Darwin's Dangerous Idea (9 page)

each is somewhat difficult to define. Each, moreover, has given rise to confusions (and anxieties ) that continue to beset our thinking about Darwin's Life on Earth has been generated over billions of years in a single branching revolutionary discovery, so we will have to revisit and reconsider these tree—the Tree of Life—by o'ne algorithmic process or another.

introductory characterizations several times before we are through: What this claim means will become clear gradually, as we sort through he (1)
substrate neutrality:
The procedure for long division works equally various ways people have tried to express it. In some versions it is utterly well with pencil or pen, paper or parchment, neon lights or skywrit-vacuous and uninformative; in others it is manifestly false. In be-52 AN IDEA IS BORN

Processes as Algorithms
53

tween lie the versions that really do explain the origin of species and promise eventually, even if you are maximally stupid in making your first choice, in to explain much else besides. These versions are becoming clearer all the which case it just takes a little longer. Achieving success on hard tasks in time, thanks as much to the determined criticisms of those who frankly hate spite of utter stupidity is what makes computers seem magical—how could the idea of evolution as an algorithm, as to the rebuttals of those who love it.

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 5. PROCESSES AS ALGORITHMS

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, When theorists think of algorithms, they often have in mind kinds of algo-pp 149-52, on the particularly interesting powers of Michael Rabin's random rithms with properties that are
not
shared by the algorithms that will concern algorithms.)

us. When mathematicians think about algorithms, for instance, they usually We can begin zeroing in on the phylum of evolutionary algorithms by con-have in mind algorithms that can be proven to compute particular sidering everyday algorithms that share important properties with them. Dar-mathematical functions of interest to them. (Long division is a homely win draws our attention to repeated waves of competition and selection, so example. A procedure for breaking down a huge number into its prime consider the standard algorithm for organizing an elimination tournament, factors is one that attracts attention in the exotic world of cryptography.) But such as a tennis tournament, which eventually culminates with quarter-finals, the algorithms that will concern us have nothing particular to do with the semi-finals, and then a final, determining the solitary winner.

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!

7? 47)

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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 Notice that this procedure meets the three conditions. It is the same or discernment to do long division. The algorithm directs you just to choose a procedure whether drawn in chalk on a blackboard, or updated in a computer digit—at random, if you like—and check out the result. If die chosen number file, or—a weird possibility—not written down anywhere, but simply turns out to be too small, increase it by one and start over; if too large, enforced by building a huge fan of fenced-off tennis courts each with two decrease it. The good thing about long division is that it always works 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.

8. Computer scientists sometimes restrict the term
algorithm
to programs that can be But what, exactly, does this algorithm do? It takes as input a set of com-proven to
terminate
—that have no infinite loops in them, for instance. But this special petitors and guarantees to terminate by identifying a single winner. But what sense, valuable as it is for some mathematical purposes, is not of much use to us. Indeed, is a winner? It all depends on the competition. Suppose the tournament in few of the computer programs in daily use around the world would qualify as algorithms question is not tennis but coin-tossing. One player tosses and the other calls; 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).

the winner advances. The winner of this tournament will be that single player Their subroutines, however, are algorithms in this strict sense—except where undetec-who has won
n
consecutive coin-tosses without a loss, depending on how ted "bugs" lurk that can cause the program to "hang."

many rounds it takes to complete the tournament.

54 AN IDEA IS BORN

Processes as Algorithms
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There is something strange and trivial about this tournament, but what is there are tournaments of skill, like tennis tournaments. Here there
is
reason to it? The winner does have a rather remarkable property. How often have you believe that the players in the later rounds would do better
again
if they ever met anyone who just won, say, ten consecutive coin-tosses without a played the players who lost in the early rounds. There is reason to believe—

loss? Probably never. The odds against there being such a person might seem but no guarantee—that the winner of such a tournament is the best player of enormous, and in the normal course of events, they surely are. If some them all, not just today but tomorrow. Yet, though any well-run tournament gambler offered you ten-to-one odds that he could produce someone who is guaranteed to produce a winner, there is no guarantee that a tournament of before your very eyes would proceed to win ten consecutive coin-tosses skill will identify the best player as the winner in any nontrivial sense. That's using a fair coin, you might be inclined to think this a good bet. If so, you why we sometimes say, in the opening ceremonies, "May the best man had better hope the gambler doesn't have 1,024 accomplices (they don't have win!"—because it is not guaranteed by the procedure. The best player—the to cheat—they play fair and square). For that is all it takes (210 competitors) one who is best by "engineering" standards (has the most reliable backhand, to form a ten-round tournament. The gambler wouldn't have a clue, as the fastest serve, most stamina, etc.)—may have an off day, or sprain his ankle, or tournament started, which person would end up being the exhibit A that get hit by lightning. Then, trivially, he may be bested in competition by a would guarantee his winning the wager, but the tournament algorithm is sure player who is not really as good as he is. But nobody would bother to produce such a person in short order—it is a sucker bet with a surefire win organizing or entering tournaments of skill if it weren't the case that
in the
for the gambler. (I am not responsible for any injuries you may sustain if you
long run,
tournaments of skill are won by the best players.
That
is guaranteed attempt to get rich by putting this tidbit of practical philosophy into use.) by the very definition of a fair tournament of skill; if there were no probability Any elimination tournament produces a winner, who "automatically" has greater than half that the better players would win each round, it would be a whatever property was required to advance through the rounds, but, as the tournament of luck, not of skill.

