10 between 1,000,000,000,000,000 and 0.000,000,000,000,001, inclusive. For storage of numbers, the machine has 100 relay registers totaling about 1200 decimal digits. Also, it can consult any one of 8 tape feeds for numbers and any one of 4 tape feeds for instructions. Effectively, the machine can read one number and one instruction from paper tape in ¹/₃₀ of a second. The machine performs all arithmetical and most logical operations. In every second it can carry out 4 multiplications, 8 additions (or subtractions), and 12 transfers. Division is performed by rapid approximation using the other operations. In each second the machine can perform 30 instructions. An instruction is expressed by 6 digits between 0 and 7 which you can select and, in effect, by 3 more digits fixed by the time (within the second) when the machine reads the instruction. For example, in the 9th instruction of the 30 instructions in each second, we can specify a multiplicand. But, if we do not want to multiply right then—a rare event if we are coding wisely—we leave the 9th instruction empty. The machine may operate as a whole, attending to one problem; or the machine may be separated into halves, and each half will attend to its own problem. The IBM Selective-Sequence Electronic Calculator The IBM Selective-Sequence Electronic Calculator was announced publicly on January 27, 1948, after some months of trial running. It is a large and powerful mechanical brain, and it is the intention of International Business Machines to devote it to solving scientific problems. The staff of the Watson Scientific Computing Laboratory in New York will be mainly in charge of the machine. The machine contains about 12,500 electronic tubes and about 21,500 relays. Numbers in the machine are regularly of either 14 or 19 decimal digits. Instructions are expressed as numbers. For storage of information, the machine has a capacity of 8 registers totaling 160 decimal digits of very rapid memory in electronic tubes. Also, it has about 150 registers totaling 3000 decimal digits of less rapid memory in relays. Also, it can consult any one of 66 paper tape feeds; each row on a paper tape can hold up to 78 punched holes or 19 decimal digits, and the machine can consult 25 rows on one tape in one second. These paper tapes together give the machine about 400,000 decimal digits of memory. For arithmetical and logical operations, the machine has an arithmetical unit using electronic tubes. This unit can carry out about 50 multiplications or about 250 additions per second, including the transfers of numbers. In each second the machine can read and perform 50 instructions, and each instruction consists, usually, of getting two numbers out of two relay registers, performing an operation, and putting the result into a third relay register. Eckert-Mauchly’s Binac As this book went to press, another mechanical brain, the Electronic Binary Automatic Computer, or BINAC, was announced on August 22, 1949. This machine was constructed by the Eckert-Mauchly Computer Corporation, Philadelphia, Pa., for Northrop Aircraft, Inc., Hawthorne, Calif. This machine has some remarkable properties. It does addition or subtraction at the rate of 3500 per second. It does multiplication or division at the rate of 1000 per second. The input is from a keyboard or magnetic tape; the output is to magnetic tape or an electric typewriter. Binac has 512 registers of very rapid memory in mercury tanks, and each register holds 30 binary digits. The machine actually is a pair of twins: the storage, the computing element, and the control are double, and each twin runs in step with the other and checks every operation of the other. In tests in July the machine ran over 10 consecutive hours with no error. Each twin has only 700 electronic tubes. Binac handles all numbers in binary notation, except that the keyboard and the typewriter express numbers in _octal notation_ (see Supplement 2). Finally, Binac is only 5 feet high, 4 feet long, and one foot wide. Chapter 11 THE FUTURE: MACHINES THAT THINK, AND WHAT THEY MIGHT DO FOR MEN The pen is mightier than the sword, it is often said. And if this is true, then the pen with a motor may be mightier than the sword with a motor. In the Middle Ages, there were few kinds of weapons, and it was easy for a man to protect himself against most of them by wearing armor. As gunpowder came into use, a man could no longer carry the weight of armor that would protect him, and so armor was given up. But in 1917, armor, equipped with a motor and carrying the man and his weapons, came back into service—as the tank. In much the same way, in the Middle Ages, there were few books, and it was easy for a man to handle nearly all the information that was in books. As the printing press came into use, man’s brain could no longer handle all recorded information, and the effort to do so was given up. But in 1944, a brain to handle information, equipped with a motor and supporting the man and his reasoning, came into existence—as the sequence-controlled calculator. In previous chapters we have examined some of the giant mechanical brains that have been finished; we have also considered the design of such machines. Now in this chapter we shall discuss the future significance of machines that think, of motorized information. We shall discuss what we can foresee if we look with imagination into the future. There are two questions we need to ask: What types of machines that think can we foresee? What types of problems to be solved by these machines can we foresee? FUTURE TYPES OF MACHINES THAT THINK The machines that already exist show that some processes of thinking can already be performed very quickly: Calculating: adding, subtracting,... Reasoning: comparing, selecting,... Referring: looking up information in lists,... We can expect other processes of thinking to come up to high speed through the further development of thinking machines. Automatic Address Book Nowadays when we wish to send out announcements of an event, like going to South America for a year, we may copy the addresses of our friends onto the envelopes by hand. In the future, we can see our address book as a spool of magnetic tape. When we wish to send out announcements, we put a stack of blank envelopes into the machine that will read the magnetic tape, and we press a button. Out will come the envelopes addressed. If we wish to select only those friends of ours whose last names we put down on a list, we can write the list on another magnetic tape, place it also in the machine, and set a few switches. Then the machine will read the names on the list, find their addresses in the address-book tape, and prepare only the envelopes we want. If a friend’s address changes, we can notify the machine. It will find his old address, erase it, and enter the new address. Automatic Library We can foresee the development of machinery that will make it possible to consult information in a library automatically. Suppose that you go into the library of the future and wish to look up ways for making biscuits. You will be able to dial into the catalogue machine “making biscuits.” There will be a flutter of movie film in the machine. Soon it will stop, and, in front of you on the screen, will be projected the part of the catalogue which shows the names of three or four books containing recipes for biscuits. If you are satisfied, you will press a button; a copy of what you saw will be made for you and come out of the machine. After further development, all the pages of all books will be available by machine. Then, when you press the right button, you will be able to get from the machine a copy of the exact recipe for biscuits that you choose. We are not yet at the end of foreseeable development. There will be a third stage. You will then have in your home an automatic cooking machine operated by program tapes. You will stock it with various supplies, and it will put together and cook whatever dishes you desire. Then, what you will need from the library will be a program or routine on magnetic tape to control your automatic cook. And the library, instead of producing a pictorial copy of the recipe for you to read and apply, will produce a routine on magnetic tape for controlling your cooking machine so that you will actually get excellent biscuits! Of course, you may have other kinds of automatic producing machinery in your home or office. The furnishing of routines to control automatic machinery will become a business of importance. Automatic Translator Another machine that we can foresee would be used for translating from one language to any other. We can call it an _automatic translator_. Suppose that you want to say “How much?” in Swedish. You dial into the machine “How much?” and press the button “Swedish,” and the machine will promptly write out “Hur mycket?” for you. It also will pronounce it, if you wish, for there would be little difficulty in recording on magnetic tape the pronunciation of the word as spoken by a good speaker of the language. The machine could be set to repeat the pronunciation several times so that the student could really learn the sound. He could learn it better, probably, by hearing it and trying to say it than he could by using any set of written symbols. Automatic Typist We now come to a possible machine that uses a new principle. This principle is that of being able to _recognize_ signs. This machine would perceive writing on a piece of paper and recognize that all the _a_’s that appear on the paper are cases of _a_, and that all the _b_’s that appear on it are instances of _b_, and so forth. The machine could then control an electric typewriter and copy the marks that it sees. The first stage of this machine would be one in which only printed characters of a high degree of likeness could be recognized. In later stages, handwriting, even rather illegible handwriting, might be recognizable by the machine. We can call it an _automatic typist_. The elements of the automatic typist would be the following: 1. _Phototubes_ (electronic tubes sensitive to the brightness of light), which could sense the difference between black and white (these already exist). 2. A memory of the shapes of 52 letters, 10 digits, and punctuation marks. Fine distinctions would be required of this memory in some cases—like the difference between the numeral 5 and the capital letter S. 3. A control that would cause the machine to _tune_ itself, so that a good matching between the marks it observed and the shapes it remembered would be reached. 4. A _triggering control_ so that, when the machine had reached good enough matching between its observations and its memory, the machine would proceed to identify the marks, read them, and transfer them. 5. An electric typewriter, which would respond to the transferred instructions. (This also already exists.) This machine is perhaps not so farfetched as it might seem. During World War II, gun-aiming equipment using the new technique _radar_ reached a high stage of development. Many shots that disabled and sank enemy ships were fired in total darkness by radar-controlled guns. On the glowing screen in the control room, there were two spots, one that marked the target and one that reported the point at which the gun was aimed. These two spots could be brought almost automatically into agreement. In the same way, a report from a phototube telling the shape of an observed mark and a report from the memory of the machine telling the shape of a similar mark could be compared by the machine for likeness and, if judged enough alike, could be approved as identical. Even the phrase “enough alike” can be applied by a machine. During World War II, tremendous advances were made in machinery for deciphering enemy messages. Machines observed various features and patterns in enemy messages, swiftly counted the frequency of these features, and carried out statistical tests. Then the machines selected those few cases in which the patterns showed meaning instead of randomness. A machine like the automatic typist, if made flexible enough, would be, of course, extremely useful. A great load of dull office work is now being thrown on clerks whose task is to translate from writing and typing into languages that machines can read, such as punch cards. At the present time, if punch-card machines are widely used in a big company, the company must employ large numbers of girls whose sole duty is to read papers and punch up cards. A still bigger chore is the work of typists in all kinds of businesses whose main duty is to read handwriting, etc., and then copy the words on a typewriter. [Illustration: Each square in the grill is watched by a phototube. FIG. 1. Scheme for distinguishing _A_ and _H_ by 15 phototubes.] Research has already begun on various features of the automatic typist because of its obvious labor-saving value. For example, many patents have been issued on schemes for dividing the area occupied by a letter or a digit into an array of spots, with a battery of phototubes each watching a spot. The reports from the phototubes together will distinguish the letter or digit. For example, if we consider _A_ and _H_ placed in a grill of fifteen spots, 5 long by 3 wide (see Fig. 1), then the phototubes can distinguish between _A_ and _H_ by sensing black or white in the spot in the middle of the top row. When we consider how easily and swiftly a human being does this, we can once more marvel at the recognizing machine we all carry around with us in our heads. Automatic Stenographer Another development that we can foresee is one that we can call the _automatic stenographer_. This is a machine that will listen to sounds and write them down in properly spelled English words. The elements of this machine can be outlined: 1. Microphones, which can sense spoken sounds (these already exist). 2. A memory storing the 40 (more or less) phonetic units or sounds that make up English, such as the 23 consonant sounds, _p_ _b_ _l_ _ng_ _f_ _v_ _m_ _th_ _t_ _d_ _n_ _r_ _s_ _z_ _h_ _y_ _k_ _g_ _w_ _ch_ _j_ _sh_ _zh_ (heard in “pleasure”) and the 17 vowel sounds, LONG SHORT OTHER _A_ (“ate”) _a_ (“cat”) _ar_ (“are”) _E_ (“eat”) _e_ (“end”) _aw_ (“awe”) _I_ (“isle”) _i_ (“in”) _er_ (“err”) _O_ (“owe”) _o_ (“on”) _ow_ (“owl”) _U_ (“cute”) _u_ (“up”) _oi_ (“oil”) _OO_ (“roof”) _oo_ (“book”) 3. A collection of the rules of spelling in English, containing many statements like The sound _b_ is always spelled _b_ The sound _sh_ may be spelled _sh_ (ship), _s_ (sugar), _ti_ (station), _ci_ (physician), _ce_ (ocean) or _tu_ (picture) and other statements based on context, word lists, derivation, etc. These are the statements by means of which a good English speller knows how to spell even words that he hears for the first time. 4. A triggering control so that, when the machine reaches good enough matching between its observations of sounds, its memory of sounds, and its knowledge of spelling rules, the machine will identify groups of sounds as words, determine their spelling, and report the letters determined. 5. An electric typewriter, which would type the reported letters. With this type of machine, you would dictate your letters into a machine (now existing) that would record your voice. Then the record would be placed on the automatic stenographer, and out would come your letters written and spaced as they should be. Automatic Recognizer We can foresee a recognizing machine with very general powers. Suppose that we call it an _automatic recognizer_ (see Fig. 2). It will have the following elements: 1. _Input._ This element will consist of a set of observing instruments, capable of perceiving sights, sounds, etc. There will be ways of positioning or _tuning_ these instruments. 2. _Memory._ This element will store knowledge. It may store the patterns of observations that we are interested in; or it may store general rules on how to find patterns of observations that we will be interested in. It will contain knowledge about acceptable groups of patterns, about actions to be performed in response to patterns, etc. 3. _Program 1._ The element “Program 1” performs a set of standard instructions. Under these instructions, the machine: Compares group after group of observations with the information in the memory. Compares these groups with patterns furnished, or seeks to organize the observations into patterns. Counts cases and tests frequencies. Finds out how much matching with patterns there is. Tunes the observing instruments in ways to increase matching. [Illustration: FIG. 2. Scheme of an automatic recognizer.] 4. _Program 2._ The element “Program 2” performs another set of standard instructions. Under these instructions, the machine, if it is tuned well, matches sets of observations one after another with the patterns and so reads them. 5. _Triggering Control._ This element shifts the control of the machine from Program 1 to Program 2. It does this when the machine reaches “good matching.” We shall set the meaning of this into the machine in much the same way as we set “warm” into a thermostat. 6. _Output._ This element performs any action that we want, depending on recognized patterns read and any other knowledge or instructions stored in the memory. The automatic recognizer will be capable of extraordinary tasks. With microphones and a large memory, this type of machine would be able to hear a foreign language spoken and translate it into spoken or written English. With phototubes and with an expanded filtering and decoding capacity as in deciphering machines, the automatic recognizer should be able to read a dead language, even those (such as Minoan or Etruscan) that have so far resisted efforts to read it. The machine would derive rules for the translation of the language and translate any sample. An automatic recognizer could perhaps be equipped with many sensitive, tiny observing instruments that could be placed around or in the brain and nervous systems of animals. Then the machine might enable us to find out what activity in the nervous system corresponds with what activity in the animal. TYPES OF PROBLEMS THAT MACHINES WILL SOLVE IN THE FUTURE We turn now to the second question regarding the future of machines that think: What types of problems can we foresee as solved by these machines? Problems of Control Probably the foremost problem which machines that think can solve is automatic control over all sorts of other machines. This involves controlling a machine that is running so that it will do the right thing at the right time in response to information. For example, suppose that you are mowing a lawn with a mowing machine. You watch the preceding strip so as to stay next to it. You watch the ends of the strips, where you turn around. If a stick is caught in the cutting blade, you stop and take it out. Now it is entirely possible to put devices on the mowing machine so that all these things will be taken care of automatically. In fact, in the case of plowing a large field, a tractor-plow can be equipped with a device that guides it next to the preceding furrow. Thus, once the first furrow around the edge has been made, riderless tractors will plow a whole field and stop in the middle. For another example, take a gas furnace for heating steam to keep a house warm. Such a furnace has automatic controls, which respond to the following information whenever reported: House too warm. House not warm enough. Too much steam pressure. Not enough water in boiler. Gas flame not lit. Daytime. Nighttime. In fact, your own meaning of “warm” can be put into the control system: you set the dial on your thermostat at the temperature that “warm” is to be for you. In the future many kinds of automatic control will be common. We shall have automatic pilots for flying and landing airplanes. We shall have automatic missiles for destructive purposes, such as bombing and killing, and for constructive purposes, such as delivering mail and fast freight. An article in the magazine _Fortune_ for November 1946 described the automatic factory (see Supplement 3). This is a factory in which there would be automatic arms for holding stuff being manufactured, and automatic feed lines for supplying material just where it is needed. All this factory would be controlled by machines that handle information automatically and produce actions that respond to information. This prospect fills us with concern as well as with amazement. How shall we control these automatic machines, these robots, these Frankensteins? What will there be left for us to do to earn our living? But more of this in the next chapter. Problems of Science Other problems for which we can foresee the use of machines that think are the understanding, and later the controlling, of nature. One of these problems is weather forecasting and weather control. The Weather Brain We can imagine the following type of machine—a _weather brain_. A thousand weather observatories all over the country observe the weather at 8 A.M. The observations are fed automatically through a countrywide network of communication lines into a central station. Here a giant machine, containing a great deal of scientific knowledge about the weather, takes in all the data reported to it. At 8:15 the weather brain starts to calculate; in half an hour it has finished, having produced an excellent forecast of the weather for the whole country. Then it proceeds to transmit its forecast all over the country. By 8:50 every weather station, newspaper, radio station, and airport in the country has the details. In October 1945, Dr. V. K. Zworykin of the Princeton Laboratories of the Radio Corporation of America proposed solving the problem of weather forecasting in this way by a giant brain. The weather brain will have a second stage of application. From time to time and here and there, the weather is unstable: it can be triggered to behave in one way or another. For example, recently, pellets of _frozen carbon dioxide_—often called Dry Ice—have been dropped from planes and have caused rain. In fact, a few pounds of Dry Ice have apparently caused several hundred tons of rain or snow. In similar ways, we may, for example, turn away a hail storm so that hail will fall over a barren mountain instead of over a farming valley and thus protect crops. Or we may dispel conditions that would lead to a tornado, thus avoiding its damage. Both these examples involve local weather disturbances. However, even the greatest