In 1901 a mathematician did try all the possible configurations of the square of six units and found that Euler was indeed correct. It was assumed that ten was impossible too, until 1958 when three American mathematicians spoiled Euler’s theory by finding workable magic squares having ten units per side. They did not do this by exhausting all the possibilities, for such a chore would have been humanly impossible. In fact, a computer labored for 100 hours and completed only a tiny fraction of the job. The square-seekers concluded that it would take even the high-speed computer upwards of a century to do the job, so instead they used hunches or inspired guesses, working out a heuristic for the task. The point of importance is that not only man, but the computer as well, despite its fantastic speed, must learn to use heuristic reasoning rather than blindly plowing through all possible solutions. There are just too many numbers!
Computers play other games too, from tick-tack-toe and Nim, which it plays flawlessly, to Go and checkers. Dr. Arthur Samuel of IBM has taught the 704 computer to play checkers well enough to beat him regularly, though Dr. Samuel, scientist that he is, admits he is not a great checker-player. He has used two types of learning in the program: “rote” and “generalization.” So far these have been used separately, while human players use both types of learning in a game.
American scientists visiting Russia recently reported that the Russians, like some of us, were amazed to hear that computer time was allotted to the mere playing of games. The real goal in all this game-playing is to learn how to do other more important things. Gaming is being applied to war strategy and to business management. Corporation executives are playing games with computers that simulate the operation of their firms, both to improve methods and to learn about themselves and their employees. A General Problem-Solver computer is being developed too; one which can solve problems like the cannibals and the missionaries and then do mathematical equations and other types of thinking. As was pointed out, when the computer’s method of solving a problem is compared with the protocol used by a person (by having him think aloud as he goes through the problem) it is seen that both use pretty much the same tricks and short cuts.
As the computer keeps closing the gap, we can push the goal back by redefining our terms. This is much like dangling a carrot on a stick, and with the computer doggedly taking the part of the donkey, it is a pretty good technological flail. By making the true test of intelligence something like artistic creativity, we can rule out the machine unless it can write poetry, compose music, or paint a picture. So far the computer has done the first two, and the last poses no particular problem, though debugging the machine might be a messy operation. True, the machine’s poetry is only about beatnik level:
Children
Sob suddenly, the bongos are moving.
Or could we find that tall child?
And dividing honestly was like praying badly,
And while the boy is obese, all blast could climb.
First you become oblong,