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

52 AN IDEA IS BORN Processes as Algorithms 53
tween lie the versions that really do explain the origin of species and promise
to explain much else besides. These versions are becoming clearer all the
time, thanks as much to the determined criticisms of those who frankly hate
the idea of evolution as an algorithm, as to the rebuttals of those who love it.
5. PROCESSES AS ALGORITHMS
When theorists think of algorithms, they often have in mind kinds of algorithms
with properties that are not shared by the algorithms that will concern
us. When mathematicians think about algorithms, for instance, they usually
have in mind algorithms that can be proven to compute particular
mathematical functions of interest to them. (Long division is a homely
example. A procedure for breaking down a huge number into its prime
factors is one that attracts attention in the exotic world of cryptography.) But
the algorithms that will concern us have nothing particular to do with the
number system or other mathematical objects; they are algorithms for
sorting, winnowing, and building things. 8
Because most mathematical discussions of algorithms focus on their guaranteed
or mathematically provable powers, people sometimes make the
elementary mistake of thinking that a process that makes use of chance or
randomness is not an algorithm. But even long division makes good use of
randomness!
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Does the divisor go into the dividend six or seven or eight times? Who
knows? Who cares? You don't have to know; you don't have to have any wit
or discernment to do long division. The algorithm directs you just to choose a
digit—at random, if you like—and check out the result. If die chosen number
turns out to be too small, increase it by one and start over; if too large,
decrease it. The good thing about long division is that it always works
8. Computer scientists sometimes restrict the term algorithm to programs that can be
proven to terminate—that have no infinite loops in them, for instance. But this special
sense, valuable as it is for some mathematical purposes, is not of much use to us. Indeed,
few of the computer programs in daily use around the world would qualify as algorithms
in this restricted sense; most are designed to cycle indefinitely, patiently waiting for
instructions (including the instruction to terminate, without which they keep on going).
Their subroutines, however, are algorithms in this strict sense—except where undetected
"bugs" lurk that can cause the program to "hang."
eventually, even if you are maximally stupid in making your first choice, in
which case it just takes a little longer. Achieving success on hard tasks in
spite of utter stupidity is what makes computers seem magical—how could
something as mindless as a machine do something as smart as that? Not
surprisingly, then, the tactic of finessing ignorance by randomly generating a
candidate and then testing it out mechanically is a ubiquitous feature of
interesting algorithms. Not only does it not interfere with their provable
powers as algorithms; it is often the key to their power. (See Dennett 1984,
pp 149-52, on the particularly interesting powers of Michael Rabin's random
algorithms.)
We can begin zeroing in on the phylum of evolutionary algorithms by considering
everyday algorithms that share important properties with them. Darwin
draws our attention to repeated waves of competition and selection, so
consider the standard algorithm for organizing an elimination tournament,
such as a tennis tournament, which eventually culminates with quarter-finals,
semi-finals, and then a final, determining the solitary winner.
Notice that this procedure meets the three conditions. It is the same
procedure whether drawn in chalk on a blackboard, or updated in a computer
file, or—a weird possibility—not written down anywhere, but simply
enforced by building a huge fan of fenced-off tennis courts each with two
entrance gates and a single exit gate leading the winner to the court where
the next match is to be played. (The losers are shot and buried where they
fall) It doesn't take a genius to march the contestants through the drill, filling
in the blanks at the end of each match ( or identifying and shooting the
losers). And it always works.
But what, exactly, does this algorithm do? It takes as input a set of competitors
and guarantees to terminate by identifying a single winner. But what
is a winner? It all depends on the competition. Suppose the tournament in
question is not tennis but coin-tossing. One player tosses and the other calls;
the winner advances. The winner of this tournament will be that single player
who has won n consecutive coin-tosses without a loss, depending on how
many rounds it takes to complete the tournament.