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.