weather disturbances, like hurricanes and blizzards, may eventually be directed to some extent. Thus the weather may become to some degree subject to man’s control, and the weather brain will be able to tell men where and when to take action. Psychological Testing Another scientific problem to which new machinery for handling information applies is the problem of understanding human beings and their behavior. This increased understanding may lead to much wiser dealing with human behavior. For example, consider tests of aptitudes. If you take one of these tests, you may be asked to mark which word out of five suggested ones is nearest in meaning to a given word. Or your test may be 40 simple arithmetical problems to be solved in 25 minutes. Or you may be given a sheet with 20 circles, and be asked to put 3 dots in the first, 7 dots in the second, 4 dots in the third, 11 dots in the fourth, and so on, irregularly; you may be given a total of 45 seconds to do this as well as you can. Now, if a vocational counselor gives you one of these tests, and if you get 84 out of 100 on it, he needs to know just what he has measured about you. Also, he needs to know whether he can reasonably forecast that, as a result of your grade of 84, you will be good at writing articles, or good at supervising the work of other people, or good at designing in a machine shop. He needs to know the records of people with scores of about 84 on this test and to have evidence supporting his forecasts. If we wish to make the most use of the tests, we need to carry out a good deal of statistics, mathematics, and logic. For example, it will turn out that answers to some questions are much more significant than answers to others, and so we can greatly improve the quality of the tests by keeping only the more significant questions. Powerful machinery for handling calculations will be very useful in the field of aptitude testing. But, you may ask, what if the person analyzing your answers has to use interpretations and judgments? If the judgments and interpretations can be expressed in words, and if the words can be translated into machine language, then the machine can carry out the analysis. Usually the difference between a rule and a judgment is simply this: a rule in a case in which it is hard to express all the factors being considered is called a judgment. Psychological Trainer It is conceivable that machines that think can eventually be applied in the actual treatment of mental illness and maladjustment. Consider what a physician does. In treating a psychiatric case, such as a _neurosis_, a physician uses words almost entirely. He asks questions. He listens to the patient’s answers. Each answer takes the physician nearer and nearer to a diagnosis. By and by the physician knows what most of the difficulty is. Then he must present his knowledge slowly to the patient, gradually guiding the patient to understanding. It is a psychological truth that telling a man in ten minutes what is wrong with him does not cure him. The physician seeks to free the patient from the tormenting circles of habit and worry in which he has been trapped. Often the diagnosis is short and the treatment is long; the reasons for the neurosis may soon be clear to the physician, but they may take months to become clear to the patient. Now let us consider the following kind of machine as an aid to the physician. We might call this kind of machine a _psychological trainer_, for in many ways it is like the training machines used in World War II for training a pilot to fly an airplane. The psychological trainer would have the following properties: 1. The machine is able to show sound movies—produce pictures and utter words. 2. It is able to put before the patient: situations, problems, questions, experiences, etc. 3. It is able to take in responses from the patient. 4. It is able to receive a program of instructions from the physician. 5. Depending on the responses of the patient and on the program from the physician, the training machine can select more material to put before the patient. 6. The training machine produces a record of what it presented and of how the patient responded, so that the physician and the patient can study the record later. What sort of films would the machine hold? The machine could be loaded with a number of films which would help in the particular type of neurosis from which the patient was suffering. What sort of responses could the patient make? The patient might have buttons in front of him which he could press to indicate such answers as: Yes I don’t know Repeat No It depends Go ahead Also, the patient might hold a device—like a lie detector, perhaps—which would report his state of tenseness, etc., and so report what he really felt. Where would the machine’s questions come from? From one or more physicians very clever in the treatment of mental illness. Suppose that the patient is inconsistent in his answers? The machine, discovering the inconsistencies, could return to the subject and ask related questions in a different way. As soon as several questions related to the same point are answered consistently, the machine could exclude groups of questions that no longer apply and could proceed to other questions that would still apply. Patients would vary in their ability to go as fast as the machine could. So from time to time the machine would ask questions to test the effect of what it had presented; and, depending on the answers, the machine would go faster or would bring in additional material to clarify some point. This machine might have a few advantages over ordinary treatment. For example, with the machine, treatment does not depend on the physician’s making the right answer in a split second, as it may in a personal interview. Also, the patient might be franker with the machine than with the physician, for it might be arranged that the patient could review his record, and then decide whether to confess it to his physician. Such a machine would enable physicians to treat many more patients than they now can. In fact, it is estimated that nearly 50 per cent of persons who consult physicians are suffering only from mental illness. Such a machine would therefore be a great help. Problems of Business Another large group of problems for which we can foresee the use of machines that think is found in business and economics. For example, consider production scheduling in a business or a factory. The machine takes in a description of each order received by the business and a description of its relative urgency. The machine knows (that is, has in its memory) how much of each kind of raw material is needed to fill the order and what equipment and manpower are needed to produce it. The machine makes a schedule showing what particular men and what particular equipment are to be set to work to produce the order. The machine turns out the best possible production schedule, showing who should do what when, so that all the orders will be filled in the best sequence. What is the “best” sequence? We can decide what we think is the best sequence, and we can set the machine for making that kind of selection, in the same way as we decide what is “warm” and set the thermostat to produce it! On a much larger scale, we can use mechanical brains to study economic relations in a society. Everything produced in a society is made by consuming some materials, labor, equipment, and skill. The output produced by one man or factory or industry becomes the input for other men, factories, industries. In this way all economic units are linked together by many different kinds and degrees of dependence. The situation is, of course, complicated: it changes as time goes on and as people want different things produced. Economists have already set up simple models of economic societies and have studied them. But with machines that think, it will be possible to set up and study far more complicated models—models that are very much like the society we live in. We can then answer questions of economics by calculation instead of by arguments and counting noses. We shall be able to solve definitely such problems as: “How will a rise in the price of steel affect the farming industry?” “How much money must be paid out as wages and salaries so that consumer purchasing power will buy back what industry produces?” Machines and the Individual What about the ordinary everyday effects of these machines upon you and me as an individual? We can see that the new machinery will apply on a small scale even to us. Small machines using a few electronic tubes—much like a radio set, for example—and containing spools of magnetic wire or magnetic tape will doubtless be available to us. We shall be able to use them to keep addresses and telephone numbers, to figure out the income tax we should pay, to help us keep accounts and make ends meet, to remember many things we need to know, and perhaps even to give us more information. For there are a great many things that all of us could do much better if we could only apply what the wisest of us knows. We can even imagine what new machinery for handling information may some day become: a small pocket instrument that we carry around with us, talking to it whenever we need to, and either storing information in it or receiving information from it. Thus the brain with a motor will guide and advise the man just as the armor with a motor carries and protects him. Chapter 12 SOCIAL CONTROL: MACHINES THAT THINK AND HOW SOCIETY MAY CONTROL THEM It is often easier for men to create a device than to guide it well afterwards: it is often easier for a scientist to study his science than to study the results for good or evil that his discoveries may lead to. But it is not right nor proper for a scientist, a man who is loyal to truth as an ideal, to have no regard for what his discoveries may lead to. This principle is now being widely recognized. Many scientists today—both as individuals and as groups, and especially the atomic scientists—are considering the results of their scientific discoveries; and they are sharing in the effort to render those results truly useful to humanity. It would be easy to leave out of this book any discussion of how machines that think may be controlled, any consideration of how they may be made truly useful to humanity. But that would be hardly right or proper. In concluding a book such as this one, that touches on many aspects of machines that think, we need to consider what can and should be done to make such machines of true benefit to all of humanity. So, we come to the most important of all our questions: What sort of control over machines that think do we need in human society? MACHINE THAT BOTH THINKS AND ACTS From a narrow point of view, a machine that only thinks produces only information. It takes in information in one state, and it puts out information in another state. From this viewpoint, information in itself is harmless; it is just an arrangement of marks; and accordingly, a machine that thinks is harmless, and no control is necessary. Although it is true that the information produced only becomes good or evil after other machinery or human beings act on the information, in reality a machine with the power to produce information is constructed only for the reason of its use. We want to know what such machines can tell us only because we can then proceed to act much more efficiently than before. For example, a guided missile needs a mechanical brain only because then it can reach its target. In all cases mechanical brains are inseparable from their uses. For the purposes of this chapter, the narrow view will be rejected because it dodges the issue. We shall be much concerned with the combination of a machine that thinks with another machine that acts; and we shall often call this combination the _robot machine_. READING THIS CHAPTER Now, before launching further into the discussion, we need to say that the conclusions suggested in this chapter are not final. Even if they are expressed a little positively in places, they are nevertheless subject to change as more information is discovered and as the appraisal of information changes with time. Also, almost any conclusions about social control—including, certainly, the conclusions in this chapter—are subject to controversy. But controversy is good: it leads to thought. The more minds that go to work on solving the problem of social control over robot machines and other products of the new technology—which is rushing upon us from the discoveries of the scientists—the better off we all will be. If, while stimulating disagreement, the ideas expressed in this chapter should succeed in stimulating thought and deliberation, the purpose of this chapter will be well fulfilled. Up to this point in this book, the emphasis has been on possibilities of benefits to humanity that may arise from machines that think. In this chapter, devoted as it is to the subject of control, the emphasis is on possibilities for harm. Both possibilities are valid, and the happening of either depends upon the actions of men. In much the same way, atomic energy is a great possibility for benefit and for harm. It is the nature of control to put a fence around danger; and so it is natural in this chapter that the weight of attention should shift to the dangerous aspects of machines that think. Perhaps a reader may feel that a chapter of this kind is rather out of place in a book, such as this one, that seeks to be scientific. If so, he is reminded that, in accordance with the general suggestions for reading this book stated in the preface, he should omit this chapter. FRANKENSTEIN Perhaps the first study of the consequences of a machine that thinks is a prophetic novel called _Frankenstein_, written more than a hundred years ago, in 1818. The author, then only 21 years old, was Mary W. Godwin, who became the wife of the poet Percy Bysshe Shelley. According to the story, a young Swiss, an ardent student of physiology and chemistry, Victor Frankenstein, finds the secret of life. He makes an extremely ugly, clever, and powerful monster, with human desires. Frankenstein promptly flees from his laboratory and handiwork. The monster, after seeking under great hardships for a year or two to earn fair treatment among men, finds himself continually attacked and harmed on account of his ugliness, and he becomes embittered. He begins to search for his creator for either revenge or a bargain. When they meet: “I expected this reception,” said the daemon. “All men hate the wretched; how then must I be hated who am miserable beyond all living things! Yet you my creator detest and spurn me, thy creature, to whom thou art bound by ties only dissoluble by the annihilation of one of us. You purpose to kill me. How dare you sport thus with life? Do your duty towards me, and I will do mine towards you and the rest of mankind. If you will comply with my conditions, I will leave them and you at peace; but if you refuse, I will glut the maw of death, until it be satiated with the blood of your remaining friends.” Frankenstein starts to comply with the main condition, which is to make a mate for the monster; but Frankenstein cannot bring himself to do it. So the monster causes the death one after another of all Frankenstein’s family and closest friends; and the tale finally ends with the death of Frankenstein and the disappearance of the monster. As the dictionary says about Frankenstein, “The name has become a synonym for one destroyed by his own works.” ROSSUM’S UNIVERSAL ROBOTS Perhaps the next study of the consequences of a machine that thinks is a remarkable play called _R.U.R._ (for Rossum’s Universal Robots), first produced in Prague in 1921. Karel Čapek, the Czech dramatist who wrote it, was then only 31. The word “robot” comes from the Czech word “robota,” meaning compulsory service. According to the play, Rossum the elder, a scientist, discovered a “method of organizing living matter” that was “more simple, flexible, and rapid” than the method used by nature. Rossum the younger, an engineer, founded a factory for the mass production of artificial workmen, robots. They had the form of human beings, intelligence, memory, and strength; but they were without feelings. In the first act, the factory under Harry Domin, General Manager, is busy supplying robots to purchasers all over the world—for work, for fighting, for any purpose at all, to anyone who could pay for them. Domin declares: “... in ten years, Rossum’s Universal Robots will produce so much corn, so much cloth, so much everything that things will be practically without price. There will be no poverty. All work will be done by living machines. Everybody will be free from worry and liberated from the degradation of labor. Everybody will live only to perfect himself.... It’s bound to happen.” In the second act, ten years later, it turns out that Domin and the others in charge of the factory have been making some robots with additional human characteristics, such as the capacity to feel pain. The newer types of robots, however, have united all the robots against man, for the robots declare that they are “more highly developed than man, stronger, and more intelligent, and man is their parasite.” In the last act, the robots conquer and slay all men except one—an architect, Alquist, who in the epilogue provides a final quirk to the plot. FACT AND FANCY Now what is fact and what is fancy in these two warnings given to us a hundred years apart? Of course, it is very doubtful that a Frankenstein monster or a Rossum robot will soon be constructed with nerves, flesh, and blood like an animal body. But we know that many types of robot machines can even now be constructed out of hardware—wheels, motors, wires, electronic tubes, etc. They can handle many kinds of information and are able to perform many kinds of actions, and they are stronger and swifter than man. Of course, it is doubtful that the robot machines, by themselves and of their own “free will,” will be dangerous to human beings. But as soon as antisocial human beings have access to the controls over robot machines, the danger to society becomes great. We want to escape that danger. Escape from Danger A natural longing of many of us is to escape to an earlier, simpler life on this earth. Victor Frankenstein longed to undo the past. He said: “Learn from me, if not by my precepts, at least by my example, how dangerous is the acquirement of knowledge, and how much happier that man is who believes his native town to be the world, than he who aspires to become greater than his nature will allow.” Any sort of return to the past is, of course, impossible. It is doubtful that men could, even if they wanted to, stop the great flood of technical knowledge that science is now producing. We all must now face the fact that the kind of world we used to live in, even so recently as 1939, is gone. There now exist weapons and machines so powerful and dangerous in the wrong hands that in a day or two most of the people of the earth could be put to death. Giant brains are closely related to at least two of these weapons: scientists have already used mechanical brains for solving problems about atomic explosives and guided missiles. In addition, thinking mechanisms designed for the automatic control of gunfire were an important part of the winning of World War II. They will be a still more important part of the fighting of any future war. Nor can we escape to another part of the earth which the new weapons will not reach. At 300 miles an hour, any spot on earth can be reached from any other in less than 48 hours. A modern plane exceeds this speed; a rocket or guided missile doubles or trebles it. Nor can we trust that some kind of good luck will pull us through and help men to escape the consequences of what men do. Both Frankenstein and Domin reaped in full the consequences of what they did. The history of life on this earth that is recorded in the rocks is full of evidence of races of living things that have populated the earth for a time and then become extinct, such as the dinosaurs. In that long history, rarely does a race survive. In our own day, insects and fungi rather than men have shown fitness to survive and spread over the earth: witness the blight that destroyed the chestnut trees of North America, in spite of the best efforts of scientists to stop it. There seems to be no kind of escape possible. It is necessary to grapple with the problem: How can we be safe against the threat of physical harm from robot machines? UNEMPLOYMENT The other chief threat from robot machines is against our economic life. Harry Domin, in _R.U.R._, you remember, prophesied: “All work will be done by living machines.” As an example, in the magazine _Modern Industry_ for Feb. 15, 1947, appeared a picture of a machine for selling books, and under the picture were the words: _Another new product in robot salesmen_—Latest in the parade of mechanical vending machines is this book salesman.... It is designed for use in hospitals, rail terminals, and stores. It offers 15 different titles, selected manually, and obtained by dropping quarter in slot. Cabinet stores 96 books. Can you feel the breath of the robot salesman, workman, engineer,—--, on the back of your neck? At the moment when we combine automatic producing machinery and automatic controlling machinery, we get a vast saving in labor and a great increase in technological unemployment. In extreme cases, perhaps, the effect of robot machines will be the disappearance of men from a factory. Such a factory will be like a modern power plant that turns a waterfall into electricity: once the machinery is installed, only one watchman is ordinarily needed. But, in most cases, this will be the effect: in a great number of factories, mines, farms, etc., the labor force needed will be cut by a great proportion. The effect is not different in quality, because the new development is robot machinery; but the amount of technological unemployment coming from robot machines is likely to be considerably greater than previously. The robot machine raises the two questions that hang like swords over a great many of us these days. The first one is for any employee: What shall I do when a robot machine renders worthless all the skill I have spent years in developing? The second question is for any businessman: How shall I sell what I make if half the people to whom I sell lose