Darwin's Dangerous Idea - Evolution and the Meaning of Life

440 THE EMPEROR'S NEW MIND, AND OTHER FABLES
Does it follow that no algorithm running on my Toshiba can achieve
checkmate? Hardly! As I have already confessed, the chess algorithms on my
Toshiba are undefeated in play against one human being—me. I'm not very
good, but I expect I have about as much "insight" as the next human being.
Someday I might beat my machine, if I practiced a lot and worked very hard,
but the programs on my Toshiba are trivial compared with the current
champion chess programs. About them you could safely bet your life that
they would checkmate me (though not Bobby Fischer) every time. I don't
recommend to anyone that you actually bet your life on the relative excellence
of these algorithms—I might improve, and I wouldn't want your death
on my conscience—but in fact, if Darwinism is right, you and your ancestors
have an unbroken string of successful gambles for similarly fatal stakes on
the algorithms embodied in your "machinery." That is what organisms have
done, every day since life began: they have bet their lives that the algorithms
that built them, and that operate within them if they are among the lucky
organisms with brains, will keep them alive long enough to have children.
Mother Nature has never aspired to absolute certainty; a good risk is enough
for her. So we would expect that, if mathematicians' brains are running
algorithms, they will be algorithms that happen to do pretty well in the truthdetecting
department, without being foolproof.
The chess algorithms on my Toshiba, like all algorithms, yield guaranteed
results, but what they are guaranteed to do is not checkmate me, but just play
legal chess. That is all they are "for." Of the Vast number of algorithms
guaranteed to play legal chess, some are much better than others, though none
is guaranteed a win against any other—at least this is not the sort of thing one
would hope to prove mathematically, even if, as a matter of brute
mathematical fact, the initial state of program x and program y were such that
x would win all possible games against y. This means that the following
argument is fallacious:
x is excellent at achieving checkmate;
there is no (practical) algorithm for checkmate in chess;
therefore: the explanation of x's talent cannot be that x is running an
algorithm.
The conclusion is obviously false: the algorithm level of explanation is
exactly the right level at which to explain the power of my Toshiba to beat
me at chess. It's not as if it had particularly potent electricity running through
it, or a secret reservoir of elan vital inside its plastic case. What makes it
better than other chess-playing computers (I can beat the really simple ones)
is that it has a better algorithm.
What kind of algorithms, then, might mathematicians be running? Algorithms
"for" trying to stay alive. As we saw in our consideration of the
survival-machine robots in the last chapter, such algorithms would have to
The Library of Toshiba 441
be capable of indefinitely resourceful discrimination and planning; they must
be good at recognizing food and shelter, telling friend from foe, learning to
discriminate harbingers of spring as harbingers of spring, telling good arguments
from bad, and even—as a sort of bonus talent thrown in—recognizing
mathematical truths as mathematical truths. Of course, such "Darwinian algorithms"
( Cosmides and Tooby 1989) wouldn't have been designed just for
this special purpose, any more than our eyes were designed for telling italics
from boldface, but that doesn't mean that they aren't superbly sensitive to
such differences if given a chance to consider them.
Now how could Penrose have overlooked this retrospectively obvious
possibility? He is a mathematician, and mathematicians are primarily interested
in that Vanishing subset of algorithms that they can prove, mathematically,
to have mathematically interesting powers. I call this the God's-eye
view of algorithms. It is analogous to the God's-eye view of volumes in the
Library of Babel. We can "prove" (for what it is worth) that there is a single
volume in the Library of Babel that lists, in perfect alphabetical order, all the
telephone subscribers in New York City whose net worth on January 10,
1994, was more than a million dollars. There has to be—there couldn't be
that many millionaire phone-owners in New York, and so some one of the
possible volumes in the Library must list them all. But finding it—or making
it—would be a huge empirical task fraught with uncertainties and judgment
calls, even if we just considered it to be a subset of the names already printed
in the actual phone book as of that date (ignoring all those with unlisted
numbers ). Even though we can't put our hands on this volume, we can name
it—just the way we named Mitochondrial Eve. Call it Megaphone. Now, we
can prove things about Megaphone, for instance, the first letter printed on the
first page on which there is printing is "A," but the first letter on the last page
on which there is printing is not "A." (This is not quite up to the standards of
mathematical proof, of course, but what are the odds that none of the people
with phones whose names begin with "A" is a million aire, or that there's
only one page of such millionaires in all New York?)
As I noted on page 52, when mathematicians think about algorithms, it is
usually from the God's-eye perspective. They are interested in proving, for
instance, that there is some algorithm with some interesting property, or that
there is no such algorithm, and in order to prove such things you needn't
actually locate the algorithm you are talking about—by picking it out from a
pile of algorithms stored on floppy disks, for instance. Our inability to locate
(the remains of) Mitochondrial Eve did not prevent us from deducing facts
about her either. The empirical issue of identification thus doesn't often arise
for such formal deductions. Godel's Theorem tells us that not a single one of
the algorithms that can run on my Toshiba ( or any other computer ) has a
certain mathematically interesting property: being a consistent generator of
proofs of arithmetic facts that generates them all if given enough run time.