The Computer as a Thinker
About the time Johnny was having all his trouble reading, a computer named JOHNNIAC was given the basic theorems needed, and then asked to prove the propositional calculus in the Principia Mathematica, a task certainly over the heads of most of us. The computer waded through the job with no particular strain, and even turned in one proof more elegant than human brains had found before. When the same problems were given to an engineer unfamiliar with that branch of mathematics, his verbalized problem-solving technique paralleled that of JOHNNIAC. Asked if he had been thinking, the engineer said he “surely thought so!”
In his interesting department in Scientific American, mathematical gamester Martin Gardner describes a simple set of punched cards for solving the type of logic problem discussed earlier in this chapter. Using these cards and a simple digital type of manipulation, we happily learn that Camille surely could. The problem is a simple, three-premise type in two-valued logic and can be solved by any self-respecting digital computer in a split second. A few demonstrations like this give a rather disconcerting insight into our brain’s limitations and build more respect for the computer’s intelligence.
When we hear of expensive computers apparently frittering away their valuable time playing games we may well wonder how come. But games, it turns out, are an ideal testing ground for problem-solving ability and hence intelligence. Back in 1957, computer experts Simon and Newell predicted that in ten years the chess champion of the world would be a computer. Master players most likely laughed up their sleeves, and thus far the electronic machine has done no better than play a routine game against a human amateur. This, of course, is not a mean achievement. Wise heads are supposed to have responded to the prediction with “So what?”
Photo at left from Organization of the Cerebral Cortex, by D. A Sholl, J. Wiley and Sons. Right, General Electric Research Laboratory
Photo at right shows a “crossed-film cryotron” shift register—an advanced computer element. The separation of active crossovers shown is comparable to the separation of nerve cells in the section of cat brain shown at left.
Alex Bernstein of IBM worked out a program for the 704 computer in which the machine looks ahead four moves before each of its plays. Even this limited look ahead requires 2,800 calculations, and the 704 takes eight minutes deliberating. Occasionally it makes a move the experts rate as masterful.
Chess is a far more complex game even than it appears to those of us on the sidelines. In an average game there are forty moves and each has about thirty possibilities. So far this sounds innocuous, but mathematics shows that there are thus 10120 possible moves in any one game. This number is a 1 followed by 120 zeros, and to underline its size it has been estimated that even if a million games a second were played, the possibilities would not be exhausted in our lifetime!
Obviously human chess wizards do not investigate all possible moves. Instead they use heuristic reasoning, or hunch playing, to cut corners. The JOHNNIAC computer is investigating such approaches to computer-playing chess, in a movement away from rigorously programmed routines or “algorithms.” Algorithms are formulas or equations such as the quadratic equation used in finding roots. If indeed the computer does dethrone the human chess champ by 1967, it will be exceedingly hard to argue that the machine is not thinking.
The word “heuristic” comes from the Greek heuriskein, meaning to discover or invent. An example of what it is and how important it is can be seen in the recent disproving of a famous conjecture made by the mathematician Euler some 180 years ago. Euler was interested in the properties of so-called “magic squares” in which letters are arranged vertically and horizontally. While it is possible to arrange the letters a, b, c, d, and e in such a square so that all are present in each row and in different order, Euler didn’t think such was the case with a square having six units on a side. He tried it, visualizing officers of different rank arranged in rows. Convinced that it would not work, he extended his educated guess to squares having units of ten, fourteen, and other even numbers not divisible by four. He didn’t actually prove his conjecture, because the amount of paperwork makes it practically impossible.