CHAPTER TWO (First two sections omitted)

An Idea Is Born

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4. Natural Selection as an Algorithmic Process

What limit can be put to this power, acting during long ages and rigidly scrutinising the whole constitution, structure, and habits of each crea­ture,—favouring the good and rejecting the bad? I can see no limit to this power, in slowly and beautifully adapting each form to the most complex relations of life.

—Charles Darwin, Origin, p. 469

The second point to notice in Darwin's summary is that he presents his principle as deducible by a formal argument—if the conditions are met, a certain outcome is assured? Here is the summary again, with some key terms in boldface.

If, during the long course of ages and under varying conditions of life, organic beings vary at all in the several parts of their organization, and I think this cannot be disputed; if there be, owing to the high geometric powers of increase of each species, at some age, season, or year, a severe struggle for life, and this certainly cannot be disputed; then, considering the infinite complexity of the relations of all organic beings to each other and to their conditions of existence, causing an infinite" diversity in struc­ture, constitution, and habits, to be advantageous to them, I think it would be a most extraordinary fact if no variation ever had oc­curred useful to each being's own welfare, in the same way as so many variations have occurred useful to man. But if variations useful to any organic being do occur, assuredly individuals thus characterized will have the best chance of being preserved in the struggle for life; and from the strong principle of inheritance they will tend to produce offspring similarly characterized. This principle of preservation, I have called, for the sake of brevity, Natural Selection. [Origin, p. 127 (facs. ed. of 1st ed.).]

The basic deductive argument is short and sweet, but Darwin himself described Origin of Species as "one long argument." That is because it

6. The ideal of a deductive (or "nomologico-deductive" ) science, modeled on Newtonian or Galilean physics, was quite standard until fairly recently in the philosophy of science, so it is not surprising that much effort has been devoted to devising and criticizing various axiomatizations of Darwin's theory—since it was presumed that in such a formalization lay scientific vindication. The idea, introduced in this section, that Darwin should be seen, rather, as postulating that evolution is an algorithmic process, permits us to do justice to the undeniable a priori flavor of Darwin's thinking without forcing it into the Procrustean (and obsolete) bed of the nomologico-deductive model. See Sober 1984a and Kitcher 1985a.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

consists of two sorts of demonstrations: the logical demonstration that a certain sort of process would necessarily have a certain sort of outcome, and the empirical demonstration that the requisite conditions for that sort of process had in fact been met in nature. He bolsters up his logical dem­onstration with thought experiments—"imaginary instances" (Origin, p. 95)—that show how the meeting of these conditions might actually ac­count for the effects he claimed to be explaining, but his whole argument extends to book length because he presents a wealth of hard-won empirical detail to convince the reader that these conditions have been met over and over again.

Stephen Jay Gould (1985) gives us a fine glimpse of the importance of this feature of Darwin's argument in an anecdote about Patrick Matthew, a Scottish naturalist who as a matter of curious historical fact had scooped Darwin's account of natural selection by many years—in an appendix to his 1831 book, Naval Timber and Arboriculture. In the wake of Darwin's ascent to fame, Matthew published a letter (in Gardeners' Chronicle?) proclaiming his priority, which Darwin graciously conceded, excusing his ignorance by noting the obscurity of Matthew's choice of venue. Respond­ing to Darwin's published apology, Matthew wrote:

To me the conception of this law of Nature came intuitively as a self-evident feet, almost without an effort of concentrated thought. Mr. Darwin here seems to have more merit in the discovery than I have had—to me it did not appear a discovery. He seems to have worked it out by inductive reason, slowly and with due caution to have made his way synthetically from fact to fact onwards; while with me it was by a general glance at the scheme of Nature that I estimated this select production of species as an a priori recognizable fact—an axiom, requiring only to be pointed out to be admitted by unprejudiced minds of sufficient grasp. [Quoted in Gould 1985, pp. 345-46.]

Unprejudiced minds may well resist a new idea out of sound conservatism, however. Deductive arguments are notoriously treacherous; what seems to "stand to reason" can be betrayed by an overlooked detail. Darwin appre­ciated that only a relentlessly detailed survey of the evidence for the his­torical processes he was postulating would—or should—persuade scientists to abandon their traditional convictions and take on his revolutionary vi­sion, even if it was in fact "deducible from first principles."

7. Gardeners' Chronicle, April 7, I860. See Hardin 1964 for more details.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

From the outset, there were those who viewed Darwin's novel mixture of detailed naturalism and abstract reasoning about processes as a dubious and inviable hybrid. It had a tremendous air of plausibility, but so do many get-rich-quick schemes that turn out to be empty tricks. Compare it to the following stock-market principle: Buy Low, Sell High. This is guaranteed to make you wealthy. You cannot fail to get rich «/you follow this advice. Why doesn't it work? It does work—for everybody who is fortunate enough to act according to it, but, alas, there is no way of determining that the con­ditions are met until it is too late to act on them. Darwin was offering a skeptical world what we might call a get-rich-slow scheme, a scheme for creating Design out of Chaos without the aid of Mind.

