Giant brains; or, Machines that think

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

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:

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.

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.

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.