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.

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

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.

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.

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:
		/——————^—————————\
No.	Principle of Scheme	Sign	Used in	Significance	Name of Scheme
(1)	(2)	(3)	(4)	(5)	(6)
Sounds
1.	Sound of new word is like sound of referent	Bobwhite[2]	Spoken English	kind of quail, so called from its note	Imitative; bowwow theory
2.	An utterance becomes a new word	Pooh![3]	Spoken English	The speaker expresses disdain	Pooh-pooh theory
3.	New word is like another word	Chortle[4]	Spoken English; invented by Lewis Carroll, 1896	“Chuckle” and “snort” blended	Analogical
4.	Word has been used through the ages	Mother[5]	Spoken English	Female parent	Historical
Sights
5.	Picture is like referent		Egyptian; Ojibwa (American Indian)	Picture of eye and tears, to mean grief	Imitative; pictographic
6.	Pattern is symbol of an idea	5	English; French; German; etc.	Five; cinq; fünf; etc.	Ideographic; mathematical; symbolic; numeric
Mapping of Sounds
7.	Object pictured as the wanted sound		Possible English	Picture of a knot to mean “not”	Rebus- writing; phonographic
8.	Pattern is symbol for a large ound unit		Ancient Cypriote (island of Cyprus)	Sign for the syllable mu	Syllable- writing
9.	Pattern is symbol for a small sound unit	Ʒ	International Phonetic Alphabet of 87 characters	The sound zh, as s in “measure”	Phonetic writing alphabetic writing;
Mapping of Sights or Symbols
10.	Systematic combinations of 26 letters	ENIAC	Abbreviations, etc.	Initial letters of a 5-word title	Alphabetic coding
11.	Systematic combinations of 10 digits	135-03-1228	Abbreviations, nomenclature, etc.	Social Security No. of a person	Numeric coding
12.	Systematic combinations of 2 marks	✓,✕,✕,✓,✓	Checking lists, etc.	“yes,” “no,” “no,” “yes,” “yes,” respectively	Binary coding

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:

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:

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

• ✓✓ 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.

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.

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.

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.

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:

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:

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:

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]):

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.

S1-2
Relay energized

S1-1
Relay not energized

Fig. 3. Register S1 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 (C1, C2, C3), 1 to store the operation governing the computer (C4), and 1 to store the result (C5). 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 S1, S2, S3, ··· S8. 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 S1 hold the number 2 ([see Fig. 3])? The number 2 in machine language is 10. Register S1 consists of two relays, S1-2 and S1-1. 10 stored in register S1 means that relay S1-2 will be energized and that relay S1-1 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 C5 into O

or, more briefly,

C5 → 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:

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, C5, 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:

On the program tape, we need to put:

I → C4
I → C1
I → C2
C5 → 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.

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 C5 the number 2 is stored. In machine language this is 10. That means the left-hand relay (C5-2) is energized and the right-hand relay (C5-1) 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 C5 register. The C5-2 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 C5-1 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 C5 register through the bus to the coils of the O register.

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 C5 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 C5 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 C5 closed contacts; and finally

7. Into the ground.

Thus relay O-2 is energized; it receives current because contact C5-2 is closed. And relay O-1 is not energized; it receives no current since contact C5-1 is open. So we have actually transferred information from the C5 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 C1, C2, and C3 take in numbers 00, 01, 10, 11, that C4 takes in an operation 00, 01, 10, 11, and that C5 holds the result. What process does Simon use so that he has the correct result in register C5?

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 C1 register, and the operation 01 meaning negation goes into the C4 register, and the correct result must be in the C5 register. So, first, we note the fact that the C4-2 relay must not be energized, since it contains 0, and that the C4-1 relay must be energized, since it contains 1.

Now the table for negation, with c = -a, is:

Negation in machine language will be:

Now if a is in the C1 register and if c is in the C5 register, then negation will be:

But each of these registers C1, C5 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:

Now, on examining the table, we see that the C5-1 relay is energized if and only if the C1-1 relay is energized. So, in order to energize the C5-1 relay, all we have to do is transfer the information from C1-1 to C5-1. 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.)

Fig. 6. Negation—
right-hand digit.

Fig. 7. Negation—
left-hand digit.

Taking another look at the table, we see also that the C5-2 relay must be energized if and only if:

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 C5 relay coils if and only if the C4 relays hold 01.

Fig. 8. Negation circuit.

Let us check this circuit. First, if there is any operation other than 01 stored in the C4 relays, then no current will be able to get through the C4 contacts shown and into the C5 relay coils, and the result is blank. Second, if we have the operation 01 stored in the C4 relays, then the C4-2 contacts will not be energized—a condition which passes current—and the C4-1 contacts will be energized—another condition which passes current—and:

Thus we have shown that this circuit is correct.

We see that this circuit uses more than one set of contacts for several relays (C1-2, C4-1, C4-2); 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.

Fig. 9. Addition circuit.

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 C1-1 (since C1 holds 01) and for C2-2 (since C2 holds 10). Then, when we trace through the circuit, remembering that addition is stored as 00 in the C4 relays, we find that both the C5 relays are energized. Hence C5 holds 11, which is 3. Thus Simon can add 1 and 2 and make 3!

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, S1 to S8, C1 to C5, 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 P8, P4, P2, P1. For example, if the P8 and P2 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 C1.

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 C5 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.

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 P8 and P2 relays are energized. Then this circuit energizes the E10 relay. The E10 relay closes the contacts between the C1 relay coils and the bus; and so it connects the C1 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 moving input 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 moving program tape. Here then is approximately the total number of relays required:

A few more relays may be needed to provide more contacts or poles. For example, a single P1 relay will probably not have enough poles to meet all the need for its contacts.

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:

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.