The theoretical power of Darwin's abstract scheme was due to several features that Darwin quite firmly identified, and appreciated better than many of his supporters, but lacked the terminology to describe explicitly. Today we could capture these features under a single term. Darwin had discovered the power of an algorithm. An algorithm is a certain sort of formal process that can be counted on—logically—to yield a certain sort of result whenever it is "run" or instantiated. Algorithms are not new, and were not new in Darwin's day. Many familiar arithmetic procedures, such as long division or balancing your checkbook, are algorithms, and so are the decision procedures for playing perfect tic-tac-toe, and for putting a list of words into alphabetical order. What is relatively new—permitting us valu­able hindsight on Darwin's discovery—is the theoretical reflection by math­ematicians and logicians on the nature and power of algorithms in general, a twentieth-century development which led to the birth of the computer, which has led in turn, of course, to a much deeper and more lively under­standing of the powers of algorithms in general.

The term algorithm descends, via Latin (algorismus) to early English (algorisme and, mistakenly therefrom, algorithm), from the name of a Persian mathematician, Muusa al-Khowarizm, whose book on arithmetical procedures, written about 835 a.d., was translated into Latin in the twelfth century by Adelard of Bath or Robert of Chester. The idea that an algorithm is a foolproof and somehow "mechanical" procedure has been present for centuries, but it was the pioneering work of Alan Turing, Kurt Godel, and Alonzo Church in the 1930s that more or less fixed our current understand­ing of the term. Three key features of algorithms will be important to us, and each is somewhat difficult to define. Each, moreover, has given rise to confusions (and anxieties) that continue to beset our thinking about Dar­win's revolutionary discovery, so we will have to revisit and reconsider these introductory characterizations several times before we are through:

(1) substrate neutrality: The procedure for long division works equally well with pencil or pen, paper or parchment, neon lights or skywrit-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ing, using any symbol system you like. The power of the procedure is due to its logical structure, not the causal powers of the materials used in the instantiation, just so long as those causal powers permit the prescribed steps to be followed exactly.

(2)  underlying mindlessness: Although the overall design of the proce­dure may be brilliant, or yield brilliant results, each constituent step, as well as the transition between steps, is utterly simple. How simple? Simple enough for a dutiful idiot to perform—or for a straightfor­ward mechanical device to perform. The standard textbook analogy notes that algorithms are recipes of sorts, designed to be followed by novice cooks. A recipe book written for great chefs might include the phrase "Poach the fish in a suitable wine until almost done," but an algorithm for the same process might begin, "Choose a white wine that says 'dry' on the label; take a corkscrew and open the bottle; pour an inch of wine in the bottom of a pan; turn the burner under the pan on high; ... "—a tedious breakdown of the process into dead-simple steps, requiring no wise decisions or delicate judg­ments or intuitions on the part of the recipe-reader.

(3)  guaranteed results: Whatever it is that an algorithm does, it always does it, if it is executed without misstep. An algorithm is a foolproof recipe.

It is easy to see how these features made the computer possible. Every computer program is an algorithm, ultimately composed of simple steps that can be executed with stupendous reliability by one simple mechanism or another. Electronic circuits are the usual choice, but the power of com­puters owes nothing (save speed) to the causal peculiarities of electrons darting about on silicon chips. The very same algorithms can be performed (even faster) by devices shunting photons in glass fibers, or (much, much slower) by teams of people using paper and pencil. And as we shall see, the capacity of computers to run algorithms with tremendous speed and reli­ability is now permitting theoreticians to explore Darwin's dangerous idea in ways heretofore impossible, with fascinating results.

What Darwin discovered was not really one algorithm but, rather, a large class of related algorithms that he had no clear way to distinguish. We can now reformulate his fundamental idea as follows:

life on Earth has been generated over billions of years in a single branching tree—the Tree of Life—by one algorithmic process or another.

What this claim means will become clear gradually, as we sort through the various ways people have tried to express it. In some versions it is utterly vacuous and uninformative; in others it is manifestly false. In be-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

tween lie the versions that really do explain the origin of species and promise to explain much else besides. These versions are becoming clearer ill 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 the 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.

 

 

 

 

 

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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.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

There is something strange and trivial about this tournament, but what is it? The winner does have a rather remarkable property. How often have you ever met anyone who just won, say, ten consecutive coin-tosses without a loss? Probably never. The odds against there being such a person might seem enormous, and in the normal course of events, they surely are. If some gambler offered you ten-to-one odds that he could produce someone who before your very eyes would proceed to win ten consecutive coin-tosses using a fair coin, you might be inclined to think this a good bet. If so, you had better hope the gambler doesn't have 1,024 accomplices (they don't have to cheat—they play fair and square). For that is all it takes (210 com­petitors) to form a ten-round tournament. The gambler wouldn't have a clue, as the tournament started, which person would end up being the exhibit A that would guarantee his winning the wager, but the tournament algorithm is sure to produce such a person in short order;—it is a sucker bet with a surefire win for the gambler. (I am not responsible for any injuries you may sustain if you attempt to get rich by putting this tidbit of practical philosophy into use.)