their jobs to robot machines? SOCIAL CONTROL AND ITS TWO SIDES The two chief harmful effects upon humanity which are to be expected from robot machines are physical danger and unemployment. These are serious risks, and some degree of social control is needed to guard against them. There will also be very great advantages from robot machines. The monster in _Frankenstein_ is right when he says, “Do your duty towards me, and I will do mine towards you and the rest of mankind.” And Harry Domin in _R.U.R._ is right as to possibility when he says, “There will be no poverty.... Everybody will be free from worry.” Social control must also be concerned with how the advantages from robot machines are to be shared. The problem of social control over men and their devices has always had two sides. The first side deals with what we might plan for control if men were reasonable and tolerant. This part of the problem seems relatively easy. The other side deals with what we must ordinarily arrange, since most men are often unreasonable and prejudiced and, as a result, often act in antisocial ways. This part of the problem is hard. Let us begin with the easier side first. TYPES OF CONTROL—IF MEN WERE REASONABLE In seeking to fulfill wants and achieve safety, men have used hundreds of types of control. The main types are usually called political and economic systems, but there are always great quantities of exceptions. The more mature and freer the society, the greater the variety of types of control that can be found in it. Probably the most widely used type of control in this country is private and public control working together, as private ownership and public regulation—for example, railroads, banks, airlines, life insurance companies, telephone systems, and many others. It would be reasonable to expect private ownership and public regulation of a great many classes of robot machines, to the end that they would never threaten the safety of people. Another common type of control is public ownership and operation; examples are toll bridges, airports, city transit systems, and water-supply systems. Atomic energy was so clearly fraught with serious implications that in 1946 the Congress of the United States placed it entirely under public control expressed as the Atomic Energy Commission. There is a class of robot machinery which has already reached the stage of acute public concern: guided missiles and automatic fire-control. It would be reasonable that in this country all activity in this subdivision should be under close control by the Department of Defense. In the international arena, again, the problem becomes soluble if we assume men to be reasonable. An international agency, such as an organ of the United Nations, would take over inspection and control of robot machine activities closely affecting the public safety anywhere in the world. Particularly, this agency would concern itself with guided missiles, robot pilots for planes, automatic gunfire control, etc. Much manufacturing skill is needed to make such products as these: the factories where they could be manufactured would thereby be determined. Also, a giant brain is a useful device for solving scientific problems about weapons of mass destruction. So the agency would need to inspect the problems being solved on such machines. This agency would be responsible to a legislature or an executive body representing all the people in the world—if men were reasonable. In regard to the effects of robot machines on unemployment, again, if men were reasonable, the problem would be soluble. The problem is equivalent to the problem of abundance: how should men distribute the advantages of a vast increase in production among all the members of society in a fair and sensible way? A vast increase in production is not so impossible as it may seem. For example, in 1939, with 45 million employed, the United States index of industrial production was at 109, and, in 1943, with 52½ million employed, the index of production was at 239. If men were reasonable, the net profits from robot machinery would be divided among (1) those who had most to do with devising the new machinery, and (2) all of society. A rule would be adopted (probably it could be less complicated than some existing tax rules) which would take into account various factors such as rewards to the inventors, incentives to continue inventing, adequate assistance to those made unemployed by the robot machines, reduction of prices to benefit consumers, and contributions to basic and applied scientific research. In fact, under the assumption “if men were reasonable,” it would hardly be necessary to devote a chapter to the problem of social control over robot machines! OBSTACLES The discussion above of how robot machines could be controlled supposing that men were reasonable, seems, of course, to be glaringly impractical. Men are not reasonable on most occasions most of the time. If we stopped at this point, again we would be dodging the issue. What are the obstacles to reasonable control? There are, it seems, two big obstacles and one smaller one to reasonable types of social control over robot machines. The smaller one is ignorance, and the two big obstacles are prejudice and a narrow point of view. Ignorance By ignorance we mean lack of knowledge and information. Now mechanical brains are a new and intricate subject. A great many people will, through no fault of their own, naturally remain uninformed about mechanical brains and robot machines for a long time. However, there is a widespread thirst for knowledge these days: witness in magazines, for example, the growth of the article and the decline of the essay. There is also a fairly steady surge of knowledge from the austere scientific fountain of new technology. We can thus see both a demand and a supply for information in such fields as mechanical brains and robot machines. We can expect, therefore, a fairly steady decline in ignorance. Prejudice Prejudice is a much more serious obstacle to reasonable control over robot machines. It will be worth our while to examine it at length. Prejudice is frequent in human affairs. For example, in some countries, but not in all, there is conflict among men, based on their religious differences. Again, in other countries, but not in all, there is wide discrimination among men, based on the color of their skin. Over the whole world today, there is a sharp lack of understanding between conservatives, grading over to reactionaries, on the one hand, and liberals, grading over to radicals, on the other hand. All these differences are based on men’s attitudes, on strongly held sets of beliefs. These attitudes are not affected by “information”; the “information” is not believed. The attitudes are not subject to “judgment”; they come “before judgment”: they are prejudices. Even in the midst of all the science of today, prejudice is widespread. In Germany, from 1933 to 1939, we saw one of the most scientific of countries become one of the most prejudiced. Prejudice is often difficult to detect. We find it hard to recognize even in ourselves. For a prejudice always seems, to the person who has it, the most natural attitude in the world. As we listen to other people, we are often uncertain how to separate information, guesses, humor, prejudice, etc. Circumstances compel us to accept provisionally quantities of statements just on other people’s say-so. A good test of a statement for prejudice, however, is to compare it with the scientific view. Prejudice is most dangerous for society. Its more extreme manifestations are aggressive war, intolerance (especially of strange people and customs), violence, race hatred, etc. In the consuming hatred that a prejudiced man has towards the object of his prejudice, he is likely to destroy himself and destroy many more people besides. In former days, the handy weapon was a sword or a pistol; not too much damage could be done when one man ran amuck. But nowadays a single use of a single weapon has slain 70,000 people (the atom bomb dropped at Hiroshima), and so a great many people live anxious and afraid. What is prejudice? How does it arise? How can it be cured, and thus removed from obstructing reasonable control over robot machines and the rest of today’s amazing scientific developments? Prejudice is a disease of men’s minds. It is infectious. The cause and development of the disease are about as follows: Deprive someone of something he deeply needs, such as affection, food, or opportunity. In this way hurt him, make him resentful, hostile; but prevent him from expressing his resentments in a reasonable way, giving him instead false outlets, such as other people to hurt, myths to believe, hostile behavior patterns to imitate. He will then break out with prejudices as if they were measles. The process of curing the disease of prejudice is about as follows: Make friends with the patient; win his trust. Encourage him to pour out his half-forgotten hates. Help him to talk them over freely, by means of questions but not criticisms, until finally the patient achieves insight, sees through his former prejudices, and drops them. In these days prejudice is a cardinal problem of society. It is perhaps conservative to say that a chief present requirement for the survival of human society—with the atom bomb, bacterial warfare, guided missiles, etc., near at hand—is cure of prejudice and its consequences, irrational and unrestrained hate. Narrow Point of View A narrow point of view regarding what is desirable or good is the third obstacle to rational control over robot machines. What do we mean by this? Our point of view as a two-year-old is based on pure self-interest. If we see a toy, we grab it. There is no prejudice about this; it is entirely natural—for two-year-olds. As we grow older, our point of view concerning what is good or desirable rapidly broadens: we think of others and their advantage besides our own. For example, we may become interested in a conservation program to conserve birds, or soil, or forests, and our point of view expands, embraces these objectives, which become part of our personality and loyalties. Unfortunately, it seems to be true that the expanding point of view, the expanding loyalties, of most people as they grow up are arrested somewhere along the line of: self, family, neighborhood, community, section of country, nation. An honorable exception is the scientists’ old and fine tradition of world-wide unity and loyalty in the search for objective truth. Now the problem of rational control over robot machines and other parts of the new technology is no respecter of national boundaries. To be solved it requires a world-wide point of view, a loyalty to human society and its best interests, a social point of view. Almost all that you and I have and do and think is the result of a long history of human society on this earth. All men on the earth today are descendants of other men who lived 1000, 2000, 3000 ... years ago, whether they were Romans or Chinese or Babylonians or Mayas or members of any other race. To ride in a subway or an airplane, to talk on the telephone, to speak a language, to calculate, to survive smallpox or the black death, etc.—all these privileges are our inheritance from countless thousands of other human beings, of many countries, and nearly all of whom are now dead. During our lives we pass on to our own children an inheritance in which our own contribution is remarkably small. Since each person is the child of two others, the number of our forefathers is huge, and we are all undoubtedly blood cousins. Because of this relationship, and because we owe to the rest of society nearly all that we are, we have a social responsibility—we need to hold a social point of view. Each of us needs to accept and welcome a world-wide social responsibility, as a member of human society, as a beneficiary and trustee of our human inheritance. Otherwise we are drones, part of the hive without earning our keep. The social point of view is equitable, it is inspiring, and it is probably required now in order for human beings to survive. We need to let go of a narrow point of view. CONCLUSION We have now outlined the problem of social control over robot machines, supposing that human beings were reasonable. We have also discussed the practical obstacles that obstruct reasonable control. It is not easy to think of any yet organized group of people anywhere that would have both the strength and the vision needed to solve this problem through its own efforts. For example, a part of the United Nations might have some of the vision needed, but it does not have the power. Consequently, it is necessary and desirable for individuals and groups everywhere to take upon themselves an added load of social responsibility—just as they tend to do in time of war. People often “want to do their share.” Through encouragement and education, the basic attitude of a number of people can contain more of “This is our business; we have a responsibility for helping to solve this problem.” We also need public responsibility; we need a public body responsible for study, education, advice, and some measure of control. It might be something like an Atomic Energy Commission, Bacterial Defense Commission, Mental Health Commission, and Robot Machine Commission, all rolled into one. When, at last, there is an effective guarantee of the two elements physical safety and adequate employment, then at last we shall all be free from the threat of the robot machine. We can then welcome the robot machine as our deliverer from the long hard chores of many centuries. Supplement 1 WORDS AND IDEAS The purpose of this book is to explain machines that think, without using technical words any more than necessary. This supplement is a digression. Its purposes are to consider how to explain in this way and to discuss the attempt made in this book to achieve simple explanation. WORDS AS INSTRUMENTS FOR EXPLAINING Words are the chief instruments we use for explaining. Of course, many other devices—pictures, numbers, charts, models, etc.—are also used; but words are the prime tools. We do most of our explaining with them. Words, however, are not very good instruments. Like a stone arrow-head, a word is a clumsy weapon. In the first place, words mean different things on different occasions. The word “line,” for example, has more than fifty meanings listed in a big dictionary. How do we handle the puzzle of many meanings? As we grow older we gather experience and we develop a truly marvelous capacity to listen to a sentence and then fit the words together into a pattern that makes sense. Sometimes we notice the time lag while our brain hunts for the meaning of a word we have heard but not grasped. Then suddenly we guess the needed meaning, whereupon we grasp the meaning of the sentence as a whole in much the same way as the parts of a puzzle click into place when solved. Another trouble with words is that often there is no good way to tell someone what a word means. Of course, if the word denotes a physical object, we can show several examples of the object and utter the word each time. In fact, several good illustrations of a word denoting a physical thing often tell most of its meaning. But the rest of its meaning we often do not learn for years, if ever. For instance, two people would more likely disagree than agree about what should be called a “rock” and what should be called a “stone,” if we showed them two dozen examples. In the case of words not denoting physical objects, like “and,” “heat,” “responsibility,” we are worse off. We cannot show something and say, “That is a ···.” The usual dictionary is of some help, but it has a tendency to tell us what some word _A_ means by using another word _B_, and when we look up the other word _B_ we find the word _A_ given as its meaning. Mainly, however, to determine the meanings of words, we gather experience: we soak up words in our brains and slowly establish their meanings. We seem to use an unconscious reasoning process: we notice how words are used together in patterns, and we conclude what they must mean. Clearly, then, words being clumsy instruments, the more experience we have had with a word, the more likely we are to be able to use it, work with it, and understand it. Therefore explanation should be based chiefly on words with which we have had the most experience. What words are these? They will be the well-known words. A great many of them will be short. SET OF WORDS FOR EXPLAINING Now what is the set of all the words needed to explain simply a technical subject like machines that think? For we shall need more words than just the well-known and short ones. This question doubtless has many answers; but the answer used in this book was based on the following reasoning. In a book devoted to explanation, there will be a group of words (1) that are supposed to be known already or to be learned while reading, and (2) that are used as building blocks in later explanation and definitions. Suppose that we call these words the _words for explaining._ There are at least three groups of such words: _Group 1._ Words not specially defined that are so familiar that every reader will know all of them; for example, “is,” “much,” “tell.” _Group 2._ Words not specially defined that are familiar, but perhaps some reader may not know some of them; for example, “alternative,” “continuous,” “indicator.” _Group 3._ Words that are not familiar, that many readers are not expected to know, and that are specially defined and explained in the body of the book; for example, “abacus,” “trajectory,” “torque.” In writing this book, it was not hard to keep track of the words in the third group. These words are now listed in the index, together with the page where they are defined or explained. (The index, of course, also lists phrases that are specially defined.) But what division should be made between the other two groups? A practical, easy, and conservative way to separate most words between the first and second groups seemed to be on the basis of number of syllables. All words of one syllable—if not specially defined—were put in Group 1. Also, if a word became two syllables only because of the addition of one of the endings “-es,” “-ed,” “-ing,” it was kept in Group 1, for these endings probably do not make a word any harder to understand. In addition, there were put into Group 1: 1. Numbers; for example, “186,000”; “³/₁₀”. 2. Places: “Philadelphia”; “Massachusetts”. 3. Nations, organizations, people, etc.: “Swedish”; “Bell”. 4. Years and dates: “February”; “1946”. 5. Names of current books or articles and their authors. Of course, not all these words would be familiar to every reader (for example, “Maya”), but in the way they occur, they are usually not puzzling, for we can tell from the context just about what they must mean. All remaining words for explaining—chiefly, words of two or more syllables and not specially defined—were put in Group 2 and were listed during the writing of this book. Many Group 2 words, of course, would be entirely familiar to every reader; but the list had several virtues. No hard words would suddenly be sprung like a trap. The same word would be used for the same idea. Every word of two or more syllables was continually checked: is it needed? can it be replaced by a shorter word? It is perhaps remarkable that there were fewer than 1800 different words allowed to stay in this list. This fact should be a comfort to a reader, as it was to the author. Now there are more words in this book than _words for explaining_. So we shall do well to recognize: _Group 4._ Words that do not need to be known or learned and that are not used in later explanation and definitions. These words occur in the book in such a way that understanding them, though helpful, is not essential. One subdivision of Group 4 are names that appear just once in the book, as a kind of side remark, for example, “a chemical, called _acetylcholine_.” Such a name will also appear in the index, but it is not a _word for explaining_. Another subdivision of Group 4 are words occurring only in quotations. For example, in the quotation from _Frankenstein_ on page 198, a dozen words appear that occur nowhere else in the book, including “daemon,” “dissoluble,” “maw,” “satiate.” Clearly we would destroy the entire flavor of the quotation if we changed any of these words in any way. But only the general drift of the quotation is needed for understanding the book, and so these words are Group 4 words. In this way the effort to achieve simple explanation in this book proceeded. But even supposing that we could reach the best set of words for explaining, there is more to be done. How do we go from simple explanation to understanding? UNDERSTANDING IDEAS _Understanding_ an idea is basically a standard process. First, we find the name of the idea, a word or phrase that identifies it. Then, we collect true statements about the idea. Finally, we practice using them. The more true statements we have gathered, and the more practice we have had in applying them, the more we understand the idea. For example, do you understand zero? Here are some true statements about zero. 1. Zero is a number. 2. It is the number that counts none or nothing. 3. It is marked 0 in our usual numeral writing. 4. The ancient Romans, however, had no numeral for it. Apparently, they did not think of zero as a number. 5. 0 is what you get when you take away 17 from 17, or when you subtract any number from itself. 6. If you add 0 to 23, you get 23; and if you add 0 to any number, you get that number unchanged. 7. If you subtract 0 from 48, you get 48; and if you subtract 0 from any number, you get that number unchanged. 8. If you multiply 0 by 71, you get 0; and if you multiply together 0 and any number, you get 0. 9. Usually you are not allowed to divide by 0: that is against the rules of arithmetic. 10. But if you do, and if you divide 12 by 0, for example—and there are times when this is not wrong—the result is called _infinity_ and is marked ∞, a sign that is like an 8 on its side. This is not all the story of zero; it is one of the most important of numbers. But, if you know these statements about zero, and have had some practice in applying them, you have a good _understanding_ of zero. Incidentally, a mechanical brain knows all these statements about zero and a few more; they must be built into it. For us to understand any idea, then, we pursue three aims: 1. We find out what it is called. 