In the previous chapters I talked about reason and math as being things that have their origin outside of the universe. One objection some readers might have relates to computers and artificial intelligence. Computers exist entirely inside the universe, of course, so if a computer does the same thing a human mind does, then that would be an argument that math and reasoning do not originate outside the universe.
Now the first response to this objection needs to be that computers only do what humans program them to do, and humans program them with mathematical laws, but I’d like to move the discussion a little beyond that.
The reader would not be blamed if he supposed that computers think something like we do, though perhaps with not quite the same level of intelligence. This idea has become popularized in so many different ways that it is quite ingrained. In fact, sometimes people even ask the question – when will computers be able to pass up humans? The question itself reveals confusion as to what a computer actually does. I’d like to offer a couple of examples describing why the thing that computers do is not the same thing as what humans do.
Can you multiply two five digit numbers in your head and give the correct answer within one second, and never make a mistake? I believe there are a few human prodigies that do that kind of thing, but I certainly can’t and you probably can’t either. But computers have been doing this for more than 70 years. So in a sense, computers passed us up 70 years ago. Let’s simplify it a little. Can you multiply two one-digit numbers in your head and give the correct answer within one second? I can, and many of you can too. If you asked me to multiple seven times eight, I could immediately say 56. The computer will do that too. However, the computer is not doing the same thing I am doing. The reason I can say 7 x 8 = 56 is because way back in elementary school some teacher made me memorize my times tables. So I have the answer memorized. The computer, on the other hand, doesn’t have the answer memorized. Every time you ask the computer to multiply something, it calculates it. The way the computer solves the problem of 7 x 8 is that it first converts 7 and 8 into binary form. Binary form is a base 2 numbering system, a system that instead of having digits from 0 to 9 only has digits 0 and 1. That’s convenient for computers because it can be modeled with electric signals on or off, or switches on or off. In binary, 7 = 00000111 and 8 = 00000100. Whenever a computer multiplies a number by 2, it “shifts” the binary number to the left, which is the same as adding a 0 to the end. To multiply by eight, it shifts to the left three times, which is the same as adding three zeroes to the end. Therefore, 7 x 8 = 00111000. It then has to convert 00111000 to decimal, making it 56. In short, the computer and I get to the same answer, but in different ways. I have 7 x 8 memorized and the computer calculates it.
Now consider what happens if the problem is just a bit more complex, say multiplying 56 x 23. The answer is 1288. The computer would use the same computational approach, using a combination of shifts and adds, and get the answer essentially instantly. But what about me? I’m better at math than some people and I can do two-digit multiplication in my head, but I timed myself just now and it took me 37 seconds to get the answer. I don’t have 56 x 23 memorized. I had to multiple 56 x 2, then multiply that by ten, then try to remember that product while I multiplied 56 by 3, and finally add those two products together. What I was doing in this case was to start with what I had memorized, then try to extend that knowledge by computing - forcing my brain to act like a computer. I could do it, but not very well. It took a while, and although I got the answer right this time, I would often get that kind of computation wrong. If I had to multiply three-digit numbers in my head, I’m not sure I could do it.
The bottom line is that when it comes to computing – computers passed us up long ago. When it comes to computing, humans can hold only the palest candle to what even the simplest computers do.
Now let’s talk about a different kind of example. Computers can be programmed to play chess. Chess is a great game for computers, because it is a “pure” game – no knowledge of the real world is involved. A human knows what a chess piece feels like and a computer doesn’t, but that doesn’t matter – the computer doesn’t need to know that and it wouldn’t help if it did. So in a chess game between a human and a computer, the human’s knowledge of the real world doesn’t help the human at all.
In 1996, a computer chess match of six games was arranged between a computer called “Deep Blue,” specially prepared by IBM to play chess against the then world champion, Garry Kasparov. Kasparov won the match. IBM went back to work and strengthened their program, and in a 1997 rematch, Deep Blue won. It was hailed as an important and momentous occasion, since computers had now passed up the best human in terms of chess-playing ability. However, I think the way we are looking at this story is upside-down. How could a human hope to even compete in a chess game against a computer? You see, what not many people understand is that when a computer is playing chess, it is not doing the same thing that humans do when a human is playing chess.