coin-tossing tournament demonstrates, the property in question
may
be Skill and luck intermingle naturally and inevitably in any real competition,

"merely historical"—a trivial fact about the competitor's past history that has but their ratios may vary widely. A tennis tournament played on very bumpy no bearing at all on his or her future prospects. Suppose, for instance, the courts would raise the luck ratio, as would an innovation in which the players United Nations were to decide that all future international conflicts would be were required to play Russian roulette with a loaded revolver before settled by a coin-toss to which each nation sends a representative (if more continuing after the first set. But even in such a luck-ridden contest, more of than one nation is involved, it will have to be some sort of tournament—it the better players would
tend,
statistically, to get to the late rounds. The might be a "round robin," which is a different algorithm ). Whom should we power of a tournament to "discriminate" skill differences in the long run may designate as our national representative? The best coin-toss caller in the land, be diminished by haphazard catastrophe, but it is not in general reduced to obviously. Suppose we organized every man, woman, and child in the U.S.A.

zero. This fact, which is as true of evolutionary algorithms in nature as of into a giant elimination tournament. Somebody would have to win, and that elimination tournaments in sports, is sometimes overlooked by person would have just won twenty-eight consecutive coin-tosses without a commentators on evolution.

loss! This would be an irrefutable historical fact about that person, but since Skill, in contrast to luck, is
protectable;
in the same or similar circum-calling a coin-toss is just a matter of luck, there is absolutely no reason to stances, it can be counted on to give repeat performances. This relativity to believe that the winner of such a tournament would do any better in circumstances shows us another way in which a tournament might be weird.

international competition than somebody else who lost in an earlier round of What if the conditions of competition kept changing (like the croquet game the tournament. Chance has no memory. A person who holds the winning in
Alice in Wonderland)?
If you play tennis the first round, chess in the lottery ticket has certainly
been
lucky, and, thanks to the millions she has just second round, golf in the third round, and billiards in the fourth round, there won, she may never need to be lucky again—which is just as well, since there is no reason to suppose the eventual winner will be particularly good, is no reason to think she is more likely than anyone else to win the lottery a compared with the whole field, in
any
of these endeavors—all the good second time, or to win the next coin-toss she calls. ( Failing to appreciate the golfers may lose in the chess round and never get a chance to demonstrate fact that chance has no memory is known as the Gambler's Fallacy; it is their prowess, and even if luck plays no role in the fourth-round billiards surprisingly popular—so popular that I should probably stress that it
is
a final, the winner might turn out to be the
second-worst
billiards player in the fallacy, beyond any doubt or controversy.)

whole field. Thus there has to be some measure of uniformity of the In contrast to tournaments of pure luck, like the coin-toss tournament, conditions of competition for there to be any
interesting
outcome to a tournament.

56 AN IDEA IS BORN

Processes as Algorithms
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But does a tournament—or any algorithm—have to do something inter-rithm to yield something of interest or value is not at all limited to what the esting? No. The algorithms we tend to talk about almost always do some-algorithm can be mathematically proven to yield in a foolproof way, and this thing interesting—that's why they attract our attention. But a procedure is especially true of evolutionary algorithms. Most of the controversies about doesn't fail to be an algorithm just because it is of no conceivable use or Darwinism, as we shall see, boil down to disagreements about just how value to anyone. Consider a variation on the elimination-tournament algo-powerful certain postulated evolutionary processes are—could they actually rithm in which the
losers
of the semi-finals play in the finals. This is a stupid do all this or all that in the time available? These are typically investigations rule, destroying the
point
of the whole tournament, but the tournament would into what an evolutionary algorithm
might
produce, or
could
produce, or is still be an algorithm. Algorithms don't have to have points or purposes. In
likely
to produce, and only indirectly into what such an algorithm would addition to all the useful algorithms for alphabetizing lists of words, there are
inevitably
produce. Darwin himself sets the stage in the wording of his kazillions of algorithms for reliably misalphabetizing words, and they work summary: his idea is a claim about what "assuredly" the process of natural perfectly every time ( as if anyone would care ). Just as there is an algorithm selection will "tend" to yield.

(many, actually) for finding the square root of any number, so there are All algorithms are guaranteed to do whatever they do, but it need not be algorithms for finding the square root of any number except 18 or 703. Some anything interesting; some algorithms are further guaranteed to tend (with algorithms do things so boringly irregular and pointless that there is no probability
p)
to do something—which may or may not be interesting. But if succinct way of saying what they are
for.
They just do what they do, and they what an algorithm is guaranteed to do doesn't have to be "interesting" in any do it every time.

way, how are we going to distinguish algorithms from other processes?

We can now expose perhaps the most common misunderstanding of Won't
any
process be an algorithm? Is the surf pounding on the beach an Darwinism: the idea that Darwin showed that evolution by natural selection algorithmic process? Is the sun baking the clay of a dried-up riverbed an is a procedure
for
producing Us. Ever since Darwin proposed his theory, algorithmic process? The answer is that there may be features of these people have often misguidedly tried to interpret it as showing that we are the processes that
are
best appreciated if we consider them as algorithms!