2. We collect true statements about it. 3. We apply those statements—we use them in situations. We can do this about any idea. Therefore, we can understand any idea, and the degree of our understanding increases as the number of true statements mastered increases. Perhaps this seems to be a rash claim. Of course, it may take a good deal of time to collect true statements about many ideas. In fact, a scientist may spend thirty years of his life trying to find out from experiment the truth or falsehood of one statement, though, when he has succeeded, the fact can be swiftly told to others. Also, we all vary in the speed, perseverance, skill, etc., with which we can collect true statements and apply them. Besides, some of us have not been taught well and have little faith in our ability to carry out this process: this is the greatest obstacle of all. But, there is in reality no idea in the field of existing science and knowledge which you or I cannot understand. The road to understanding lies clear before us. Supplement 2 MATHEMATICS In the course of our discussion of machines that think, we have had to refer without much explanation to a number of mathematical ideas. The purpose of this supplement is to explain a few of these ideas a little more carefully than seemed easy to do in the text and, at the end of the supplement, to put down briefly some additional notes for reference. DEVICES FOR MULTIPLICATION Suppose that we have to multiply 372 by 465. With the ordinary school method, we write 465 under the 372 and proceed about as follows: 5 times 2 is 10, put down the 0 and carry the 1; 5 times 7 is 35, 35 and 1 is 36, put down the 6 and carry the 3; 5 times 3 is 15, 15 and 3 is 18, put down the 8 and carry the 1; ... The method is based mainly on a well-learned subroutine of continually changing steps: 1. Select a multiplicand digit. 2. Select a multiplier digit. 3. Refer to the multiplication table with these digits. 4. Obtain the value of their product, called a _partial product_. 5. Add the preceding carry. 6. Set down the right-hand digit. 7. Carry the left-hand digit. We can, however, simplify this subroutine for a machine by delaying the carrying. We collect in one place all the right-hand digits of partial products, collect in another place all the left-hand digits, and delay all addition until the end. For example, let us multiply 372 by 465 with this method: RIGHT-HAND LEFT-HAND USUAL METHOD, DIGITS DIGITS FOR COMPARISON 372 372 372 × 465 × 465 × 465 —————— —————— —————— 550 131 1860 822 141 2232 288 120 1488 ————— ————— —————— 37570 13541 172980 FINAL ADDITION 37570 + 13541 ———————— 172980 37570 is called the _right-hand component_ of the product. It is convenient to fill in with 0 the space at the end of 13541 and to call 135410 the _left-hand component_ of the product. This process is called _multiplying by right- and left-hand components_. It has the great advantage that no carrying is necessary to complete any line of the original multiplications. Some computing machines use this process. Built into the hardware of the machine is a multiplication table up to 9 × 9. The machine, therefore, can find automatically the right-hand digit and the left-hand digit of any partial product. In a computing machine that uses this process, all the left-hand digits are automatically added in one register, and all the right-hand digits are added in another register. The only carrying that is needed is the carrying as the right-hand digits are accumulated and as the left-hand digits are accumulated. At the end of the multiplication, one of the registers is automatically added into the other, giving the product. Another device used in computing machines for multiplying is to change the multiplier into a set of digits 0 to 5 that are either positive or negative. For example, suppose that we want to multiply 897 by 182. We note that 182 equals 200 minus 20 plus 2, and so we can write it as _ 222. The minus over the 2 marks it as a _negative digit_ 2. Then to multiply we have: 897 _ 222 ———— 1794 - 1794 1794 —————— 163254 The middle 1794 is subtracted. This process is usually called _short-cut multiplication_. Everybody discovers this trick when he decides that multiplying by 99 is too much work, that it is easier to multiply by 100 and subtract once. BINARY OR TWO NUMBERS We are well accustomed to decimal notation in which we use 10 decimal digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and write them in combinations to designate decimal numbers. In _binary notation_ we use two binary digits 0, 1 and write them in combinations to designate _binary numbers_. For example, the first 17 numbers, from 0 to 16 in the decimal notation, correspond with the following numbers in binary notation: DECIMAL BINARY DECIMAL BINARY 0 0 1 1 9 1001 2 10 10 1010 3 11 11 1011 4 100 12 1100 5 101 13 1101 6 110 14 1110 7 111 15 1111 8 1000 16 10000 In decimal notation, 101 means one times a hundred, no tens, and one. In binary notation, 101 means one times four, no twos, and one. The successive digits in a decimal number from right to left count 1, 10, 100, 1000, 10000, ...—successive _powers_ of 10 (for this term, see the end of this supplement). The successive digits in a binary number from right to left count 1, 2, 4, 8, 16, ...—powers of 2. The decimal notation is convenient when equipment for computing has ten positions, like the fingers of a man, or the positions of a counter wheel. The binary notation is convenient when equipment for computing has just two positions, like “yes” or “no,” or current flowing or no current flowing. Addition, subtraction, multiplication, and division can all be carried out unusually simply in binary notation. The addition table is simple and consists only of four entries. + 0 1 +—————— 0 | 0 1 | 1 | 1 10 The multiplication table is also simple and contains only four entries. × 0 1 +—————— 0 | 0 0 | 1 | 0 1 Suppose that we add in binary notation 101 and 1001: BINARY ADDITION CHECK 101 5 + 1001 9 —————— ——— 1110 14 We proceed: 1 and 1 is 10; write down 0 and carry 1; 0 and 0 is 0, and 1 to carry is 1; and 1 and 0 is 1; and then we just copy the last 1. To check this we can convert to decimal and see that 101 is 5, 1001 is 9, and 1110 is 14, and we can verify that 5 and 9 is 14. One of the easiest ways to subtract in binary notation is to add a _ones complement_ (that is, the analogue of the nines complement) and use end-around-carry (for these two terms, see the end of this supplement). A ones complement can be written down at sight by just putting 1 for 0 and 0 for 1. For example, suppose that we subtract 101 from 1110: SUBTRACTION BY DIRECT ADDING ONES SUBTRACTION CHECK COMPLEMENT 1110 14 1110 - 101 -5 + 1010 ————— ———— —————— 1001 9 (1)1000 ↓ ⎯→ 1 —————— 1001 Multiplication in the binary notation is simple. It amounts to (1) adding if the multiplier digit is 1 and not adding if the multiplier digit is 0, and (2) moving over or shifting. For example, let us multiply 111 by 101: BINARY MULTIPLICATION CHECK 111 7 × 101 × 5 —————— 111 111 —————— ——— 100011 35 The digit 1 in the 6th (or _n_th) _binary_ place from the right in 100011 stands for 1 times 2 to the 5th (or _n_-1 th) power, 2 × 2 × 2 × 2 × 2 = 32. The result 100011 is translated into 32 plus 2 plus 1, which equals 35 and verifies. Division in the binary notation is also simple. It amounts to (1) subtracting (yielding a quotient digit 1) or not subtracting (yielding a quotient digit 0), and (2) shifting. We never need to try multiples of the divisor to find the largest that can be subtracted yet leave a positive remainder. For example, let us divide 1010 (10 in decimal) into 10001110 (142 in decimal): 1110 (14 in decimal) —————————— 1010)10001110 1010 —————— 1111 1010 ————— 1011 1010 ————— 10 (remainder, 2 in decimal) In decimal notation, digits to the right of the decimal point count powers of ⅒. In binary notation, digits to the right of the _binary point_ count powers of ½: ½, ¼, ⅛, ¹/₁₆.... For example, 0.1011 equals ½ + ⅛ + ¹/₁₆, or ¹¹/₁₆. If we were accustomed to using binary numbers, all our arithmetic would be very simple. Furthermore, binary numbers are in many ways much better for calculating machinery than any other numbers. The main problem is converting numbers from decimal notation to binary. One method depends on storing the powers of 2 in decimal notation. The rule is: subtract successively smaller powers of 2; start with the largest that can be subtracted, and count 1 for each power that goes and 0 for each power that does not. For example, 86 in decimal becomes 1010110 in binary: 86 64 64 goes 1 ——— 22 32 does not go 0 16 16 goes 1 ——— 6 8 does not go 0 4 4 goes 1 ——— 2 2 goes 1 2 1 does not go 0 ——— 0 It is a little troublesome to remember long series of 1’s and 0’s; in fact, to write any number in binary notation takes about 3⅓ times as much space as decimal notation. For this reason we can separate binary numbers into triples beginning at the right and label each triple as follows: TRIPLE LABEL 000 0 001 1 010 2 011 3 100 4 101 5 110 6 111 7 For example, 1010110 would become 1 010 110 or 126. This notation is often called _octal notation_, because it is notation in the scale of eight. BIQUINARY OR _TWO-FIVE_ NUMBERS Another kind of notation for numbers is _biquinary notation_, so called because it uses both 2’s and 5’s. Essentially this notation is very like Roman numerals, ancient style. By ancient style we mean, for example, VIIII instead of IX. In the following table we show the first two dozen numbers in decimal, biquinary, and ancient Roman notation: DECIMAL BIQUINARY ROMAN 0 0 1 1 I 2 2 II 3 3 III 4 4 IIII 5 10 V 6 11 VI 7 12 VII 8 13 VIII 9 14 VIIII 10 100 X 11 101 XI 12 102 XII 13 103 XIII 14 104 XIIII 15 110 XV 16 111 XVI 17 112 XVII 18 113 XVIII 19 114 XVIIII 20 200 XX 21 201 XXI 22 202 XXII 23 203 XXIII The biquinary columns alternate in going from 0 to 4 and from 0 to 1. The digits from 0 to 4 are not changed. The digits from 5 to 9 are changed into 10 to 14. We see that the _biquinary digits_ are 0 to 4 in odd columns and 0, 1 in even columns, counting from the right. This is the notation actually expressed by the _abacus_. The beads of the abacus show by their positions groups of 2 and 5 (see Fig. 1). [Illustration: FIG. 1. Abacus and notations.] SOME OPERATIONS OF ALGEBRA One of the operations of algebra that is important for a mechanical brain is _approximation_, the problem of getting close to the right value of a number. Take, for example, finding _square root_ (see the end of this supplement). The ordinary process taught in school is rather troublesome. We can set down another process, however, using a desk calculator to do division, which gives us square root with great speed. Suppose that we want to find the square root of a number _N_, and suppose that we have _x_₀ as a guessed square root correct to one figure. For example, _N_ might be 67.2 and _x_₀ might be 8, chosen because 8 × 8 is 64, and 9 × 9 is 81, and it seems as if 8 should be near the square root of 67.2. Here is the process: 1. Divide _x_₀ into _N_, and obtain _N_/_x_₀. 2. Multiply _x_₀ + _N_/_x_₀ by 0.5 and call the result _x_₁. Now repeat: 1. Divide _x_₁ into _N_ and obtain _N_/_x_₁. 2. Multiply _x_₁ + _N_/_x_₁ by 0.5 and call the result _x_₂. Every time this process is repeated, the new _x_ comes a great deal closer to the correct square root. In fact it can be shown that, if _x_₀ is correct to one figure, then: APPROXIMATION IS CORRECT TO ··· FIGURES _x_₁ 2 _x_₂ 4 _x_₃ 8 _x_₄ 16 Let us see how this actually works out with 67.2 and a 10-column desk calculator. Round 1: 8 divided into 67.2 gives 8.4. One half of 8 plus 8.4 is 8.2. This is _x_₁. Round 2: 8.2 divided into 67.2 gives 8.195122. One half of 8.2 plus 8.195122 is 8.197561. This is _x_₂. Round 3: 8.197561 divided into 67.2 gives 8.197560225. One half of 8.197561 and 8.197560225 is 8.1975606125. This is _x_₃. Checking _x_₃, we find that 8.1975606125 divided into 67.2 gives 8.1975606126 approximately. In this case, then, _x_₃ is correct to more than 10 figures. In other words, with a reasonable guess and two or three divisions we can obtain all the accuracy we can ordinarily use. This process is called _rapid approximation_, or _rapidly convergent approximation_, since it _converges_ (points or comes together) very quickly to the number we are seeking. Another important operation of algebra is _interpolation_, the problem of putting values smoothly in between other values. For example, suppose that we have the table: _x y_ 5 26 6 37 7 50 8 65 9 82 Suppose that we want to find the value that _y_ (or _yₓ_) ought to have when _x_ has the value of 7.2. This is the problem of _interpolating y_ so as to find _y_ at the value of 7.2, _y_₇ˌ₂. One way of doing this is to discover the formula that expresses _y_ and then to put _x_ into that formula. This is not always easy. Another way is to take the difference between _y_₇ and _y_₈, 15, and share the difference appropriately over the distance 7 to 7.2 and 7.2 to 8. We can, for example, take ²/₁₀ of 15 = 3, add that to _y_₇ = 50, and obtain an estimated _y_₇ˌ₂ = 53. This is called _linear interpolation_, since the difference 0.2 in the value of _x_ is used only to the first power. It is a good practical way to carry out most interpolation quickly and approximately. Actually here _y_ = _x_² + 1, and so the true value of _y_₇ˌ₂ is (7.2 × 7.2) + 1, or 52.84, which is rather close to 53. Types of interpolation procedures more accurate than linear interpolation will come much nearer still to the true value. ALGEBRA OF LOGIC We turn now to the _algebra of logic_. The first half of Chapter 9, “Reasoning” (through the section “Logical-Truth Calculation by Algebra”), introduces this subject. There the terms _truth values_, _truth tables_, _logical connectives_, and _algebra of logic_ are explained. The part of Chapter 3, “A Machine That Will Think,” that discusses the operations _greater-than_ and _selection_, also explains some of the algebra of logic. It introduces, for example, the formula _p_ = _T_(_a_ > _b_) = 1, 0 This is a way of saying briefly that the truth value of the statement “_a_ is greater than _b_” equals _p_; _p_ is 1 if the statement is true and 0 if the statement is false. The truth value 1 corresponds with “yes.” The truth value 0 corresponds with “no.” With mechanical brains we are especially interested in handling mathematics and logic without any sharp dividing line between them. For example, suppose that we have a register in which a ten-digit number like 1,765,438,890 may be stored. We should be able to use that register to store a number consisting of only 1’s and 0’s, like 1,100,100,010. Such a number may designate the answers to 10 successive questions: yes, yes, no, no, yes, no, no, no, yes, no. Or it may tell 10 successive binary digits. The register then is three times as useful: it can store either decimal numbers or truth values or binary digits. We need, of course, a way to obtain from the register any desired digit. For this purpose we may have two instructions to the machine: (1) read the left-hand end digit; (2) shift the number around in a circle. The second instruction is the same as multiplying by 10 and then putting the left-most digit at the right-hand end. For example, suppose that we want the 3rd digit from the left in 1,100,100,010. The result of the first circular shift is 1,001,000,101; the result of the second circular shift is 0,010,001,011; and reading the left-most digit gives 0. A process like this has been called _extraction_ and is being built into the newest mechanical brains. Using truth values, we can put down very neatly some truths of ordinary algebra. For example: (the _absolute value_ of _a_) = _a_ × (the truth of _a_ greater than or equal to 0) - _a_ × (the truth of _a_ less than 0) ⎮_a_⎮ = _a_ · _T_(_a_ ≥ 0) - _a_ · _T_(_a_ < 0) For another example: Either _a_ is greater than _b_, or else _a_ equals _b_, or else _a_ is less than _b_ _T_(_a_ > _b_) + _T_(_a_ = _b_) + _T_(_a_ < _b_) = 1 Many common logical operations, like selecting and comparing, and the behavior of many simple mechanisms, like a light or a lock, can be expressed by truth values. Chapter 4, on punch-card mechanisms, contains a number of examples. * * * * * pronoun, variable In ordinary language, a _pronoun_, like “he,” “she,” “it,” “the former,” “the latter,” is a word that usually stands for a noun previously referred to. A pronoun usually stands for the last preceding noun that the grammar allows. In mathematics, a _variable_, like “_a_,” “_b_,” “_x_,” “_m₁_,” “_m₂_” closely resembles a pronoun in ordinary language. A variable is a symbol that usually stands for a number previously referred to, and usually it stands for the same number throughout a particular discussion. multiplicand, dividend, augend, etc. IN THE THE NAME THE NAME THE NAME EQUATION: OF _a_ IS: OF _b_ IS: OF _c_ IS: _a_ + _b_ = _c_ augend addend sum _a_ - _b_ = _c_ minuend subtrahend remainder _a_ × _b_ = _c_ multiplicand multiplier product _a_ ÷ _b_ = _c_ dividend divisor quotient _Augend_ and _addend_ are names of registers in the Harvard Mark II calculator (see Chapter 10). subtraction by adding, nines complement Two digits that add to 9 (0 and 9, 1 and 8, 2 and 7, 3 and 6, 4 and 5) are called _nines complements_ of each other. The _nines complement_ of a number _a_ is the number _b_ in which each digit of _b_ is the nines complement of the corresponding digit of _a_; for example, the nines complement of 173 is 826. Ordinary subtraction is the same as addition as of the nines complement, with a simple correction; for example, 562 less 173 (equal to 389) is the same as 562 plus 826 (equal to 1388) less 1000 plus 1. end-around-carry The correction “less 1000 plus 1” of the foregoing example may be thought of as carrying the 1 (in the result 1388) around from the left-hand end to the right-hand end, where it is there added. So the 1 is called _end-around-carry_. tens complement Two digits that add to 10 are called _tens complements_ of each other. The _tens complement_ of a number _a_, however, is equal to the nines complement of the number plus 1. For example, the tens complement of 173 is 827. When subtracting by adding a tens complement, the left-most digit 1 in the result is dropped. For example, 562 less 173 (equal to 389) is the same as 562 plus 827 (equal to 1389) less 1000. power, square, cube, reciprocal, etc. A _power_ of any number _a_ is _a_ multiplied by itself some number of times. _a_ × _a_ × _a_ ... × _a_ where _a_ appears _b_ times is written _a_ᵇ and is read _a_ to the _b_th power. _a_², a to the 2nd power, is _a_ × _a_ and is called _a squared_ or the _square_ of _a_. _a_³, _a_ to the 3rd power, _a_ × _a_ × _a_, is called _a cubed_, or the _cube_ of _a_. _a_⁰, _a_ to the zero power, is equal to 1 for every _a_. _a_¹, _a_ to the power 1, is _a_ itself. The first power is often called _linear_. _a_ to some negative power is the same as 1 divided by that power; that is, _a_⁻ᵇ = 1/_a_ᵇ. _a_⁻¹, _a_ to the power minus 1, is 1/_a_, and is called the _reciprocal_ of _a_. _a_¹ᐟ², _a_ to the one-half power, is a number _c_ such that _c_ × _c_ = _a_, and is called the _square root_ of _a_ and often denoted by √_a_. table, tabular value, argument, etc. An example of a _table_ is: 0.025 0.03 +—————————————————— 1 | 1.02500 1.03000 | 2 | 1.05063 1.06090 | 3 | 1.07689 1.09273 The numbers in the body of the table, called _tabular values_, depend on or are determined by the numbers along the edge of the table, called _arguments_. In this example, if 1, 2, 3 are choices of a number _n_, and if 0.025, 0.03 are choices of a number _i_, then each tabular value _y_ is equal to 1 plus _i_ raised to the _n_th power. _n_ and _i_ are also called _independent variables_, and _y_ is called the _dependent variable_. The table expresses a _function_ or _formula_ or _rule_. The rule could be stated as: add _i_ to 1; raise the result to the _n_th power. constant A number is said to be a _constant_ if it has the same value under all conditions. For example, in the formula: (area of a circle) = π × (radius)², π is a constant, equal to 3.14159 ..., applying equally well to all circles. infinity Mathematics recognizes several kinds of infinity. One of them occurs when numbers become very large. For example, the quotient of 12 divided by a number _x_, as _x_ becomes closer and closer to 0, becomes indefinitely large, and the limit is called _infinity_ and is denoted ∞. equation, simultaneous, linear An example of two linear simultaneous _equations_ is: 7_x_ + 8_t_ = 22 3_x_ + 5_t_ = 11 _x_ and _t_ are called _unknowns_—that is, unknown variables—because the objective of solving the equations is to find them. These equations are called _simultaneous_ because they are to be solved together, at the same time, for values of _x_ and _t_ which will fit in both equations. The equations are called _linear_ because the only powers of the unknowns that appear are the first power. Values that solve equations are said to _satisfy_ them. It is easy to solve these two equations and find that _x_ = 2 and _t_ = 1 is their solution. But it is a long process to solve 10 linear simultaneous equations in 10 unknowns, and it is almost impossible (without using a mechanical brain) to solve 100 linear simultaneous equations in 100 unknowns. derivative, integral, differential equation, etc. See the sections in Chapter 5 entitled “Differential Equations,” “Physical Problems,” and “Solving Physical Problems.” There these ideas and, to some extent, also the following ideas were explained: formula, equation, function, differential function, instantaneous rate of change, interval, inverse, integrating. See also a textbook on calculus. If _y_ is a function of _x_, then a mathematical symbol for the derivative of _y_ with respect to _x_ is _Dₓ y_, and a symbol for the integral of _y_ with respect to _x_, is ∫_y dx_. An integral with given initial conditions (see p. 83) is a _definite integral_. exponential A famous mathematical function is the _exponential_. It equals the constant _e_ raised to the _x_ power, _eˣ_, where _e_ equals 2.71828.... The exponential lies between the powers of 2 and the powers of 3. It can be computed from: _x_² _x_³ _eˣ_ = 1 + _x_ + —————— + ————————— + ... 