As an illustration, I selected a position from game 6 of the 1997 Kasparov-Deep Blue match. If this is white’s move, he has a lot of choices. Each choice of moves could lead to advantages and disadvantages. How many potential chess moves do you think you could evaluate in one minute? I asked my son and he said he could evaluate ten moves in one minute. That seemed high to me, but let’s go with that. In this particular position from the 1997 match, I counted 41 possible moves for white. I may have counted wrong, but if that’s wrong it’s still close and it is still representative of what you would commonly see in the middle of a chess match. At the moment it looks like black has 37 possible responses, though that might change a little based on where white moves. Therefore, after one move by each player, there are 41 x 37 possible positions, or over 1000 possible positions. After two moves by each player, there will be over one million possible positions, and after three moves there will be over a billion. It is safe to say that no human chess player is evaluating a billion possible positions. However, that is what Deep Blue was doing, and it could look more than three moves ahead in just a few seconds. The computer looks at every possible move and evaluates how strong it is after each one. It does this by assigning a numerical value to each piece, something like a pawn = 1, a knight = 3, a rook = 5, and so on. Deep Blue will look as far into the future as its computing power allows and pick the move that gives it the best numerical value. A chess computer’s human programmers will enhance the computer’s ability by providing it with a set of the best-known chess game openings to ensure it never gets started on the wrong foot. Furthermore, within the limits of this kind of program, the computer will never make a mistake. It will never accidentally put its queen in the path of a knight, or anything foolish like that which human players do from time to time.
So given all that, maybe we are looking at the human vs computer chess match all wrong. How is it that a human ever managed to beat a computer in the first place? How did we keep the advantage until 1997? Garry Kasparov was not evaluating a billion positions, or a million, or even a thousand. And unlike the computer, Kasparov could certainly make a mistake. The computer never did.
To play chess, the computer is computing. The human is not doing that, at last not very much. The human player will have learned some principles about chess. The principles will be things like don’t bring your rook out too early in the game, because it is likely to get trapped by pieces of lesser value. On the other hand, at the end of a game, it’s best to have your rook ahead of your pawns rather than behind them. A human is likely to apply those principles when making a move, though they are hard to quantify. It may be far into the future before the principle produces any material advantage that a computer could see. Furthermore, a very advanced human is doing something else that you and I do not – and the computer doesn’t either.
I once played a chess game against Susan Polgar when she was 17 years old. At the time, she was the top-rated female player in the world, though her younger sister Judit soon passed her up. (I lost, by the way.) Susan once participated in an exercise in which she sat at an outdoor café as a truck drove by. The truck had a chessboard painted on its side, with pieces in position for the middle of a game. Though she only saw the truck for a moment, Susan was able to correctly recreate the position on her own chess board. Next, the exercise was repeated, but this time, the chess pieces were in a position which was not possible (for example, a pawn can never be on the first rank since pawns start on the second rank and can only move forward.)
Susan was not able to recreate the illegal position. Further study has shown that very advanced chess players like Susan Polgar actually have adapted the facial recognition portion of their brain to recognize chess positions. Humans may not be very good at computing, but we are great at facial recognition. If we once meet someone and look well at their face, we are likely to recognize that same face for years, even if we don’t remember their name or where we met them. So humans playing chess don’t compute much – they compute a little bit, but choose largely based on principles, with the best players recognizing positions with the facial recognition portion of their brain.
Speaking of facial recognition – computers are beginning to do that too. How do computers recognize faces? Facial recognition software makes lots of three-dimensional measurements on the face, closely measuring things like the distance between the eyes, the width of the nose, the depth of the eye sockets, etc. How does the human brain recognize faces? It’s not the same way. Neither you nor I measure the length of someone’s jaw line in order to recognize them.
The conclusion I am trying to get to is this: Computers compute, while the human brain computes very little and not very well. What the human mind does is different, and the human brain to computer analogy is not as strong as we often think it is. Everything that goes on inside a computer is obviously part of the physical universe. But the human mind is very different from a computer, so some of the things that happen in a human mind can be outside of it.
Suggested reading on this subject would be the book Computer Power and Human Reason, by Joseph Weizenbaum. It’s quite an old book for one on computers, but don’t be put off by that – Mr. Weizenbaum says much of what I was trying to say in this section, and he does so more clearly than I do.
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