Great Grandpa Willy died at the age of 101, leaving an estate of $968,767 to be divided equally among his 67 descendants. How much, to the penny, will each of them get?

(The answer, nothing, lawyers will get it all, is plausible but for our purposes unacceptable.)

Three hundred years ago, knowing how to solve the problem of Grandpa Willy's estate would have been considered a major talent. Samuel Pepys, Secretary of the British Navy and also the keeper of a famous diary, records rising before dawn to be given lessons in arithmetic. Oliver Goldsmith, in "The Deserted Village," remarked of the village schoolmaster, "he could write and cipher, too" - cipher just being another word for doing arithmetic. If you could do sums, you were smart.

Fifty years ago, Grandpa Willy's estate problem would have presented my father or my mother with no difficulty. They didn't regard themselves as especially smart, but arithmetic was well within their powers. They would simply have taken a sheet of paper, done the necessary "long division," and come up with the right answer in a couple of minutes. Can you? You may well say, probably, but why bother? Today we operate differently. We take a calculator, press the buttons, and have an answer in seconds.

Of course, with no calculator handy, a large fraction of today's population will be stymied. What was once considered strictly something that only thinking people could do has now become the almost exclusive province of "dumb" machines.

We don't consider that our calculators, or our computers, can think. Even as they balance our check books, figure our taxes, and proofread and spell-check our letters, all of which half a century ago required human powers, we comfort ourselves with the thought that computers are dumb. They only do what they are told to do, and only if told in precisely the right way. On the other hand, humans often fail to do what they are told, too. We misunderstand, or we pretend to understand because we don't want to look stupid.

Even so, computers are dumb. Right?

What would it take to make us change our minds about that? A few columns back, I wrote one called "How smart can they get?" It was about computers, but I cheated. What I really wrote about was how fast computers might become, and that's a very different question. The idea of a "thinking machine" forces us to ask the basic question, what do we mean by thinking? How can we possibly tell if a machine is thinking, or just doing some complicated calculations?

This sounds as though it ought to take us into philosophical deep waters, involving self-awareness and consciousness and the nature of thought. However, in 1950 Alan Turing swept all of that to one side and replaced it by a practical test. Turing was a mathematician, a shy, lonely man, a homosexual at a time when that was not only widely regarded as morally wrong but was illegal. After suffering much physical and mental abuse from the British authorities, he killed himself at the age of 42 by eating an apple laced with cyanide.

He was also a genius who solved one of the outstanding mathematical problems of his day (the "Halting Problem"), possessed code-breaking talents that affected the outcome of the Second World War, and became a leading pioneer in the development of digital computers.

The famous "Turing Test" to decide if a machine can think is simple. Put a human on one end of a fax line and a computer on the other. If the human cannot decide, by asking questions and examining the answers, whether he is dealing with a computer or with another human, then the machine has passed the test and should be regarded as able to think, a "thinking machine." Of course, the computer has to be allowed to lie when asked certain questions. ("Are you a computer?" "No.")

Are we there yet? Do we have computers today that can pass the Turing Test?

Yes, and no. This is where we run into a hidden snag. There is a problem in the apparently straightforward procedure proposed by Alan Turing. It arises because we have not said anything about the intelligence of the human who asks the questions.

More than 30 years ago, computer programs had been built that seemed to hold intelligent conversations. One of them, ELIZA, served in the role of a psychoanalyst, feeding back to the human at the other end of the line plausible questions or comments constructed from key words in the human's own remarks. Many people who interacted with ELIZA became absolutely convinced that they were dealing with a human therapist, to the point where they tried to use the program to sort out personal problems they were having. Another program, PARRY, was designed to appear as a human suffering from paranoid delusions. Yet ELIZA and PARRY were no more truly intelligent than a programmable VCR.

Computer hardware and computer software have come a long way since ELIZA and PARRY and other early programs giving an appearance of intelligence. In 20 years or less, we will have programs capable of convincing 99 percent of all human interrogators that there is real, rational thought, in the person of another human, at the other end of the line. And at that point, we have to stop and ask what more should we expect. If it quacks like a duck, walks like a duck, and swims like a duck....

Of course, this still leaves out the tricky question of self-awareness. Will we at some point have a computer that knows of its own existence? Will it regret past follies, work in its own best interests, and show embarrassment at its own acts of stupidity?

When such a computer arrives it will not only equal human intelligence, it will far surpass it. If you doubt this, take a look at the daytime TV talk shows.

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