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:

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: ac
0 0123 00
1 1230 13
2 2301 22
3 3012 31

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 0000
1 1000
2 1100
3 1110

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 01230000
1 01231111
2 01232222
3 01233333

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.