1 · 2 1 · 2 · 3 It is a solution of the differential equation _Dₓy_ = _y_. See also a textbook on calculus. The _exponential to the base 10_ is 10ˣ. logarithm Another important mathematical function is the _logarithm_. It is written log _x_ or logₑ _x_ and can be computed from the two equations: log _uv_ = log _u_ + log _v_ _x_² _x_³ log(1 + _x_) = _x_ - —————— + —————— - ..., _x_² < 1 2 3 It is a solution of the differential equation _Dₓy_ = 1/_y_. If _y_ is the logarithm of _x_, then _x_ is the _antilogarithm_ of _y_. The _logarithm to the base 10_ of _x_, log₁₀ _x_, equals the _logarithm to the base e_ of _x_, logₑ _x_, divided by logₑ 10. See also textbooks on algebra and calculus. sine, cosine, tangent, antitangent These also are important mathematical functions. The _sine_ and _cosine_ are solutions of the differential equation _Dₓ_(_Dₓy_) =-_y_ and are written as sin _x_ and cos _x_. They can be computed from _x_³ _x_⁵ sin _x_ = _x_ - —————— + ————————— - ... 1·2·3 1·2·3·4·5 _x_² _x_₄ cos _x_ = 1 - —————— + —————— - ... 1·2 1·2·3·4 The _tangent_ of _x_ is simply sine of _x_ divided by cosine of _x_. If _y_ is the tangent of _x_, then _x_ is the _antitangent_ of _y_. See also references on trigonometry and on calculus. _Trigonometric_ tables include sine, cosine, tangent, and related functions. Bessel functions These are mathematical functions that were named after Friedrich W. Bessel, a Prussian astronomer who lived from 1784 to 1846. Bessel functions are found as some of the solutions of the differential equation _x_² _Dₓ_(_Dₓy_) + x _Dₓy_ + (_x_² - _n_²)_y_ = O This equation arises in a number of physical problems in the fields of electricity, sound, heat flow, air flow, etc. matrix A _matrix_ is a table (or _array_) of numbers in rows and columns, for which addition, multiplication, etc., with similar tables is specially defined. For example, the matrix ⎮1 2⎮ ⎮ ⎮ ⎮3 4⎮ plus the matrix ⎮5 20⎮ ⎮ ⎮ ⎮60 100⎮ equals the matrix ⎮6 22⎮ ⎮ ⎮ ⎮63 104⎮. (Can you guess the rule defining addition?) Calculations using matrices are useful in physics, engineering, psychology, statistics, etc. To add a _square matrix_ of 100 terms in an array of 10 columns and 10 rows to another such matrix, 100 ordinary additions of numbers are needed. To multiply one such matrix by another, 1000 ordinary multiplications and 900 ordinary additions are needed. See references on matrix algebra and matrix calculus. differences, smoothness, checking On p. 221, a sequence of values of _y_ is shown: 26, 37, 50, 65, 82. Suppose, however, the second value of _y_ was reported as 47 instead of 37. Then the _differences_ of _y_ as we pass down the sequence would not be 11, 13, 15, 17 (which is certainly regular or _smooth_) but 21, 3, 15, 17 (which is certainly not smooth). The second set of differences would strongly suggest a mistake in the reporting of _y_. The _smoothness_ of differences is often a useful check on a sequence of reported values. Supplement 3 REFERENCES A book like the present one can cover only a part of the subject of machines that think. To obtain more information about these machines and other topics to which they are related there are many references that may be consulted. There are still few books directly on the subject of machines that think, but there are many articles and papers, most of them rather specialized. The purpose of this supplement is to give a number of these references and to provide a brief, general introduction to some of them. The references are subdivided into groups, each dealing with a branch of the subject. The references in each group are in alphabetical order by name of author (with “anonymous” last), and under each author they are in chronological order by publication date. Some publications, especially a forum or symposium, are listed more than once, according as the topic discussed falls in different groups. In this supplement, the sign three dots ( ...) next to the page numbers for an article indicates that the article is continued on later, nonconsecutive pages. It seemed undesirable to try to make the group of references dealing with a subject absolutely complete, so long as enough were given to provide a good introduction to the subject. It proved impractical to try to make the citation of every single reference technically complete, so long as enough citation was given so that the reference could certainly be found. Furthermore, in a list of more than 250 references, errors are almost certain to occur. If any reader should send me additions or corrections, I shall be more than grateful. THE HUMAN BRAIN No one yet knows specifically how particular ideas are thought about in the human brain. The references listed in this section, however, contain some information about such topics as: The structural differences, development, and evolution of the brains of animals, apes, primitive man, and modern man. The effect on the brain of blood composition, body temperature, supply of oxygen, and other biochemical factors. The structure and physiology of the brain, the nervous system, and nerve impulses. The theory of learning, intelligence, and memory. BARCROFT, JOSEPH, _The Brain and Its Environment_, New Haven: Yale University Press, 1948, 117 pp. BEACH, FRANK A., Payday for Primates, _Natural History_, vol. 56, no. 10, Dec. 1947, pp. 448-451. BEACH, FRANK A., Can Animals Reason? _Natural History_, vol. 57, no. 3, Mar. 1948, pp. 112-116 ... BERRY, R. J. A., _Brain and Mind, or the Nervous System of Man_, New York: The Macmillan Co., 1928, 608 pp. BORING, EDWIN G., _A History of Experimental Psychology_, New York: Century Co., 1929, 699 pp. FRANZ, SHEPHERD I., _The Evolution of an Idea; How the Brain Works_, Los Angeles: University of California, 1929, 35 pp. HERRICK, C. JUDSON, _The Thinking Machine_, Chicago: University of Chicago Press, 1929, 374 pp. HERRICK, C. JUDSON, _Brains of Rats and Men_, Chicago: University of Chicago Press, 1930, 382 pp. LASHLEY, KARL S., _Brain Mechanisms and Intelligence_, Chicago: University of Chicago Press, 1929, 186 pp. PIERON, HENRI, _Thought and the Brain_, London: Kegan, Paul, Trench, Trübner & Co., 1927, 262 pp. Also New York: Harcourt, Brace & Co. SCHRÖDINGER, ERWIN, _What is Life?_, New York: The Macmillan Co., 1945, 90 pp. SHERRINGTON, CHARLES S., _The Brain and Its Mechanism_, Cambridge, England: The University Press, 1933, 35 pp. TILNEY, FREDERICK, _The Brain from Ape to Man_, New York: P. B. Hoeber, Inc., 1928, 2 vol., 1075 pp. WIENER, NORBERT, _Cybernetics, or Control and Communication in the Animal and the Machine_, New York: John Wiley & Sons, 1948, 194 pp. ANONYMOUS, Ten Billion Relays, _Time_, Feb. 14, 1949, p. 67. MATHEMATICAL BIOPHYSICS There has recently been another approach to the problem: How does a brain think? A group of men, many of them in and near Chicago, have been saying: “We know the properties of nerves, nerve impulses, and simple nerve networks. We know the activity of the brain. What mathematical model of nerve networks is necessary to account for the activity of the brain?” These men have used mathematics, statistics, and mathematical logic in the effort to attack this problem, and they support a _Bulletin of Mathematical Biophysics_. HOUSEHOLDER, ALSTON S., A Neural Mechanism for Discrimination, _Psychometrika_, vol. 4, no. 1, Dec. 1939, pp. 45-58. HOUSEHOLDER, ALSTON S., and Herbert D. Landahl, _Mathematical Biophysics of the Central Nervous System_, Bloomington, Ind.: Principia Press, 1945. LANDAHL, HERBERT D., Contributions to the Mathematical Biophysics of the Central Nervous System, _Bulletin of Mathematical Biophysics_, vol. 1, no. 2, June 1939, pp. 95-118. LANDAHL, HERBERT D., WARREN S. MCCULLOCH, and WALTER PITTS, A Statistical Consequence of the Logical Calculus of Nervous Nets, _Bulletin of Mathematical Biophysics_, vol. 5, no. 4, Dec. 1943, pp. 135-137. LANDAHL, HERBERT D., A Note on the Mathematical Biophysics of Central Excitation and Inhibition, _Bulletin of Mathematical Biophysics_, vol. 7, no. 4, Dec. 1945, pp. 219-221. LETTVIN, JEROME Y., and WALTER PITTS, A Mathematical Theory of the Affective Psychoses, _Bulletin of Mathematical Biophysics_, vol. 5, no. 4, Dec. 1943, pp. 139-148. MCCULLOCH, WARREN S., and WALTER PITTS, A Logical Calculus of the Ideas Immanent in Nervous Activity, _Bulletin of Mathematical Biophysics_, vol. 5, no. 4, Dec. 1943, pp. 115-133. RASHEVSKY, N., _Mathematical Biophysics_, Chicago: University of Chicago Press. Revised edition, 1948, 669 pp. RASHEVSKY, N., Mathematical Biophysics of Abstraction and Logical Thinking, _Bulletin of Mathematical Biophysics_, vol. 7, no. 3, Sept. 1945, pp. 133-148. RASHEVSKY, N., Some Remarks on the Boolean Algebra of Nervous Nets in Mathematical Biophysics, _Bulletin of Mathematical Biophysics_, vol. 7, no. 4, Dec. 1945, pp. 203-211. RASHEVSKY, N., A Suggestion for Another Statistical Interpretation of the Fundamental Equations of the Mathematical Biophysics of the Central Nervous System, _Bulletin of Mathematical Biophysics_, vol. 7, no. 4, Dec. 1945, pp. 223-226. RASHEVSKY, N., The Neural Mechanism of Logical Thinking, _Bulletin of Mathematical Biophysics_, vol. 8, no. 1, Mar. 1946, pp. 29-40. LANGUAGES: WORDS AND SYMBOLS FOR THINKING Hardly any field of techniques for thinking is more fascinating than language. The following list of references, of course, is short; it is meant chiefly as an introduction pointing out a number of different paths into the field of language and languages. Such topics as the following are introduced by the references in this list: The origin of languages and alphabets. The languages of the world, and speech communities. The comparison of words and structure from language to language. The significance of grammar and syntax. The problem of clear meanings. Writing and speaking that is easy to understand. BLOOMFIELD, LEONARD, _Language_, New York: Henry Holt & Co., 1933, 564 pp. BODMER, FREDERICK, and LAUNCELOT HOGBEN, _The Loom of Language_, New York: W. W. Norton & Co., 1944, 692 pp. FLESCH, RUDOLF, _The Art of Plain Talk_, New York: Harper & Brothers, 1946, 210 pp. GRAFF, WILLEM L., _Language and Languages: An Introduction to Linguistics_, New York: D. Appleton & Co., 1932, 487 pp. HAYAKAWA, S. I., _Language in Action_, New York: Harcourt, Brace & Co., 1941, 345 pp. JESPERSEN, OTTO, _The Philosophy of Grammar_, New York: Henry Holt & Co., 1929 (third printing), 359 pp. JESPERSEN, OTTO, _Analytic Syntax_, In this book, by means of a well-contrived system of letters and signs, the great linguistic scholar Jespersen depicts all the important inter-relations of English words and parts of words in connected speech. OGDEN, C. K., _The System of Basic English_, New York: Harcourt, Brace & Co., 1934, 320 pp. SCHLAUCH, MARGARET, _The Gift of Tongues_, New York: Modern Age Books, 1942, 342 pp. WALPOLE, HUGH R., _Semantics: The Nature of Words and Their Meanings_, New York: W. W. Norton & Co., 1941, 264 pp. LANGUAGES: MACHINES FOR THINKING For many years, nearly all references about machines as a language for thinking have been specialized and limited. Colleges with scholars who write textbooks usually have not had a variety of expensive and versatile computing machinery. As a result, the main environment for stimulating possible authors has until recently been missing. The list of references is accordingly brief. AIKEN, HOWARD H., and others, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Cambridge, Mass.: Harvard University Press, 1948, 302 pp. COMRIE, JOHN LESLIE, The Application of Commercial Calculating Machines to Scientific Computing, _Mathematical Tables and Other Aids to Computation_, vol. 2, no. 16, Oct. 1946, pp. 149-159. CREW, E. W., Calculating Machines, _The Engineer_, vol. 172, Dec. 1941, pp. 438-441. FRY, MACON, _Designing Computing Mechanisms_, Cleveland, Ohio: Penton Publishing Co., 1946, 48 pp. (Reprinted from _Machine Design_, Aug. 1945 through Feb. 1946.) HARTREE, D. R., _Calculating Machines: Recent and Prospective Developments and Their Impact on Mathematical Physics_, Cambridge, England: The University Press, 1947, 40 pp. HORSBURGH, E. H., _Modern Instruments and Methods of Calculation_, London: G. Bell and Sons, Ltd., 1914, 343 pp. LILLEY, S., Mathematical Machines, _Nature_, vol. 149, Apr. 25, 1942, pp. 462-465. MURRAY, FRANCIS J., _The Theory of Mathematical Machines_, New York: King’s Crown Press, 1947, 116 pp. The author states that a mathematical machine is a mechanism that provides information concerning the relationships among a specified set of mathematical concepts. TURCK, J. A. V., _The Origin of Modern Calculating Machines_, Chicago: Western Society of Engineers, 1921. Recently, however, some magazine and newspaper publishers have seen news value in machines that think, and some good general articles with appeal to a wide audience have appeared. For the references to these articles, see the section of this supplement entitled “Digital Machines—Miscellaneous.” PUNCH-CARD CALCULATING MACHINES There are a few general references on punch-card calculating machines: BAEHNE, G. WALTER, editor, and others, _Practical Applications of the Punched Card Method in Colleges and Universities_, New York: Columbia University Press, 1935, 442 pp. This is a collection of many contributions from a number of authors, describing various applications, chiefly educational. ECKERT, W. J., _Punched-Card Methods in Scientific Computation_, New York: Columbia University, The Thomas J. Watson Astronomical Computing Bureau, 1940, 136 pp. This is a scientific treatise, chiefly relating to the computation of orbits in astronomy. HARTKEMEIER, HARRY PELLE, _Principles of Punch-Card Machine Operation_ (Subtitle: _How to Operate Punch-Card Tabulating and Alphabetic Accounting Machines_), New York: Thomas Y. Crowell Co., 1942, 269 pp. This is based on the author’s experience in teaching statistical analysis using IBM tabulators. The book does not deal with the collator or multiplying punch. HEDLEY, K. J., _The Development of the Punched-Card Method_, Actuarial Society of Australasia, 1946, 20 pp. INTERNATIONAL BUSINESS MACHINES CORPORATION, _International Business Machines_ (form no. A-4036-6-45), New York: International Business Machines Corporation, 1945, 65 pp. Pages 6 to 31 show pictures and brief descriptions of about 20 punch-card machines, available in 1945. SCHNACKEL, H. G., and H. C. LANG, _Accounting by Machine Methods_, New York: Ronald Press Co., 1939, 53 pp. WOLF, ARTHUR W., and EDMUND C. BERKELEY, _Advanced Course in Punched Card Operations_, Newark, N. J.: Prudential Insurance Company of America, 1942, 98 pp. A useful and authoritative description of IBM punch-card calculating machinery is the following: INTERNATIONAL BUSINESS MACHINES CORPORATION, DEPARTMENT OF EDUCATION, _Machine Methods of Accounting_, Endicott, N. Y.: International Business Machines Corporation, 1936-41, 385 pp. This is a collection of 28 separate booklets telling the detailed operation of IBM punch-card machinery. They were written for employees of IBM and users of IBM equipment. The following list of the booklets is useful in locating them: NO. OF TITLE FORM NO. DATE PAGES Machine Methods of Accounting—Foreword AM 1936 6 Development of IBM Corporation AM-1-1 1936 14 Principles of the Electric Accounting Machine Method AM-2 1936 12 The Tabulating Card AM-3-1 1936 20 Design of Tabulating Cards AM-4-1 1936 16 Preparation and Use of Codes AM-5 1936 28 Organization and Supervision of the Tabulating Department AM-6 1936 16 Selection and Training of Key Punch Operators AM-7 1936 12 Accounting Control AM-8 1936 8 Punches AM-9 1936 12 Alphabetic Printing Punches AM-10 1936 7 Facts to Know about Key Punches AM-11 1936 4 Verifiers AM-12 1936 4 Gang Punches AM-13 1936 8 Card-Operated Sorting Machines AM-14 1936 12 Facts to Know about Sorters AM-14a 1936 4 Electric Tabulating Machines AM-15 1936 20 Electric Accounting Machines (Type 285 and Type 297) AM-16 1936 16 Alphabetic Direct Subtraction Accounting Machine AM-17 1936 28 Numerical Interpreters AM-18 1936 8 Electric Punched-Card Interpreter (Type 552) AM-18a 1941 8 Reproducing Punches (Type 512) AM-19 1936 16 Automatic Summary Punches for Use with the Numerical Accounting Machines (Type 285-297) AM-20 1936 16 Automatic Summary Punches for Use with the Alphabetic Accounting Machines (Type 405) AM-20a 1940 16 Multiplying Punches AM-21 1936 16 Application of Machines to Accounting Functions AM-22 1936 24 Other International Products AM-23-2 1936 19 The International Automatic Carriage (Type 921) AM-24 1938 15 The Department of Education of IBM has begun a second series of booklets on the principles of operation of punch-card calculating machinery: INTERNATIONAL BUSINESS MACHINES CORPORATION, DEPARTMENT OF EDUCATION, _Principles of Operation_, Endicott, N. Y.: International Business Machines Corporation, 1942 and later (except for one published in 1939). Many of the booklets in this series have good examples of machine operation and applications. Also, for the first time, letters and numbers have been used as coordinates to label the hubs on the plugboards. This series includes the following: NO. OF TITLE FORM NO. DATE PAGES CARD PUNCHES AND VERIFIERS Card-Punching and Verifying Machines 52-3176-0 1946 21 Alphabetical Verifier, Type 055 52-3295-1 1946 4 INTERPRETERS Card Interpreters, Type 550, 551, and 552 52-3178-0 1946 14 REPRODUCERS Automatic Reproducing Punch, Type 513 52-3180-0 1945 22 End Printing Reproducing Punch, Type 519 52-3292-1 1946 26 Electric Document-Originating Machine, June Type 519 52-3292-2 1948 26 COLLATORS Collator AM-25 1943 31 Collator Counting Device C.R. 9178 1942 12 CALCULATING PUNCHES Electric Multiplier, Type 601 52-3408-1 1947 47 Calculating Punch, Type 602 52-3409-0 1946 83 Calculating Punch, Type 602 52-3409-5 1947 93 Calculating Punch, Type 602-A (Preliminary Manual) 22-5489-0 1948 59 Electronic Multiplier, Type 603 52-3561-0 1946 5 Electronic Calculating Punch, Type 604 22-5279-0 1948 51 TABULATORS Accounting Machine, Type 402 and 403 (Preliminary Manual) 22-5654-0 1949 146 Alphabetical Accounting Machine, Type 404 52-3395-1 1946 96 Typical Applications, Alphabetical Accounting Machine, Type 404, with Multiple Line Printing 22-3771-1 1947 47 Alphabetical Accounting Machine, Type 405 AM 17 (1), 1943 90 Revised 1/1/43 Nov. Alphabetical Accounting Machine, Type 405 52-3179-2 1948 81 AUTOMATIC PRINTING CARRIAGES Bill Feed, Type 920 52-3184-0 1945 21 Form Feeding Device 52-3235-0 1946 11 Automatic Carriage, Type 921 52-3183-0 1945 36 Tape-Controlled Carriage (Preliminary Manual, Revised) 22-5415-1 1948 27 TEST SCORING MACHINE Test Scoring Machine 94-2333-0 1939 19 May Test Scoring Machine 32-9145-1 1946 20 Published Tests Adapted for Use with June the IBM Electric Test Scoring Machine 27-4286-9 1948 8 In addition to the new types of punch-card machines referred to in the above list, an elaborate punch-card calculating machine is described in the following reference: ECKERT, W. J., The IBM Pluggable Sequence Relay Calculator, _Mathematical Tables and Other Aids to Computation_, vol. 3, no. 23, July 1948, pp. 149-161. A description of punch-card machinery in rather a light vein is contained in: ANONYMOUS, Speaking of Pictures: New Mechanical Monsters Ease _Life’s_ Growing Pains, _Life_, Sept. 15, 1947, pp. 15-16. ANONYMOUS, _540_, Chicago: Time-Life-Fortune Magazine, Subscription Fulfillment Office, 1948, 15 pp. New types of punch-card machinery are continually coming into use. Among them are: machines that take in punch cards and make punched paper tape (such as teletype tape), and vice versa—useful for transmitting punch-card information over wires; an electric typewriter operated by punch cards—useful for preparing almanacs for sea and air navigation, etc.; a calculator programmed by punch cards, consisting of an assembly of a tabulator, an electronic calculating punch, and an auxiliary storage unit, all cabled together—useful for some types of long calculation; etc. For information about such machinery, the manufacturers may be consulted. PUNCH-CARD CALCULATING MACHINERY: APPLICATIONS There are many articles in scientific journals on applications of punch-card calculating machinery to technical problems. The fields of engineering, education, indexing, mathematics, surveying, statistics, and others are all represented in the following list of sample references: ALT, FRANZ L., Multiplication of Matrices, _Mathematical Tables and Other Aids to Computation_, vol. 2, no. 13, Jan. 1946, pp. 12-13. BAILEY, C. F., and others, Punch Cards for Indexing Scientific Data, _Science_, vol. 104, Aug. 23, 1946, p. 181. BOWER, E. C., On Subdividing Tables, _Lick Observatory Bulletin_, vol. 16, no. 455, Nov. 1933, pp. 143-144. BOWER, E. C., Systematic Subdivision of Tables, _Lick Observatory Bulletin_, vol. 17, no. 467, Apr. 1935, pp. 65-74. CLEMENCE, G. M., and PAUL HERGET, Optimum-Interval Punched-Card Tables, _Mathematical Tables and Other Aids to Computation_, vol. 1, no. 6, Apr. 1944, pp. 173-176. CULLEY, FRANK L., Use of Accounting Machines for Mass-Transformation from Geographic to Military-Grid Coordinates, Washington, D. C.: National Research Council, _American Geophysical Union Transactions of 1942_, part 2, pp. 190-197. DEMING, W. EDWARDS, and MORRIS H. HANSEN, On Some Census Aids to Sampling, _Journal of the American Statistical Association_, vol. 38, no. 225, Sept. 1943, pp. 353-357. DUNLAP, JACK W., The Computation of Means, Standard Deviations, and Correlations by the Tabulator When the Numbers Are Both Positive and Negative, _Proceedings of the Educational Research Forum_, International Business Machines Corporation, Aug. 1940, pp. 16-19. DWYER, PAUL S., The Use of Tables in the Form of Prepunched Cards, _Proceedings of the Educational Research Forum_, International Business Machines Corporation, Aug. 1940, pp. 125-127. DWYER, PAUL S., Summary of Problems in the Computation of Statistical Constants with Tabulating and Sorting Machines, _Proceedings of the Educational Research Forum_, International Business Machines Corporation, Aug. 1940, pp. 20-28. DWYER, PAUL S., and ALAN D. MEACHAM, The Preparation of Correlation Tables on a Tabulator Equipped with Digit Selection, _Journal of the American Statistical Association_, vol. 32, 1937, pp. 654-662. DYER, H. S., Making Test Score Data Effective in the Admission and Course Placement of Harvard Freshmen, _Proceedings of the Research Forum_, International Business Machines Corporation, 1946, pp. 55-62. ECKERT, W. J., and RALPH F. HAUPT, The Printing of Mathematical Tables, _Mathematical Tables and Other Aids to Computation_, vol. 2, no. 17, Jan. 1947, pp. 196-202. FEINSTEIN, LILLIAN, and MARTIN SCHWARZCHILD, Automatic Integration of Linear Second-Order Differential Equations by Means of Punched-Card Machines, _Review of Scientific Instruments_, vol. 12, no. 8, Aug. 1941, pp. 405-408. HOTELLING, HAROLD, Some New Methods in Matrix Calculation, _The Annals of Mathematical Statistics_, vol. 14, no. 1, Mar. 1943, pp. 1-34. INTERNATIONAL BUSINESS MACHINES CORPORATION, editor, and others, _Proceedings of the Educational Research Forum_, Endicott, N. Y.: International Business Machines Corporation, 1941. INTERNATIONAL BUSINESS MACHINES CORPORATION, editor, and others, _Proceedings of the Research Forum_, Endicott, N. Y.: International Business Machines Corporation, 1946, 94 pp. KING, GILBERT W., Punched-Card Tables of the Exponential Function, _Review of Scientific Instruments_, vol. 15, no. 12, Dec. 1944, pp. 349-350. KING, GILBERT W., and GEORGE B. THOMAS, Preparation of Punched-Card Tables of Logarithms, _Review of Scientific Instruments_, vol. 15, no. 12, Dec. 1944, p. 350. KORMES, MARK, A Note on the Integration of Linear Second-Order Differential Equations by Means of Punched Cards, _Review of Scientific Instruments_, vol. 14, no. 4, Apr. 1943, p. 118. KORMES, MARK, Numerical Solution of the Boundary Value Problem for the Potential Equation by Means of Punched Cards, _Review of Scientific Instruments_, vol. 14, no. 8, Aug. 1943, pp. 248-250. KORMES, MARK, and JENNIE P. KORMES, Numerical Solution of Initial Value Problems by Means of Punched-Card Machines, _Review of Scientific Instruments_, vol. 16, no. 1, Jan. 1945, pp. 7-9. KUDER, G. FREDERIC, Use of the IBM Scoring Machine for Rapid Computation of Tables of Intercorrelations, _Journal of Applied Psychology_, vol. 22, no. 6, Dec. 1938, pp. 587-596. MAXFIELD, D. K., Library Punched Card Procedures, _Library Journal_, vol. 71, no. 12, June 15, 1946, pp. 902-905 ... MCLAUGHLIN, KATHLEEN, Adding Machines Nip AEF Epidemics, New York: _New York Times_, Apr. 27, 1945. MCPHERSON, JOHN C., On Mechanical Tabulation of Polynomials, _Annals of Mathematical Statistics_, Sept. 1941, pp. 317-327. MCPHERSON, JOHN C., Mathematical Operations with Punched Cards, _Journal of the American Statistical Association_, vol. 37, June 1942, pp. 275-281. MILLIMAN, WENDELL A., Mechanical Multiplication by the Use of Tabulating Machines, _Transactions of the Actuarial Society of America_, vol. 35, part 2, Oct. 1934, pp. 253-264; for discussion see also vol. 36, part 1, May 1935, pp. 77-84. ROYER, ELMER B., A Machine Method for Computing the Biserial Correlation Coefficient in Item Validation, _Psychometrika_, vol. 6, no. 1, Feb. 1941, pp. 55-59. WHITTEN, C. A., Triangulation Adjustment by International Business Machines, Washington, D. C.: National Research Council, _American Geophysical Union Transactions of 1943_, part 1, p. 31. The following bibliography may be obtained on request to the Watson Scientific Computing Laboratory, Columbia University, 612 West 116 Street, New York 27, N. Y.: WATSON SCIENTIFIC COMPUTING LABORATORY, _Bibliography: The Use of IBM Machines in Scientific Research, Statistics, and Education_, New York: International Business Machines Corporation (form no. 50-3813-0), Sept. 1947, 25 pp. The organization and equipment of this laboratory are described in: ECKERT, W. J., Facilities of the Watson Scientific Computing Laboratory, _Proceedings of the Research Forum_, International Business Machines Corporation, 1946, pp. 75-80. THE DIFFERENTIAL ANALYZER The basic scientific articles on the two differential analyzers at Massachusetts Institute of Technology are: BUSH, VANNEVAR, The Differential Analyzer: A New Machine for Solving Differential Equations, _Journal of the Franklin Institute_, vol. 212, no. 4, Oct. 1931, pp. 447-488. BUSH, VANNEVAR, and SAMUEL H. CALDWELL, A New Type of Differential Analyzer, _Journal of the Franklin Institute_, vol. 240, no. 4, Oct. 1945, pp. 255-326. Some of the less technical articles about the second differential analyzer at M.I.T. are: CALDWELL, SAMUEL H., Educated Machinery, _Technology Review_, vol. 48, no. 1, Nov. 1945, pp. 31-34. GENET, N., 100-Ton Brain at M.I.T., _Scholastic_, vol. 48, Feb. 4, 1946, p. 36. ANONYMOUS, Mathematical Machine; New Electronic Differential Analyzer, _Science News Letter_, vol. 48, Nov. 10, 1945, p. 291. ANONYMOUS, Robot Einstein: Differential Analyzer at M.I.T., _Newsweek_, vol. 26, Nov. 12, 1945, p. 93. ANONYMOUS, M.I.T.’s 100-Ton Mathematical Brain is Now to Tackle Problems of Peace, _Popular Science_, vol. 148, Jan. 1946, p. 81. ANONYMOUS, The Great Electro-Mechanical Brain; M.I.T.’s Differential Analyzer, _Life_, vol. 20, Jan. 14, 1946, pp. 73-74 ... ANONYMOUS, All the Answers at Your Fingertips; in the Laboratory of M.I.T., _Popular Mechanics_, vol. 85, Mar. 1946, pp. 164-167 ... A differential analyzer was built at the Moore School of Electrical Engineering: TRAVIS, IRVEN, Differential Analyzer Eliminates Brain Fag, _Machine Design_, July 1935, pp. 15-18. A differential analyzer was built at the General Electric Company, Schenectady, N. Y. Instead of using a mechanical or electrical amplifier of the motion of the little turning wheel riding on the disc, this machine follows the motion using polarized light. This machine is described in: BERRY, T. M., Polarized Light Servo System, _Transactions of the American Institute of Electrical Engineers_, vol. 63, Apr. 1944, pp. 195-197. KUEHNI, H. P., and H. A. PETERSON, A New Differential Analyzer, _Transactions of the American Institute of Electrical Engineers_, vol. 63, May 1944, pp. 221-227. A differential analyzer has been put into use at the University of California: BOELTER, L. M. K., and others, _The Differential Analyzer of the University of California_, Los Angeles: University of California, 1947, 25 pp. A differential analyzer was built at Manchester University, England. It was built first from “Meccano” parts, at a total cost of about 20 pounds, and later refined for more exact work. Some articles dealing with this differential analyzer are: HARTREE, D. R., The Differential Analyzer, _Nature_, vol. 135, June 8, 1935, p. 940. HARTREE, D. R., The Mechanical Integration of Differential Equations, _The Mathematical Gazette_, vol. 22, 1938, pp. 342-364. HARTREE, D. R., and A. PORTER, The Construction of a Model Differential Analyser, _Memoirs and Proceedings of the Manchester Literary and Philosophical Society_, vol. 79, July 1935, pp. 51-72. Other small scale differential analyzers built in England are covered in: BEARD, R. E., The Construction of a Small Scale Differential Analyser and Its Application to the Calculation of Actuarial Functions, _Journal of the Institute of Actuaries_, vol. 71, 1942, pp. 193-227. MASSEY, H. S. W., J. WYLIE, and R. A. BUCKINGHAM, A Small Scale Differential Analyser: Its Construction and Operation, _Proceedings of the Royal Irish Academy_, vol. 45, 1938, pp. 1-21. A differential analyzer constructed in Germany is briefly described in the following: SAUER, R., and H. POESCH, Integrating Machine for Solving Ordinary Differential Equations, _Engineers Digest_ (American Edition), vol. 1, May 1944, pp. 326-328. From the historical point of view there are some interesting papers on a machine for solving differential equations by Sir William Thomson (Lord Kelvin), including one by his brother James Thomson. They are in the _Proceedings of the Royal Society_, vol. 24, Feb. 1876, pp. 262-275. The method of integration by a machine is described, but the state of machine tools at the time was such that no accurate mechanism was constructed. Another interesting paper foreshadowing the differential analyzer is: WAINWRIGHT, LAWRENCE L., _A Ballistic Engine_, Chicago: University of Chicago, thesis for Master’s Degree, 1923, 28 pp. Some of the applications and mathematical limitations of differential analyzers are covered in: BUSH, V., and S. H. CALDWELL, Thomas-Fermi Equation Solution by the Differential Analyzer, _Physical Review_, vol. 38, no. 10, 1931, pp. 1898-1902. HARTREE, D. R., A Great Calculating Machine: the Bush Differential Analyser and Its Applications in Science and Industry, _Proceedings of the Royal Institution of Great Britain_, vol. 31, 1940, pp. 151-170. HARTREE, D. R., and A. PORTER, The Application of the Differential Analyser to Transients on a Distortionless Transmission Line, _Journal of the Institute of Electrical Engineering_, vol. 83, no. 503, Nov. 1938, pp. 648-656. HARTREE, D. R., and J. R. WOMERSLEY, A Method for the Numerical or Mechanical Solution of Certain Types of Partial Differential Equations, _Proceedings of the Royal Society of London_, series A, vol. 161, 1937, pp. 353-366. MAGINNISS, F. J., Differential Analyzer Applications, _General Electric Review_, vol. 48, no. 5, May 1945, pp. 54-59. SHANNON, CLAUDE E., Mathematical Theory of the Differential Analyzer, _Journal of Mathematics and Physics_, Cambridge, Mass.: Massachusetts Institute of Technology, vol. 20, no. 4, 1941, pp. 337-354. HARMONIC ANALYZERS AND SYNTHESIZERS Another branch of the analogue calculating machine is the harmonic analyzer and synthesizer. These are machines that study wave motions and related physical and mathematical functions. A brief list of articles on this type of machine follows: ARCHER, R. M., Projecting Apparatus for Compounding Harmonic Vibrations, _Journal of Scientific Instruments_, vol. 14, 1937, pp. 408-410. BROWN, S. L., A Mechanical Harmonic Synthesizer-Analyzer, _Journal of the Franklin Institute_, vol. 228, 1939, pp. 675-694. BROWN, S. L., and L. L. WHEELER, A Mechanical Method for Graphical Solution of Polynomials, _Journal of the Franklin Institute_, vol. 231, 1941, pp. 223-243. BROWN, S. L., and L. L. WHEELER, Use of the Mechanical Multiharmonograph for Graphing Types of Functions and for Solution of Pairs of Non-Linear Simultaneous Equations, _Review of Scientific Instruments_, vol. 13, Nov. 1942, pp. 493-495. BROWN, S. L., and L. L. WHEELER, The Use of a Mechanical Synthesizer to Solve Trigonometric and Certain Types of Transcendental Equations, and for the Double Summations Involved in Patterson Contours, _Journal of Applied Physics_, vol. 14, Jan. 1943, pp. 30-36. FÜRTH, R., and R. W. PRINGLE, A New Photo-Electric Method for Fourier Synthesis and Analysis, _London, Edinburgh and Dublin Philosophical Magazine and Journal of Science_, vol. 35, series 7, 1944, pp. 643-656. INTERNATIONAL HYDROGRAPHIC BUREAU, _Tide Predicting Machines_, International Hydrographic Bureau, Special Publication 13, July 1926. KRANZ, FREDERICK W., A Mechanical Synthesizer and Analyzer, _Journal of the Franklin Institute_, vol. 204, 1927, pp. 245-262. MARBLE, F. G., An Automatic Vibration Analyzer, _Bell Laboratories Record_, vol. 22, Apr. 1944, pp. 376-380. MAXWELL, L. R., An Electrical Method for Compounding Sine Functions, _Review of Scientific Instruments_, vol. 11, Feb. 1940, pp. 47-54. MILLER, DAYTON C., A 32-Element Harmonic Synthesizer, _Journal of the Franklin Institute_, vol. 181, 1916, pp. 51-81. MILLER, DAYTON C., The Henrici Harmonic Analyzer and Devices for Extending and Facilitating Its Use, _Journal of the Franklin Institute_, vol. 182, 1916, pp. 285-322. MILNE, J. R., A “Duplex” Form of Harmonic Synthetiser and Its Mathematical Theory, _Proceedings of the Royal Society of Edinburgh_, vol. 39, 1918-19, pp. 234-242. MONTGOMERY, H. C., An Optical Harmonic Analyzer, _Bell System Technical Journal_, vol. 17, no. 3, July 1938, pp. 406-415. RAYMOND, W. J., An Harmonic Synthesizer Having Components of Incommensurable Period and Any Desired Decrement, _Physical Review_, vol. 11, series 2, 1918, pp. 479-481. ROBERTSON, J. M., A Simple Harmonic Continuous Calculating Machine, _London, Edinburgh and Dublin Philosophical Magazine and Journal of Science_, vol. 13, 1932, pp. 413-419. SOMERVILLE, J. M., Harmonic Synthesizer for Demonstrating and Studying Complex Wave Forms, _Journal of Scientific Instruments_, vol. 21, Oct. 1944, pp. 174-177. STRAITON, A. W., and G. K. TERHUNE, Harmonic Analysis by Photographic Method, _Journal of Applied Physics_, vol. 14, 1943, pp. 535-536. WEGEL, R. L., and C. R. MOORE, An Electrical Frequency Analyzer, _Bell System Technical Journal_, vol. 3, 1924, pp. 299-323. NETWORK ANALYZERS A third branch of the analogue calculating machine is the network analyzer. To solve problems, this machine uses the laws governing a network of electrical circuits. For example, an electric power company with a system of power lines over hundreds of miles may have a problem about electrical power: will an accident or a sudden demand cause a breakdown anywhere in the system? In the General Electric Company in Schenectady, N. Y., there is a machine called the A.C. Network Analyzer. All the properties of the power company’s network of lines can be fed on a small scale into the analyzer. Certain dials are turned and certain plugwires are connected. Then various kinds of “accidents” and “sudden demands” are fed into the machine, and the response of the system is noted. The answers given by the machine are multiplied by the proper scale factor, and in this way the problem of the power company is solved. There are two kinds of problems that network analyzers are built to solve: the steady state conditions and the transient conditions. For example, you may not overload a fuse with an electric iron when it is plugged in and being used, but as you pull out the cord, you may blow the fuse: the steady state does not overstrain the system, but the transient does. Some articles on network analyzers are: ENNS, W. E., A New Simple Calculator of Load Flow in A.C. Networks, _Transactions of the American Institute of Electrical Engineers_, vol. 62, 1943, pp. 786-790. HAZEN, H. L., and others, _The M.I.T. Network Analyzer_, Cambridge, Mass.: Massachusetts Institute of Technology, Department of Electrical Engineering, Serial No. 69, Apr. 1931. KUEHNI, H. P., and R. G. LORRAINE, A New A.C. Network Analyzer, _Transactions of the American Institute of Electrical Engineers_, vol. 57, 1938, pp. 67-73. PARKER, W. W., Dual A.C. Network Calculator, _Electrical Engineering_, May 1945, pp. 182-183. PARKER, W. W., The Modern A.C. Network Calculator, _Transactions of the American Institute of Electrical Engineers_, vol. 60, Nov. 1941, pp. 977-982. PETERSON, H. A., An Electric Circuit Transient Analyzer, _General Electric Review_, Sept. 1939, pp. 394-400. VARNEY, R. N., An All-Electric Integrator for Solving Differential Equations, _Review of Scientific Instruments_, vol. 13, Jan. 1942, pp. 10-16. Some of the articles on applications of network analyzers to various problems are: KRON, GABRIEL, Equivalent Circuits of the Elastic Field, _Journal of Applied Mechanics_, vol. A11, Sept. 1944, pp. 146-161. KRON, GABRIEL, Tensorial Analysis and Equivalent Circuits of Elastic Structures, _Journal of the Franklin Institute_, vol. 238, Dec. 1944, pp. 399-442. KRON, GABRIEL, Numerical Solution of Ordinary and Partial Differential Equations by Means of Equivalent Circuits, _Journal of Applied Physics_, vol. 16, 1945, pp. 172-186. KRON, GABRIEL, Electric Circuit Models for the Vibration Spectrum of Polyatomic Molecules, _Journal of Chemical Physics_, vol. 14, no. 1, Jan. 1946, pp. 19-31. KRON, G., and G. K. CARTER, A.C. Network Analyzer Study of the Schrödinger Equation, _Physical Review_, vol. 67, 1945, pp. 44-49. KRON, G., and G. K. CARTER, Network Analyzer Tests of Equivalent Circuits of Vibrating Polyatomic Molecules, _Journal of Chemical Physics_, vol. 14, no. 1, Jan. 1946, pp. 32-34. PETERSON, H. A., and C. CONCORDIA, Analyzers for Use in Engineering and Scientific Problems, _General Electric Review_, vol. 48, no. 9, Sept. 1945, pp. 29-37. MACHINES FOR SOLVING ALGEBRAIC EQUATIONS Another branch of the analogue calculating machine is a type of machine that will solve various kinds of algebraic equations (see Supplement 2). A list of some articles follows. The article by Mallock describes a machine for solving up to 10 linear simultaneous equations in 10 unknowns, and the article by Wilbur, a machine for solving up to 9. DIETZOLD, ROBERT L., The Isograph—A Mechanical Root-Finder, _Bell Laboratories Record_, vol. 16, no. 4, Dec. 1937, pp. 130-134. DUNCAN, W. J., Some Devices for the Solution of Large Sets of Simultaneous Linear Equations, _London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science_, vol. 35, series 7, 1944, pp. 660-670. FRAME, J. SUTHERLAND, Machines for Solving Algebraic Equations, _Mathematical Tables and Other Aids to Computation_, vol. 1, no. 9, Jan. 1945, pp. 337-353. HART, H. C., and IRVEN TRAVIS, Mechanical Solution of Algebraic Equations, _Journal of the Franklin Institute_, vol. 225, Jan. 1938, pp. 63-72. HERR, D. L., and R. S. GRAHAM, An Electrical Algebraic Equation Solver, _Review of Scientific Instruments_, vol. 9, Oct. 1938, pp. 310-315. MALLOCK, R. R. M., An Electrical Calculating Machine, _Proceedings of the Royal Society_, series A, vol. 140, 1933, pp. 457-483. MERCNER, R. O., The Mechanism of the Isograph, _Bell Laboratories Record_, vol. 16, no. 4, Dec. 1937, pp. 135-140. STIBITZ, GEORGE R., Electric Root-finder, _Mathematical Tables and Other Aids to Computation_, vol. 3, no. 24, Oct. 1948, pp. 328-329. WILBUR, J. B., The Mechanical Solution of Simultaneous Equations, _Journal of the Franklin Institute_, vol. 222, Dec. 1936, pp. 715-724. ANALOGUE MACHINES—MISCELLANEOUS Some articles referring to various other kinds of analogue machines and their applications are here listed together: BUSH, V., F. D. GAGE, and R. R. STEWART, A Continuous Integraph, _Journal of the Franklin Institute_, vol. 203, 1927, pp. 63-84. GRAY, T. S., A Photo-Electric Integraph, _Journal of the Franklin Institute_, vol. 212, 1931, pp. 77-102. HAZEN, H. L., G. S. BROWN, and W. R. HEDEMAN, The Cinema Integraph: A Machine for Evaluating a Parametric Product Integral (two parts and appendix), _Journal of the Franklin Institute_, vol. 230, July 1940, pp. 19-44, and Aug. 1940, pp. 183-205. MCCANN, G. D., and H. E. CRINER, Mechanical Problems Solved Electrically, _Westinghouse Engineer_, vol. 6, no. 2, March 1946, pp. 49-56. MYERS, D. M., An Integraph for the Solution of Differential Equations of the Second-Order, _Journal of Scientific Instruments_, vol. 16, 1939, pp. 209-222. PEKERIS, C. L., and W. T. WHITE, Differentiation with the Cinema Integraph, _Journal of the Franklin Institute_, vol. 234, July 1942, pp. 17-29. SMITH, C. E., and E. L. GOVE, An Electromechanical Calculator for Directional-Antenna Patterns, _Transactions of the American Institute of Electrical Engineers_, vol. 62, 1943, pp. 78-82. YAVNE, R. O., High Accuracy Contour Cams, _Product Engineering_, vol. 19, part 2, Aug. 1948, 3 pp. ANONYMOUS, Electrical Gun Director Demonstrated, _Bell Laboratories Record_, vol. 22, no. 4, Dec. 1943, pp. 157-167. ANONYMOUS, Development of the Electric Director, _Bell Laboratories Record_, vol. 22, no. 5, Jan. 1944, pp. 225-230. ANONYMOUS, Old Field Fortune Teller: Electronic Oil Pool Analyzer, _Popular Mechanics_, vol. 86, Sept. 1946, p. 154. HARVARD IBM AUTOMATIC SEQUENCE-CONTROLLED CALCULATOR The basic scientific description of this machine as of September 1, 1945, is contained in: AIKEN, HOWARD H., and STAFF OF THE COMPUTATION LABORATORY, _A Manual of Operation for the Automatic Sequence-Controlled Calculator_, Cambridge, Mass.: Harvard University Press, 1946, 561 pp. The machine has changed rather a good deal since Sept. 1, 1945. Some circuits have been removed. Other circuits have been added. The capacity of the machine to do problems has been greatly increased. The Computation Laboratory at Harvard University is cordial towards scientific inquiries, and some unpublished, mimeographed information is available at the laboratory regarding the details of these changes. Some shorter scientific and technical descriptions of the machine are contained in: AIKEN, HOWARD H., and GRACE M. HOPPER, The Automatic Sequence Controlled Calculator (3 parts), _Electrical Engineering_, vol. 65, nos. 8, 9, and 10, Aug. to Nov. 1946, p. 384 ... (21 pp.). BLOCH, RICHARD M., Mark I Calculator, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Harvard University Press, 1948, pp. 23-30. HARRISON, JOSEPH O., JR., The Preparation of Problems for the Mark I Calculator, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Harvard University Press, 1948, pp. 208-210. INTERNATIONAL BUSINESS MACHINES CORPORATION, _IBM Automatic Sequence-Controlled Calculator_, Endicott, N. Y.: International Business Machines Corporation, 1945, 6 pp. Some of the less technical articles regarding the machine are: GENET, N., Got a Problem? Harvard’s Amazing New Mathematical Robot, _Scholastic_, vol. 45, Sept. 18, 1944, p. 35. TORREY, V., Robot Mathematician Knows All the Answers, _Popular Science_, vol. 145, Oct. 1944, pp. 86-89.... ANONYMOUS, Giant New Calculator, _Science News Letter_, vol. 46, Aug. 12, 1944, p. 111. ANONYMOUS, Mathematical Robot Presented to Harvard, _Time_, vol. 44, Aug. 14, 1944, p. 72. ANONYMOUS, World’s Greatest Machine for Automatic Calculation, _Science News Letter_, vol. 46, Aug. 19, 1944, p. 123. ANONYMOUS, Superbrain, _Nation’s Business_, vol. 32, Sept. 1944, p. 8. ANONYMOUS, Robot Works Problems Never Before Solved, _Popular Mechanics_, vol. 82, Oct. 1944, p. 13. ENIAC, THE ELECTRONIC NUMERIC INTEGRATOR AND CALCULATOR There is as yet no full-scale, published scientific account of the Eniac. At the Ballistic Research Laboratories, Aberdeen, Md., where the machine now is, there are a few copies of some long mimeographed reports on the machine and the way it works. These were prepared by H. H. Goldstine and others when at the Moore School of Electrical Engineering, as a part of the contract under which the machine was constructed for the U. S. Government. It is possible that these reports might be consulted on request by serious students. Some scientific descriptions of the machine and its properties are: BURKS, ARTHUR W., Electronic Computing Circuits of the ENIAC, _Proceedings of the Institute of Radio Engineers_, vol. 35, no. 8, Aug. 1947, pp. 756-767. CLIPPINGER, R. F., _A Logical Coding System Applied to the Eniac_, B. R. L. Report No. 673, Aberdeen, Md.: Ballistic Research Laboratories, Sept. 29, 1948, 41 pp. ECKERT, J. PRESPER, JR., JOHN W. MAUCHLY, HERMAN H. GOLDSTINE, and J. G. BRAINERD, Description of the ENIAC and Comments on Electronic Digital Computing Machines, Applied Mathematics Panel Report 171.2R, Washington, D. C.: National Defense Research Committee, Nov. 1945, 78 pp. GOLDSTINE, HERMAN H., and ADELE GOLDSTINE, The Electronic Numerical Integrator and Computer (ENIAC), _Mathematical Tables and Other Aids to Computation_, vol. 2, no. 15, July 1946, pp. 97-110. HARTREE, D. R., The ENIAC, an Electronic Computing Machine, _Nature_, vol. 158, Oct. 12, 1946, pp. 500-506. HARTREE, D. R., _Calculating Machines: Recent and Prospective Developments and Their Impact on Mathematical Physics_, Cambridge, England: The University Press, 1947, 40 pp. (Pages 14 to 27 are devoted to the Eniac.) TABOR, LEWIS P., Brief Description and Operating Characteristics of the ENIAC, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Harvard University Press, 1948, pp. 31-39. Some of the less technical articles on Eniac are: ROSE, A., Lightning Strikes Mathematics: ENIAC, _Popular Science_, vol. 148, Apr. 1946, pp. 83-86. ANONYMOUS, Robot Calculator: ENIAC, All Electronic Device, _Business Week_, Feb. 16, 1946, p. 50 ... ANONYMOUS, Answers by ENY: Electronic Numerical Integrator and Computer, ENIAC, _Newsweek_, vol. 27, Feb. 18, 1946, p. 76. ANONYMOUS, Adds in ¹/₅₀₀₀ Second: Electronic Computing Machine at the University of Pennsylvania, _Science News Letter_, vol. 49, Feb. 23, 1946, p. 113 ... ANONYMOUS, ENIAC: at the University of Pennsylvania, _Time_, vol. 47, Feb. 25, 1946, p. 90. ANONYMOUS, It Thinks with Electrons; the ENIAC, _Popular Mechanics_, vol. 85, June 1946, p. 139. ANONYMOUS, Electronic Calculator: ENIAC, _Scientific American_, vol. 174, June 1946, p. 248. BELL LABORATORIES RELAY COMPUTERS As yet no full-scale scientific report is available on the Bell Laboratories general-purpose relay computers that went to Aberdeen and Langley Field. However, there is some information about these and other Bell Laboratories relay computing machines in the following articles: ALT, FRANZ L., A Bell Telephone Laboratories’ Computing Machine (two parts), _Mathematical Tables and Other Aids to Computation_, vol. 3, no. 21, Jan. 1948, pp. 1-13, and vol. 3, no. 22, Apr. 1948, pp. 69-84. CESAREO, O., The Relay Interpolator, _Bell Laboratories Record_, vol. 24, no. 12, Dec. 1946, pp. 457-460. JULEY, JOSEPH, The Ballistic Computer, _Bell Laboratories Record_, vol. 25, no. 1, Jan. 1947, pp. 5-9. WILLIAMS, SAMUEL B., A Relay Computer for General Application, _Bell Laboratories Record_, vol. 25, no. 2, Feb. 1947, pp. 49-54. WILLIAMS, SAMUEL B., Bell Telephone Laboratories’ Relay Computing System, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Harvard University Press, 1948, pp. 40-68. ANONYMOUS, Complex Computer Demonstrated, _Bell Laboratories Record_, vol. 19, no. 2, Oct. 1940, pp. v-vi. ANONYMOUS, _Computer Mark 22 Mod. 0: Development and Description_, Navord Report No. 178-45, Washington, D. C.: Navy Department, Dec. 6, 1945, 225 pp. ANONYMOUS, Relay Computer for the Army, _Bell Laboratories Record_, vol. 26, no. 5, May 1948, pp. 208-209. THE KALIN-BURKHART LOGICAL-TRUTH CALCULATOR As yet there are no published references on the Kalin-Burkhart Logical-Truth Calculator. Some books covering a good deal of mathematical logic are: QUINE, W. V., _Mathematical Logic_, New York: W. W. Norton & Co., 1940, 348 pp. REICHENBACH, HANS, _Elements of Symbolic Logic_, New York: The Macmillan Co., 1947, 444 pp. TARSKI, ALFRED, _Introduction to Logic_, New York: Oxford University Press, 1941, 239 pp. WOODGER, J. H., _The Axiomatic Method in Biology_, Cambridge, England: The University Press, 1937, 174 pp. Chapter 2, pp. 18-52, is an excellent and understandable summary of the concepts of mathematical logic. Several papers on the application of mathematical logic to the analysis of practical situations are: BERKELEY, EDMUND C., Boolean Algebra (The Technique for Manipulating “And,” “Or,” “Not,” and Conditions) and Applications to Insurance, _Record of the American Institute of Actuaries_, vol. 26, Oct. 1937, pp. 373-414. BERKELEY, EDMUND C., Conditions Affecting the Application of Symbolic Logic, _Journal of Symbolic Logic_, vol. 7, no. 4, Dec. 1942, pp. 160-168. SHANNON, CLAUDE E., A Symbolic Analysis of Relay and Switching Circuits, _Transactions of the American Institute of Electrical Engineers_, vol. 57, 1938, pp. 713-723. This paper has had a good deal of influence here and there on the development of electric circuits using relays. The following report discusses the solution of some problems of mathematical logic by means of a large-scale digital calculator: TARSKI, ALFRED, _A Decision Method for Elementary Algebra and Geometry_, Report R-109, California: Rand Corporation, Aug. 1, 1948, 60 pp. OTHER DIGITAL MACHINES FINISHED OR UNDER DEVELOPMENT The Aiken Mark II Relay Calculator The Computation Laboratory of Harvard University finished during 1947 a second large relay calculator, called the Aiken Mark II Relay Calculator. This machine is alluded to briefly at the end of Chapter 10 and is described more fully in the following: CAMPBELL, ROBERT V. D., Mark II Calculator, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Cambridge, Mass.: Harvard University Press, 1948, pp. 69-79. FREELAND, STEPHEN L., Inside the Biggest Man-Made Brain, _Popular Science_, May 1947, pp. 95-100. MILLER, FREDERICK G., Application of Printing Telegraph Equipment to Large-Scale Calculating Machinery, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Cambridge, Mass.: Harvard University Press, 1948, pp. 213-222. The Edsac The Edsac is a machine under construction in England. WILKES, M. V., The Design of a Practical High-Speed Computing Machine: the EDSAC, _Proceedings of the Royal Society_, series A, vol. 195, 1948, pp. 274-279. WILKES, M. V., and W. RENWICK, An Ultrasonic Memory Unit for the EDSAC, _Electronic Engineering_, vol. 20, no. 245, July 1948, pp. 208-213. The Edvac The Edvac is a machine under construction at the Moore School of Electrical Engineering, Philadelphia. KOONS, FLORENCE, and SAMUEL LUBKIN, Conversion of Numbers from Decimal to Binary Form in the EDVAC, _Mathematical Tables and Other Aids to Computation_, vol. 3, no. 26, Apr. 1949, pp. 427-431. ANONYMOUS, EDVAC Replaces ENIAC, _The Pennsylvania Gazette_, Philadelphia: University of Pennsylvania, vol. 45, no. 8, Apr. 1947, pp. 9-10. The IBM Selective-Sequence Electronic Calculator The IBM Selective-Sequence Electronic Calculator was finished and announced in January 1948, and is alluded to briefly at the end of Chapter 10. More information about this machine is in the following references: ECKERT, W. J., Electrons and Computation, _The Scientific Monthly_, vol. 67, no. 5, Nov. 1948, pp. 315-323. INTERNATIONAL BUSINESS MACHINES CORPORATION, _IBM Selective-Sequence Electronic Calculator_, New York: International Business Machines Corporation (form no. 52-3927-0), 1948, 16 pp. The Raytheon Computer The Raytheon Computer is a machine under construction at the Raytheon Manufacturing Co., Waltham, Mass. BLOCH, R. M., R. V. D. CAMPBELL, and M. ELLIS, The Logical Design of the Raytheon Computer, _Mathematical Tables and Other Aids to Computation_, vol. 3, no. 24, Oct. 1948, pp. 286-295. BLOCH, R. M., R. V. D. CAMPBELL, and M. ELLIS, General Design Considerations for the Raytheon Computer, _Mathematical Tables and Other Aids to Computation_, vol. 3, no. 24, Oct. 1948, pp. 317-323. A “System of Electric Remote-Control Accounting” During the 1930’s a system using connected punch-card machinery was experimented with in a department store in Pittsburgh. The purpose of the system was automatic accounting and analysis of sales. This system is described in: WOODRUFF, L. F., A System of Electric Remote-Control Accounting, _Transactions of the American Institute of Electrical Engineers_, vol. 57, Feb. 1938, pp. 78-87. The Univac The Univac is a machine under construction at the Eckert-Mauchly Computer Corporation, Philadelphia. A similar but smaller digital computer called the Binac is also being developed. ECKERT-MAUCHLY COMPUTER CORPORATION, _The Univac System_, Philadelphia: Eckert-Mauchly Computer Corp., 1948, 8 pp. ELECTRONIC CONTROL CO. (now ECKERT-MAUCHLY COMPUTER CORP.), _A Tentative Instruction Code for a Statistical Edvac_, Philadelphia: Electronic Control Co. (now Eckert-Mauchly Computer Corp.), May 7, 1947, 19 pp. SNYDER, FRANCES E., and HUBERT M. LIVINGSTON, Coding of a Laplace Boundary Value Problem for the UNIVAC, _Mathematical Tables and Other Aids to Computation_, vol. 3, no. 25, Jan. 1949, pp. 341-350. The Zuse Computer The Zuse Computer is a small digital computer constructed in Germany. LYNDON, ROGER C., The Zuse Computer, _Mathematical Tables and Other Aids to Computation_, vol. 2, no. 20, Oct. 1947, pp. 355-359. THE DESIGN OF DIGITAL MACHINES Following are a number of references on various aspects of the design of digital computing machines: Organization BURKS, ARTHUR W., Super-Electronic Computing Machine, _Electronic Industries_, vol. 5, no. 7, July 1946, p. 62. BURKS, ARTHUR W., HERMAN H. GOLDSTINE and JOHN VON NEUMANN, _Preliminary Discussion of the Logical Design of an Electronic Computing Instrument_, Princeton, N. J.: Institute for Advanced Study, 2nd edition, Sept. 1947, 42 pp. ECKERT, J. PRESPER, JR., JOHN W. MAUCHLY, and J. R. WEINER, An Octal System Automatic Computer, _Electrical Engineering_, vol. 68, no. 4, Apr. 1949, p. 335. FORRESTER, JAY W., WARREN S. LOUD, ROBERT R. EVERETT, and DAVID R. BROWN, _Lectures by Project Whirlwind Staff on Electronic Digital Computation_, Cambridge, Mass.: Massachusetts Institute of Technology, Servo-mechanisms Laboratory, Mar. and Apr. 1947, 149 pp. LUBKIN, SAMUEL, Decimal Point Location in Computing Machines, _Mathematical Tables and Other Aids to Computation_, vol. 3, no. 21, Jan. 1948, pp. 44-50. PATTERSON, GEORGE W., editor, and others, _Theory and Techniques for Design of Electronic Digital Computers_ (subtitle: _Lectures Given at the Moore School 8 July 1946-31 August 1946_), Philadelphia: The University of Pennsylvania, Moore School of Electrical Engineering, vol. 1, lectures 1-10, Sept. 10, 1947, 161 pp.; vol. 2, lectures 11-21, Nov. 1, 1947, 173 pp.; vol. 3 and 4 in preparation. STIBITZ, GEORGE R., _Relay Computers_, Applied Mathematics Panel Report 171.1R, Washington, D. C.: National Defense Research Council, Feb. 1945, 83 pp. STIBITZ, GEORGE R., Should Automatic Computers be Large or Small? _Mathematical Tables and Other Aids to Computation_, vol. 2, no. 20, Oct. 1947, pp. 362-364. STIBITZ, GEORGE R., The Organization of Large-Scale Calculating Machinery, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Cambridge, Mass.: Harvard University Press, 1948, pp. 91-100. STIBITZ, GEORGE R., A New Class of Computing Aids, _Mathematical Tables and Other Aids to Computation_, vol. 3, no. 23, July 1948, pp. 217-221. Input and Output Devices ALEXANDER, SAMUEL N., Input and Output Devices for Electronic Digital Calculating Machinery, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Cambridge, Mass.: Harvard University Press, 1948, pp. 248-253. FULLER, HARRISON W., The Numeroscope, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Cambridge, Mass.: Harvard University Press, 1948, pp. 238-247. O’NEAL, R. D., Photographic Methods for Handling Input and Output Data, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Cambridge, Mass.: Harvard University Press, 1948, pp. 260-266. TYLER, ARTHUR W., Optical and Photographic Storage Techniques, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Cambridge, Mass.: Harvard University Press, 1948, pp. 146-150. ZWORYKIN, V. K., L. E. FLORY, and W. S. PIKE, Letter-Reading Machine, _Electronics_, vol. 22, no. 6, June 1949, pp. 80-86. ANONYMOUS, Letter-Printing Cathode-Ray Tube, _Electronics_, vol. 22, no. 6, June 1949, pp. 160-162. Storage Devices BRILLOUIN, LEON N., Electromagnetic Delay Lines, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Cambridge, Mass.: Harvard University Press, 1948, pp. 110-124. FORRESTER, JAY W., High-Speed Electrostatic Storage, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Cambridge, Mass.: Harvard University Press, 1948, pp. 125-129. HAEFF, ANDREW V., The Memory Tube and its Application to Electronic Computation, _Mathematical Tables and Other Aids to Computation_, vol. 3, no. 24, Oct. 1948, pp. 281-286. KORNEI, OTTO, Survey of Magnetic Recording, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Cambridge, Mass.: Harvard University Press, 1948, pp. 223-237. MOORE, BENJAMIN L., Magnetic and Phosphor Coated Discs, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Cambridge, Mass.: Harvard University Press, 1948, pp. 130-132. RAJCHMAN, JAN A., The Selectron—A Tube for Selective Electrostatic Storage, _Mathematical Tables and Other Aids to Computation_, vol. 2, no. 20, Oct. 1947, pp. 359-361 and frontispiece. SHARPLESS, T. KITE, Mercury Delay Lines as a Memory Unit, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Cambridge, Mass.: Harvard University Press, 1948, pp. 103-109. SHEPPARD, C. BRADFORD, Transfer Between External and Internal Memory, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Cambridge, Mass.: Harvard University Press, 1948, pp. 267-273. Programming or Coding EVERETT, ROBERT R., _Digital Computing Machine Logic_ (memorandum M-63), Cambridge, Mass.: Massachusetts Institute of Technology, Servo-mechanisms Laboratory, Mar. 19, 1947, 48 pp. GOLDSTINE, HERMAN H., and JOHN VON NEUMANN, _Planning and Coding of Problems for an Electronic Computing Instrument_, Princeton, N. J.: Institute for Advanced Study, 1947, 69 pp. GOLDSTINE, HERMAN H., and JOHN VON NEUMANN, _Planning and Coding of Problems for an Electronic Computing Instrument_, Princeton, N. J.: Institute for Advanced Study, part 2, vol. 3, 1948, 23 pp. MAUCHLY, JOHN W., Preparation of Problems for Edvac-Type Machines, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Cambridge, Mass.: Harvard University Press, 1948, pp. 203-207. DIGITAL MACHINES—MISCELLANEOUS Many of the following articles are nontechnical and contain much interesting information about machines that think: ALT, FRANZ L., New High-Speed Computing Devices, _The American Statistician_, vol. 1, no. 1, Aug. 1947, pp. 14-15. BUSH, VANNEVAR, As We May Think, _Atlantic Monthly_, July 1945, pp. 101-108. CONDON, EDWARD U., _The Electronic Brain Means a Better Future for You_ (broadcast), Columbia Broadcasting System, Jan. 4, 1948. DAVIS, HARRY M., Mathematical Machines, _Scientific American_, vol. 180, no. 4, Apr. 1949, pp. 29-39. LAGEMANN, JOHN K., It All Adds Up, _Collier’s Magazine_, May 31, 1947, pp. 22-23 ... LOCKE, E. L., Modern Calculators, _Astounding Science Fiction_, vol. 52, no. 5, Jan. 1949, pp. 87-106. MACLAUGHLAN, LORNE, Electrical Mathematicians, _Astounding Science Fiction_, vol. 53, no. 3, May 1949, pp. 93-108. MANN, MARTIN, Want to Buy a Brain? _Popular Science_, vol. 154, no. 5, May 1949, pp. 148-152. NEWMAN, JAMES R., Custom-Built Genius, _New Republic_, June 23, 1947, pp. 14-18. PFEIFFER, JOHN E., The Machine That Plays Gin Rummy, _Science Illustrated_, vol. 4, no. 3, Mar. 1949, pp. 46-48 ... RIDENOUR, LOUIS N., Mechanical Brains, _Fortune_, vol. 39, no. 5, May 1949, pp. 108-118. TUMBLESON, ROBERT C., Calculating Machines, _Federal Science Progress_, June 1947, pp. 3-7. ANONYMOUS, Almost Human, _Home Office News_, Newark, N. J.: Prudential Insurance Company of America, Feb. 1947, p. 8. APPLICATIONS OF DIGITAL MACHINES Some of the problems that mechanical brains can solve, some of the methods for controlling them to solve problems, and some of the implications of mechanical brains for future problems are covered in the following references: Solving Problems BERKELEY, EDMUND C., Electronic Machinery for Handling Information, and its Uses in Insurance, _Transactions of the Actuarial Society of America_, vol. 48, May 1947, pp. 36-52. BERKELEY, EDMUND C., Electronic Sequence Controlled Calculating Machinery and Applications in Insurance, _Proceedings of 1947 Annual Conference, Life Office Management Association_, New York: Life Office Management Association, 1947, pp. 116-129. CURRY, HASKELL B., and WILLA A. WYATT, _A Study of Inverse Interpolation of the Eniac_, B. R. L. Report No. 615, Aberdeen, Md.: Ballistic Research Laboratories, Aug. 19, 1946, 100 pp. HARRISON, JOSEPH O., JR., and HELEN MALONE, Piecewise Polynomial Approximation for Large-Scale Digital Calculators, _Mathematical Tables and Other Aids to Computation_, vol. 3, no. 26, Apr. 1949, pp. 400-407. HOFFLEIT, DORRIT, A Comparison of Various Computing Machines Used in Reduction of Doppler Observations, _Mathematical Tables and Other Aids to Computation_, vol. 3, no. 25, Jan. 1949, pp. 373-377. LEONTIEF, WASSILY W., Computational Problems Arising in Connection with Economic Analysis of Interindustrial Relationships, _Proceedings of a Symposium on Large-Scale Digital Calculating Machinery_, Cambridge, Mass.: Harvard University Press, 1948, pp. 169-175. LOTKIN, MAX, _Inversion on the Eniac Using Osculatory Interpolation_, B. R. L. Report No. 632, Aberdeen, Md.: Ballistic Research Laboratories, July 15, 1947, 42 pp. LOWAN, ARNOLD N., The Computation Laboratory of the National Bureau of Standards, _Scripta Mathematica_, vol. 15, no. 1, Mar. 1949, pp. 33-63. MATZ, ADOLPH, Electronics in Accounting, _Accounting Review_, vol. 21, no. 4, Oct. 1946, pp. 371-379. MCPHERSON, JAMES L., Applications of High-Speed Computing Machines to Statistical Work, _Mathematical Tables and Other Aids to Computation_, vol. 3, no. 22, Apr. 1948, pp. 121-126. MITCHELL, HERBERT F., JR., Inversion of a Matrix of Order 38, _Mathematical Tables and Other Aids to Computation_, vol. 3, no. 23, July 1948, pp. 161-166. ANONYMOUS, Revolutionizing the Office, _Business Week_, May 28, 1949, no. 1030, pp. 65-72. Speech Some of the possibilities of machines dealing with voice and speech are indicated in: DUDLEY, HOMER, R. R. RIESZ, and S. S. A. WATKINS, A Synthetic Speaker, _Journal of the Franklin Institute_, vol. 227, June 1939, pp. 739-764. This is an article on the _Voder_, which is an abbreviation of _V_oice _O_peration _De_monstrator. The machine was exhibited at the New York World’s Fair, 1939. DUDLEY, HOMER, The Vocoder, _Bell Laboratories Record_, vol. 18, no. 4, Dec. 1939, pp. 122-126. This is a more general type of machine than the Voder. The Vocoder is both an analyzer and synthesizer of human speech. POTTER, RALPH K., GEORGE A. KOPP, and HARRIET C. GREEN, _Visible Speech_, New York: D. Van Nostrand Co., 1947, 441 pp. ANONYMOUS, Pedro the Voder: A Machine that Talks, _Bell Laboratories Record_, vol. 17, no. 6, Feb. 1939, pp. 170-171. Weather Some of the possibilities of machines dealing with weather information are covered in: LAGEMANN, JOHN K., Making Weather to Order, _New York Herald Tribune: This Week_, Feb. 23, 1947. SHALETT, SIDNEY, Electronics to Aid Weather Figuring, _The New York Times_, Jan. 11, 1946. ZWORYKIN, V. K., _Outline of Weather Proposal_, Princeton, N. J.: Radio Corporation of America Research Laboratories, Oct. 1945, 11 pp. ANONYMOUS, Weather Under Control, _Fortune_, Feb. 1948, pp. 106-111 ... The Robot Machine ČAPEK, KAREL, _R. U. R._ (translated from the Czech by Paul Selver), New York: Doubleday, Page & Co., 1923. LAGEMANN, JOHN K., From Piggly Wiggly to Keedoozle, _Collier’s Magazine_, vol. 122, no. 18, Oct. 30, 1948, pp. 20-21 ... LEAVER, E. W., and J. J. BROWN, Machines Without Men, _Fortune_, vol. 34, no. 5, Nov. 1946, pp. 165 ... PEASE, M. C., Devious Weapon, _Astounding Science Fiction_, vol. 53, no. 2, Apr. 1949, pp. 34-43. SHANNON, CLAUDE E., _Programming a Computer for Playing Chess_, Bell Telephone Laboratories, Oct. 8, 1948, 34 pp. SHELLEY, MARY W., _Frankenstein_ (in Everyman’s Library, No. 616), New York: E. P. Dutton & Co., last reprinted 1945, 242 pp. SPILHAUS, ATHELSTAN, Let Robot Work for You, _The American Magazine_, Dec. 1948, p. 47 ... ANONYMOUS, Another New Product for Robot Salesmen, _Modern Industry_, vol. 13, no. 2, Feb. 15, 1947. ANONYMOUS, The Automatic Factory, _Fortune_, vol. 34, no. 5, Nov. 1946, p. 160 ... ANONYMOUS, Machines Predict What Happens in Your Plant, _Business Week_, Sept. 25, 1948, pp. 68-69 ... NAME INDEX _Note: This list of persons mentioned in the text includes names of fictional characters. The subject index, which follows, includes all other names._ Aiken, Howard H., 90-112, 177-8, 232, 245-6 Alexander, Samuel N., 251 Alquist, 200 Alt, Franz L., 142, 237, 247, 253 Archer, R. M., 241 Aristotle, 152 Babbage, Charles, 89 Baehne, G. Walter, 232 Bailey, C. F., 237 Barcroft, Joseph, 229 Beach, Frank A., 229 Beard, R. E., 88, 240 Berkeley, Edmund C., 233, 248, 254 Berry, R. J. A., 229 Berry, T. M., 240 Bloch, Richard M., 246, 250 Bloomfield, Leonard, 231 Bodmer, Frederick, 231 Boelter, L. M. K., 240 Boole, George, 152 Boring, Edwin G., 229 Bower, E. C., 237 Brainerd, J. G., 247 Brillouin, Leon N., 252 Brown, David R., 251 Brown, G. S., 245 Brown, J. J., 255 Brown, S. L., 241-2 Buckingham, R. A., 240 Burkhart, William, 144, 155-6 Burks, Arthur W., 246, 251 Bush, Vannevar, 72, 74, 239, 241, 245, 253 Caldwell, Samuel H., 74, 239, 241 Campbell, Robert V. D., 249-50 Čapek, Karel, 199, 255 Carroll, Lewis, 12 Carter, G. K., 244 Cesareo, O., 248 Clemence, G. M., 237 Clippinger, R. F., 246 Comrie, John Leslie, 232 Concordia, C., 244 Condon, Edward U., 253 Crew, E. W., 232 Criner, H. E., 245 Culley, Frank L., 237 Curry, Haskell B., 254 Davis, Harry M., 253 Deming, W. Edwards, 237 Dietzold, Robert L., 244 Domin, Harry, 199 Dudley, Homer, 254-5 Duncan, W. J., 244 Dunlap, Jack W., 237 Dwyer, Paul S., 237 Dyer, H. S., 237 Eckert, J. Presper, Jr., 114, 178, 247, 251 Eckert, W. J., 233, 236-7, 239, 250 Edison, Thomas A., 15 Ellis, M., 250 Enns, W. E., 243 Everett, Robert R., 251-2 Feinstein, Lillian, 237 Flesch, Rudolf, 231 Flory, L. E., 252 Forrester, Jay W., 251-2 Frame, J. Sutherland, 244 Frankenstein, Victor, 198, 200 Franz, Shepherd I., 229 Freeland, Stephen L., 249 Fry, Macon, 232 Fuller, Harrison W., 252 Fürth, R., 242 Gage, F. D., 245 Genet, N., 239, 246 Godwin, Mary W. (Mary W. Shelley), 198, 255 Goldstine, Adele, 247 Goldstine, Herman H., 247, 251, 253 Gove, E. L., 245 Graff, Willem L., 231 Graham, R. S., 244 Gray, T. S., 245 Green, Harriet C., 255 Haeff, Andrew V., 252 Hansen, Morris H., 237 Harrison, Joseph O., Jr., 246, 254 Hart, H. C., 244 Hartkemeier, Harry Pelle, 233 Hartree, D. R., 232, 240-1, 247 Haupt, Ralph F., 237 Hayakawa, S. I., 231 Hazen, H. L., 243, 245 Hedeman, W. R., 245 Hedley, K. J., 233 Herget, Paul, 237 Herr, D. L., 244 Herrick, C. Judson, 229 Hoffleit, Dorrit, 254 Hogben, Launcelot, 231 Hollerith, Herman, 43 Hopper, Grace M., 246 Horsburgh, E. H., 232 Hotelling, Harold, 237 Householder, Alston S., 230 Jespersen, Otto, 231 Juley, Joseph, 248 Kalin, Theodore A., 144, 155-6 Kelvin, Lord, 72, 240 King, Gilbert W., 238 Koons, Florence, 249 Kopp, George A., 255 Kormes, Jennie P., 238 Kormes, Mark, 238 Kornei, Otto, 252 Kranz, Frederick W., 242 Kron, Gabriel, 243-4 Kuder, G. Frederic, 238 Kuehni, H. P., 240, 243 Lagemann, John K., 253, 255 Landahl, Herbert D., 230 Lang, H. C., 233 Lashley, Karl S., 229 Leaver, E. W., 255 Leontief, Wassily W., 254 Lettvin, Jerome Y., 230 Lilley, S., 232 Livingston, Hubert M., 250 Locke, E. L., 253 Lorraine, R. G., 243 Lotkin, Max, 254 Loud, Warren S., 251 Lowan, Arnold N., 254 Lubkin, Samuel, 249, 251 Lyndon, Roger C., 250 MacLaughlan, Lorne, 253 Maginniss, F. J., 241 Mallock, R. R. M., 244 Malone, Helen, 254 Mann, Martin, 253 Marble, F. G., 242 Massey, H. S. W., 240 Mastukazi, Kiyoshi, 19 Matz, Adolph, 254 Mauchly, John W., 114, 178, 247, 251, 253 Maxfield, D. K., 238 Maxwell, L. R., 242 McCann, G. D., 245 McCulloch, Warren S., 230 McLaughlin, Kathleen, 238 McPherson, James L., 254 McPherson, John C., 238 Meacham, Alan D., 237 Mercner, R. O., 244 Miller, Dayton C., 242 Miller, Frederick G., 249 Milliman, Wendell A., 238 Milne, J. R., 242 Mitchell, Herbert F., Jr., 254 Montgomery, H. C., 242 Moore, Benjamin L., 252 Moore, C. R., 242 Murray, Francis J., 232 Myers, D. M., 245 Newman, James R., 253 Ogden, C. K., 231 O’Neal, R. D., 252 Parker, W. W., 243 Patterson, George W., 251 Pease, M. C., 255 Pekeris, C. L., 245 Peterson, H. A., 240, 243-4 Pfeiffer, John E., 253 Pieron, Henri, 229 Pike, W. S., 252 Pitts, Walter, 230 Poesch, H., 240 Porter, A., 240-1 Potter, Ralph K., 255 Pringle, R. W., 242 Quine, W. V., 248 Rajchman, Jan A., 252 Rashevsky, N., 230 Raymond, W. J., 242 Reichenbach, Hans, 248 Renwick, W., 249 Ridenour, Louis N., 253 Riesz, R. R., 254 Robertson, J. M., 242 Rose, A., 247 Rossum, 199 Royer, Elmer B., 238 Sauer, R., 240 Schlauch, Margaret, 231 Schnackel, H. G., 233 Schrödinger, Erwin, 229 Schwarzchild, Martin, 237 Shalett, Sidney, 255 Shannon, Claude E., 153-5, 241, 248, 255 Sharpless, T. Kite, 252 Shelley, Mary W., 198, 255 Shelley, Percy Bysshe, 198 Sheppard, C. Bradford, 252 Sherrington, Charles S., 229 Smith, C. E., 245 Snyder, Frances E., 250 Somerville, J. M., 242 Spilhaus, Athelstan, 255 Stewart, R. R., 245 Stibitz, George R., 129-30, 244, 251 Straiton, A. W., 242 Tabor, Lewis P., 247 Tarski, Alfred, 248-9 Terhune, G. K., 242 Thomas, George B., 238 Thomson, James, 240 Thomson, William, 72, 240 Tilney, Frederick, 229 Torrey, V., 246 Travis, Irven, 239, 244 Tumbleson, Robert C., 253 Turck, J. A. V., 232 Tyler, Arthur W., 252 Varney, R. N., 243 von Neumann, John, 124, 251 Wainwright, Lawrence L., 72, 241 Walpole, Hugh R., 231 Watkins, S. S. A., 254 Wegel, R. L., 242 Weiner, J. R., 251 Wheeler, L. L., 241-2 Whitten, C. A., 238 Wiener, Norbert, 229 Wilbur, J. B., 244 Wilkes, M. V., 249 Williams, Samuel B., 248 Wolf, Arthur W., 233 Womersley, J. R., 241 Wood, Thomas, 19 Woodger, J. H., 248 Woodruff, L. F., 250 Wyatt, Willa A., 254 Wylie, J., 240 Yavne, R. O., 245 Zworykin, V. K., 190, 252, 255 SUBJECT INDEX _Notes: Phrases consisting of an adjective and a noun, or of a noun and a noun, are entered in their alphabetical place according to the first word. For example, “electrostatic storage tube” is under_ e, _and “punch card” is under_ p. _A_ field, 99 _A_ tape, 82-3 abacus, 17-9, 133, 220 _abax_ (Greek), 18 absolute value, 101, 222 accumulator, 115-6 accumulator decade, 118 accuracy, 67, 89 acetylcholine, 3 add output, 120 addend, 223 adder, 77 adder mechanism, 77-8 adding, 24-5, 27, 37, 55, 100, 119, 139 addition circuit, 37 Aiken Mark I Calculator, 10, 89-112, 245-6; _see also_ Harvard IBM Automatic Sequence-Controlled Calculator Aiken Mark II Relay Calculator, 176-8, 249 Aiken Mark III Electronic Calculator, 177 air resistance coefficient, 80-2 algebra of logic, 26, 36, 56-62, 105, 140, 151-2, 164, 221-3, 248 algebraic equations, machines for solving, 244 all-or-none response, 3 alphabet, 14 alphabetic coding, 13, 54 alphabetic punching, 46 alphabetic writing, 13 amplify, 73 analogous, 65 analogue, 65 analogue machines (machines that handle information expressed as measurements), 65; MIT Differential Analyzer No. 2, 65-88; references, 239-45 analytical engine, 90 analyzer, 68, 241-4; _see also_ differential analyzer and, 146-8 and/or, 149 angle-indicator, 74-5 animal thinking, 4, 8, 188 annuities, 88 antecedent, 158 antilogarithm, 139, 226 antitangent, 139, 226 approximation, 220; _see also_ rapid approximation aptitude testing, 190 argument (in a mathematical table or function), 96, 103-4, 122, 136, 224 arithmetical operations, 55-6, 173 armor with a motor, 180, 195 array, 173, 227 Atomic Energy Commission, 203, 208 attitudes, 205 augend, 223 _aut_ (Latin), 149 automatic address-book, 181 automatic carriage, 53 “Automatic Computing Machinery” (section in _Mathematical Tables and Other Aids to Computation_), 177 automatic control: house-furnace, 189; lawn-mower, 188; tractor-plow, 188; weather, 189 automatic cook, 181 automatic factory, 189 automatic library, 9, 181 automatic machinery, 182 automatic pilot, 189 automatic recognizer, 186-7 automatic sequence-controlled calculator, 90; _see also_ Harvard IBM Automatic Sequence-Controlled Calculator automatic stenographer, 185 automatic switching circuits, 248 automatic translator, 182 automatic typist, 182, 184 axon, 3 _B_ field, 99 _B_ tape, 82-3 Ballistic Research Laboratories, 1, 113-5, 127-8, 132, 142 base _e_, 226 base 10, 226 beam of electrons, 172 behavior, 4, 7-8, 29 Bell Telephone Laboratories, 4-5, 128-43, 247-8 Bell Telephone Laboratories’ general-purpose relay computer, 128-43, 247-8; cost, 142; reliability, 141; speed, 142 Bessel functions, 111, 226 Binac, 179 binary coding, 11, 13 binary digit, 14 binary numbers, 14, 216-9 biophysics, 230 biquinary numbers, 133, 219-20 blocks of arguments, 137 Boolean algebra, 152, 248; _see also_ mathematical logic both, 149 bowwow theory, 12 brain evolution, 229 brain with a motor, 180, 195 BTL frames, 138-9 bus, 32, 119 button, 91, 94 _C_ field, 99 _C_ tape, 82-3 _calcis_ (Latin), 18 calculating punch, 47, 51-2, 235 calculator frames, 138 calculator programmed by punch cards, 236 cam, 94-5 cam contact, 91, 94-5 capacitance, 117 capacitor, 117 capacity: counter, 59; selecting, 59 carbon dioxide, 190 card channel, 47, 52 card column, 48 card feed, 48, 91 card punch, 91, 97 card reader, 116, 118 card sorter, 96 card stacker, 48 card station, 47 Carnegie Institution of Washington, 113 carry impulse, 118 cell nucleus, 2-3 census, 43, 53 channel, 47, 52, 170 characteristic of a logarithm, 107 check counter, 105 check-marks, 151 checking, 105, 110, 179, 227 chess game, 117 chestnut blight, 201 chortle, 12 class selector, 59 clearing, 100 codes, 29, 54, 96, 99 coding, 30, 130, 252-3 coding line, 99 column (in a punch card), 45 connective, 148, 158-9 connective grouping, 159 collating, 51, 173 collator, 47, 51, 235 collator counting device, 51, 235 combining information, 15 combining operations, 173 Common, 59-60 comparer, 57-8 comparing, 50, 57-8 complement, 55; _see also_ nines complement, ones complement, tens complement Complex Computer, 129-30 complex numbers, 128-9 computer, 6, 27 Computer 1 and Computer 2, 132, 138 conflicts between statements, 149-50 consequent, 158 constant, 224 constant ratio, 77 constant register, 96, 99 constant switch, 99 Constant Transmitter, 116, 118 consulting a table, 103, 122 convergent, 221 Converter, 115 context, 144 continuous annuities, 88 continuous contingent insurances, 88 continuously running gear, 93 control, 6, 28, 90-1 control brushes, 51-2 control frames, 138-9 Control Instrument Company, 43 control over robot machines, 196-208 control tape, 28 controversy, 197 cosine, 75, 85, 139, 226 cost of mechanical brains, 87, 109, 126, 142, 165, 168 counter, 52, 74, 93-4 counter position, 93 counter wheel, 93, 118 counting, 55 coupling (numbers), 106 cube, 105, 224 Current (input of comparer), 57 cycle, 29, 45 Cycling Unit, 115-6 Cypriote, 13 Dartmouth College, 131 decade, 118 decimal digit, 11, 14 decimal position, 118 deciphering, 184, 188 decoding, 184, 188 definite integral, 111, 225 delay lines, 17, 20, 171-2 dendrite, 3 denial, 147 dependent variable, 81, 224 derivative, 68-71, 225 design of mechanical brains, 167-79, 251 desk calculating machines, 4, 11, 17, 19 detail cards, 50 dial switch, 92, 95-6 dial telephone, 17, 19, 128 differences, 110, 227 differential, 68, 70, 78 differential analyzer, 68, 72-88, 239-41 Differential Analyzer No. 2, 65-88; accuracy, 86; cost, 87; reliability, 87; speed, 87 differential equation, 68-9, 71, 111, 141, 225-6 differential function, 70 differential gear assembly, 78 digit, 11, 14 Digit Pickup, 60 digit selector, 60 digit tray, 119 digit trunk lines, 119 digit trunks, 119 digital machines (machines that handle information expressed as digits or letters): Bell Laboratories’ general-purpose relay calculator, 128-43; Eniac, 113-27; Harvard IBM Automatic Sequence-Controlled Calculator, 89-112; punch-card calculating machinery, 42-64; references, 232-9, 245-55 directions, 24 disc, 78-80 discrimination, 140 discriminator, 140-1 distance, 68-9 distinguishing _A_ and _H_, 184 dividend, 103, 223 Divider-Square-Rooter, 115-7 dividing, 55-6, 98, 102, 121, 140 divisor counter, 102 doorpost, 65-6 doubling, 76-7, 100 doubling mechanism, 76-7 drafting rules, 149 drag coefficient, 80 drive, 86 Dry Ice, 190 echo, 171 Eckert-Mauchly Computer Corporation, 179, 250 economic relations, 194 Edsac, 249 “educated” machine, 101 Edvac, 177, 249 Egyptian, 12 either, 149 electric charge, 172 electric remote-control accounting, 250 electric typewriter, 91, 97, 236 electromagnet, 168 Electronic Binary Automatic Computer, 179 electronic calculating punch, 236 Electronic Control Company, 250 Electronic Numerical Integrator and Calculator (Eniac), 113-27, 246-7; _see also_ Eniac electronic tubes, 17, 20-1, 178-9; Cathode, 21; Grid, 21; Plate, 21 electrostatic storage tube, 17, 20, 172 11 position, 45 11 punch, 58 else, 146-7 end-around-carry, 95, 217, 223 engine, 90 Eniac, 113-27, 246-7; cost, 126; panels, 115; reliability, 126; speed, 125; unbalance, 124 “enough alike,” 184 Equal (output of sequencer), 61-2 equation, 68, 225 equivalent, 14 erase key, 134 Etruscan, 188 explanation, 209-13 explicit equation, 86 exponential, 85, 106, 225-6 extraction, 222 falsity, 147 farad, 117 fingers, 16, 18 fire-control instrument, 17, 19, 67, 131 5 impulse, 56 flights, 70 flip-flop, 119 following logically, 145 form feeding device, 236 formal logic, 152 formula, 68, 70, 224 Frankenstein’s monster, 198 function, 68, 70, 81, 103, 116, 118, 224 function table, 80-1, 116, 118 gang punching, 50 gearbox, 77-8 General Electric A.C. Network Analyzer, 243 General Electric Company, 243 geographic code, 54 giant brain, 1, 5-8 globe, 65-6 graph, 81 great circle, 69 greater-than, 25-7, 37, 222 greater-than circuit, 37 Greek letters, 120 guided missile, 197, 206 gun, 69 hail storm, 190 hand perforator, 132, 134 handling information, 10-18 harmonic analyzers, 241-2 harmonic synthesizers, 241-2 Harvard Computation Laboratory, 89, 176-7, 245, 249 Harvard IBM Automatic Sequence-Controlled Calculator (Mark I), 10, 89-112, 245-6; cost, 109; efficiency, 111; reliability, 110; speed, 109 Harvard Sequence-Controlled Electronic Calculator (Mark III), 177 Harvard Sequence-Controlled Relay Calculator (Mark II), 176-8, 249 Harvard University, 1, 4, 8, 89, 176-7, 245, 249 hatred, 206 hoppers, 51 hub, 46, 98 human brain, 2-4, 16, 229 humidity, 63 IBM (International Business Machines), 43-64, 89-90, 177, 233-9, 249-50 IBM Automatic Sequence-Controlled Calculator, 10, 89-112, 245-6; _see also_ Harvard IBM Automatic Sequence-Controlled Calculator IBM card-programmed calculator, 236 IBM pluggable sequence relay calculator, 236 IBM punch-card machinery, 43-64, 233-9 IBM Selective-Sequence Electronic Calculator, 177-9, 249 ideographic writing, 12 if, 146-7 if ... then, 149 ignorance, 205 illness, 191-2 imitative scheme, 12 in-code, 99 in-field, 99 independent variable, 81, 224 infinity, 86, 133, 212, 225 information, 10 initial conditions, 83, 225 Initiating Unit, 115-6 input, 6, 90-1 input devices, 175, 251-2 input register, 27 instantaneous rate of change, 70-1 Institute of Advanced Study, 124 instructions, 28, 83, 97, 178-9 insurance company, 42 insurance policies, 42 insurance values, 88 integral, 68, 71-2, 225 integral sign, 85, 225 integrating, 71-2, 78 integrator, 78-80 integrator mechanism, 78-9 International Business Machines Corporation (IBM), 43; _see_ IBM International Hydrographic Bureau, 242 International Phonetic Alphabet, 13 interpolating, 131, 221 interposing, 102 interpreter, 47, 49, 235 interpreting, 49 interval, 68, 70 intuitive thinking, 8 inverse, 71 judgments, 191 Kalin-Burkhart Logical-Truth Calculator, 144-66, 248; cost, 165; reliability, 166; speed, 166 key punch, 47-8, 96, 235 keyboard, 48 knots, 17 language of logic, 56-62, 105, 140; _see also_ mathematical logic languages, 10-21, 231 latch relay, 40-1 left-hand components, 56, 121, 215 library, 9, 181 Library of Congress, 15 lie detector, 192 line of coding, 99 linear, 224-5 linear interpolation, 221 linear simultaneous equations, 141, 225 lobe, 94-5 logarithm, 67, 85, 106-8, 139, 225 Logarithm-In-Out counter, 107 logic, 144; _see also_ mathematical logic logical choice, 4; _see also_ mathematical logic logical connective, 148, 222 logical operations, 56-62, 173 logical pattern, 145-6 logical truth, 144-56, 166 Logical-Truth Calculator, 144-66; _see_ Kalin-Burkhart Logical-Truth Calculator loopholes, 149 Low Primary (output of sequencer), 61-2 Low Secondary (output of sequencer), 61-2 Lower Brushes, 52 loxodrome, 69-70 machine call number, 99 machine cycle, 56 machine language, 29, 99, 175, 191 machines as a language for thinking, 19-20; references, 231-2 machines involving voice and speech, 185-6, 254 magnetic surfaces, 17, 20, 168-70, 179 magnetic tape, 169-70, 179 magnetic wire, 168 magnetized spot, 168-70 main connective, 160 many-wire cable, 50 Mark I (Harvard IBM Automatic Sequence-Controlled Calculator), 10, 89-112, 245-6; _see also_ Harvard IBM Automatic Sequence-Controlled Calculator Mark II (Harvard Sequence-Controlled Relay Calculator), 176-8, 249 Mark III (Harvard Sequence-Controlled Electronic Calculator), 177 Massachusetts Institute of Technology, 1, 20, 65, 72-88, 153 Massachusetts Institute of Technology’s Differential Analyzer No. 2, 65-88; accuracy, 86; cost, 87; reliability, 87; speed, 87 master card, 50 Master Programmer, 115-6 matching, 173 mathematical biophysics, 230 mathematical logic, 26, 36, 56-62, 105, 140, 151-2, 164, 221-3, 248 matrices, 173, 227 matrix, 173, 227 meanings, 209, 231 measurements, 65-6, 68 mechanical brain, 1, 5-8, 20; crucial devices for, 20 mechanical brains under construction, 176-9 memory, 27, 90-1 mentality, 24, 27 mercury tank, 171, 179 merging, 173 metal fingers, 135 mica, 172 microphone, 185 mimeograph stencil, 16 Minoan, 188 miscellaneous field, 99 mistake, 134 Moore School of Electrical Engineering, 7, 113-27, 177, 249 multiplicand, 223 multiplicand counter, 101 multiplication schemes, 214-6 multiplier, 115-6 multiplier counter, 101 multiply-divide unit, 103 multiplying, 55-6, 101, 121, 140 multiplying punch, 47, 52, 235 National Advisory Committee for Aeronautics, 128, 132 Naval Proving Ground, 177 negation, 24-5, 27, 34-6 negation circuit, 36 negative, 147 negative digit, 215 neon bulb, 119 nerve, 2-4 nerve cell, 2, 3, 16 nerve fiber, 2, 3 nerve networks, 230 nervous system, 188 network analyzers, 242-4 neurosis, 191 nine-pulses, 120-1 nines complement, 95, 121, 223 No X, 59 Northrop Aircraft, Inc., 179 not, 146-8 numeric coding, 13, 54 numerical X position, 45 numerical Y position, 45 occupation code, 54 octal notation, 179, 219 ohm, 117 Ojibwa, 12 ones complement, 217 only, 146-7 operation code, 103 operations with numbers, 24-7 or, 146-9 organization of digital machines, 251 out-code, 99 out-field, 99 output, 6, 90-1, 251-2 output devices, 176, 251-2 output register, 27 paper channel, 52 partial differential equations, 87 partial products, 115, 214 Pearl Assurance Company, 88 pebbles, 17-8 pen with a motor, 180, 195 permanent table frames, 138-9 personal income tax, 141 phonetic writing, 13 phonograph, 15-6 phonographic writing, 13 phototube, 81-2, 183-4 physical equipment for handling information, 11, 15-21, 91 physical problems, 69-72 physical quantities, 67-9 pictographic writing, 12 plugboard, 46, 98 plug-in units, 117-8 point of view, 207 pooh-pooh theory, 12 position (in a punch card), 45 position frames, 138-9 power, 43, 65, 133, 216, 224 prejudice, 205 Previous (input of comparer), 57 Primary (input of sequencer), 61-2 Primary Brushes, 51, 62 Primary Feed, 51, 61 Primary Sequence Brushes, 51 printer, 137 printer frames, 138 problem frames, 138 problem position, 132, 135 problem tape, 134 processor, 132, 134, 175 product, 70, 102, 223 product counter, 102 production scheduling, 193 program, 122, 173, 252-3 program-control switch, 123 program pulse, 122 program-pulse input terminal, 123 program register, 38 program tape, 28-9 program trays, 119 program trunk lines, 119 programming method of von Neumann, 124 pronoun, 223 psychological testing, 190 psychological trainer, 191-2 pulses, 120, 171 punch card, 17, 44-5, 95, 97 punch-card column, 45 punch-card machinery, 17, 20, 42-64, 232-9; cost, 63; reliability, 63-4; speed, 62-3 punch feed, 51-2 punched paper tape, 17, 23, 82, 95 punching channel, 50 punching dies, 48, 51-2 pyramid circuit, 39 quantity of information, 11, 14-15 quartz, 171 quotient, 98, 103 _R.U.R._, 199 radar, 183 railroad line, 6, 119 rapid approximation, 106-8, 220-1 rate of change, 68, 70-1 ratio, 77, 83 Raytheon Computer, 250 reading, 57 reading brushes, 51-2 reading channel, 50 reading of punch cards, 44 reasoning, 144 rebus-writing, 13 reciprocal, 85, 224 recognizing, 8, 182-5 recorder, 132, 137 rectifier, 32 referent, 12 register, 27 reject, 49 relay, 17, 20-1, 23, 92, 129, 133, 178; Common, 21; Ground, 21; Normally Closed, 21; Normally Open, 21; Pickup, 21 release key, 48 reliability, 63-4, 110, 126, 128, 141-2, 166, 168, 174 Remington-Rand, 43 reperforator, 137 rephrasing, 163-4 reproducer, 47, 49-50, 235 reproducing, 49 reset code, 100 resetting, 100 resistance, 80, 117 resistance coefficient, 80 resistor, 117 right-hand components, 56, 121, 215 robot machine, 197, 198-208, 255 robot salesman, 201 _robota_ (Czech), 199 Roman numerals, 212; ancient style, 219 room, 70 Rossum’s Universal Robots, 199 rounding off, 55-6 routine, 8, 167, 173 routine frames, 138-9 routine tape, 28, 134 rules, 191, 224 satisfy, 225 scale factor, 74, 86 schemes for expressing meanings, 11-15 screen, 172 screw, 78 Secondary (input of sequencer), 61-2 Secondary Brushes, 51, 62 Secondary Feed, 61 Select-Receiving-Register circuit, 39 selecting, 26, 58, 104 selection, 26-7, 38, 222 selection circuit, 38 selection counter, 104 selector, 58-60 sensing digits, 108 separation sign, 129 sequence-control tape, 98 sequence-control-tape code, 98 sequence-controlled, 89 sequence-tape feed, 98 sequencer, 61 sequencing, 61 shifting, 217 short-cut multiplication, 215-6 Simon, 22-40 simultaneous, 225 simultaneous equations, 85, 225 sine, 75, 85, 106, 139, 226 sink (of a circuit), 154 slab, 18 slide rule, 65, 67 smoothness, 110, 227 social control, types, 203 sorter, 47-9 sorting, 57, 173 soundtracks, 16, 18 source (of a circuit), 154 space key, 48 speedometer, 68 spelling rules, 185 spoken English, 11 square, 224 square matrix, 227 square root, 116-7, 173, 220, 224 Start Key, 98 statements, 26, 144-51 static electricity, 63 storage, 6 storage counter, 93 storage devices, 252 storage register, 28, 93 storing information, 15 storing register frames, 138 storing registers, 139 string, 65-6 stylus, 16 subroutine, 106 Subsidiary Sequence Mechanism, 90, 106 subtract output, 120 subtracting, 55, 100, 119, 139, 223 subtracting by adding, 223 summary punch, 50, 116, 119 summary-punching, 50 switch open and current flowing, 154 switchboard, 76 switches in parallel, 154 switches in series, 154 switching circuits, 155 syllable-writing, 13 syllables, 211 syllogism, 146, 152 symbolic logic, 221-3, 248; _see also_ mathematical logic symbolic writing, 12 synapse, 3 System of Electric Remote-Control Accounting, 250 systems for handling information, 10 table tape, 134 tables (of values), 103, 136, 224 tabular value, 136, 224 tabulator, 47, 52, 119, 235 tallies, 17 tangent, 105, 226 tank (armored), 180, 195 tank (mercury tank), 171, 179 tape-controlled carriage, 236 tape feed, 91, 178-9 tape punch, 91, 97-8, 137 tape reels, 170 tape transmitter, 135, 137 telegraph line, 6, 119 telephone central station, 138 teletype, 17 teletype transmitter, 133, 135 teletypewriter, 130, 137 ten-position relay, 91-3 ten-position switch, 91-2 ten-pulses, 120-1 tens complement, 224 test scoring machine, 236 then, 146-7 thermostat, 187 thinking, 1-5, 10, 97 timed electrical currents, 44 timing contact, 94 tolerances, 67, 105 torque, 73, 86 torque amplifier, 73 trajectories, 69, 114, 141 transfer circuit, 33 transferring, 31, 34, 100, 119, 167 translating, 57 transmitter, 74 triggering control, 183, 186-7 trigonometric tables, 226 trigonometric tangent, 105, 226 truth, 144 truth table, 147, 155, 222 truth value, 26, 58, 105, 147, 222 tuning, 183 turning force, 72 12 position, 45 two-position relay, 21, 91-2; _see also_ relay two-position switch, 91-2 typewriter, 16, 18 typewriter carriage, 53 unattended operation, 174 understanding, 212-3, 231 unemployment, 201-2 Unequal (output of comparer), 57 unit of information, 11, 14-5, 169 United Nations, 203, 208 United States Army Ordnance Department, 113-4 Univac, 250 University of Pennsylvania, 7, 113 unknowns, 141 Upper Brushes, 52 value tape code, 96 value tape feed, 95-6 variables, 84, 223 _vel_ (Latin), 149 verifier, 47-8, 235 vibration, 69 Vocoder, 255 Voder, 254 voltage, 74 Watson Scientific Computing Laboratory, 239 weather control, 189, 255 weather forecasting, 189, 255 wheel (of a counter), 78 white elephant, 73, 114 winch, 73 words for explaining, 209-12 X, 59 X distributor, 59 X Pickup, 59 X punch, 45, 58 X selector, 59 zero, 133, 212 _zh_ (sound), 13, 185 Zuse Computer, 250 *** END OF THE PROJECT GUTENBERG EBOOK 68991 ***