Any elimination tournament produces a winner, who "automatically" has whatever property was required to advance through the rounds, but, as the coin-tossing tournament demonstrates, the property in question may be "merely historical"—a trivial fact about the competitor's past history that has no bearing at all on his or her future prospects. Suppose, for instance, the United Nations were to decide that all future international conflicts would be settled by a coin-toss to which each nation sends a representative (if more than one nation is involved, it will have to be some sort of tour­nament—it might be a "round robin," which is a different algorithm). Whom should we designate as our national representative? The best coin-toss caller in the land, obviously. Suppose we organized every man, woman, and child in the U.SA. into a giant elimination tournament. Somebody would have to win, and that person would have just won twenty-eight consecutive coin-tosses without a loss! This would be an irrefutable historical fact about that person, but since calling a coin-toss is just a matter of luck, there is abso­lutely no reason to believe that the winner of such a tournament would do any better in international competition than somebody else who lost in an earlier round of the tournament. Chance has no memory. A person who holds the winning lottery ticket has certainly been lucky, and, thanks to the millions she has just won, she may never need to be lucky again—which is just as well, since there is no reason to think she is more likely than anyone else to win the lottery a second time, or to win the next coin-toss she calls. (Failing to appreciate the fact that chance has no memory is known as the Gambler's Fallacy; it is surprisingly popular—so popular that I should prob­ably stress that it is a fallacy, beyond any doubt or controversy.)

In contrast to tournaments of pure luck, like the coin-toss tournament,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

there are tournaments of skill, like tennis tournaments. Here there is reason to believe that the players in the later rounds would do better again if they played the players who lost in the early rounds. There is reason to believe— but no guarantee—that the winner of such a tournament is the best player of them all, not just today but tomorrow. Yet, though any well-run tourna­ment is guaranteed to produce a winner, there is no guarantee that a tour­nament of skill will identify the best player as the winner in any nontrivial sense. That's why we sometimes say, in the opening ceremonies, "May the best man win!"—because it is not guaranteed by the procedure. The best player—the one who is best by "engineering" standards (has the most reliable backhand, fastest serve, most stamina, etc.)—may have an off day, or sprain his ankle, or get hit by lightning. Then, trivially, he may be bested in competition by a player who is not really as good as he is. But nobody would bother organizing or entering tournaments of skill if it weren't the case that in the long run, tournaments of skill are won by the best players. That is guaranteed by the very definition of a fair tournament of skill; if there were no probability greater than half that the better players would win each round, it would be a tournament of luck, not of skill.

Skill and luck intermingle naturally and inevitably in any real competi­tion, but their ratios may vary widely. A tennis tournament played on very bumpy courts would raise the luck ratio, as would an innovation in which the players were required to play Russian roulette with a loaded revolver before continuing after the first set. But even in such a luck-ridden contest, more of the better players would tend, statistically, to get to the late rounds. The power of a tournament to "discriminate" skill differences in the long run may be diminished by haphazard catastrophe, but it is not in general reduced to zero. This fact, which is as true of evolutionary algorithms in nature as of elimination tournaments in sports, is sometimes overlooked by commentators on evolution.

Skill, in contrast to luck, is projectable; in the same or similar circum­stances, it can be counted on to give repeat performances. This relativity to circumstances shows us another way in which a tournament might be weird. What if the conditions of competition kept changing (like the croquet game in Alice in Wonderland)? If you play tennis the first round, chess in the second round, golf in the third round, and billiards in the fourth round, there is no reason to suppose the eventual winner will be particularly good, compared with the whole field, in any of these endeavors—all the good golfers may lose in the chess round and never get a chance to demonstrate their prowess, and even if luck plays no role in the fourth-round billiards final, the winner might turn out to be the second-worst billiards player in the whole field. Thus there has to be some measure of uniformity of the conditions of competition for there to be any interesting outcome to a tournament.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

But does a tournament—or any algorithm—have to do something inter­esting? No. The algorithms we tend to talk about almost always do some­thing interesting—that's why they attract our attention. But a procedure doesn't fail to be an algorithm just because it is of no conceivable use or value to anyone. Consider a variation on the elimination-tournament algo­rithm in which the losers of the semi-finals play in the finals. This is a stupid rule, destroying the point of the whole tournament, but the tournament would still be an algorithm. Algorithms don't have to have points or pur­poses. In addition to all the useful algorithms for alphabetizing lists of words, there are kazillions of algorithms for reliably alphabetizing words, and they work perfectly every time ( as if anyone would care ). Just as there is an algorithm (many, actually) for finding the square root of any number, so there are algorithms for finding the square root of any number except 18 or 703. Some algorithms do things so boringly irregular and pointless that there is no succinct way of saying what they are for. They just do what they do, and they do it every time.

We can now expose perhaps the most common misunderstanding of Darwinism: the idea that Darwin showed that evolution by natural selection is a procedure for producing Us. Ever since Darwin proposed his theory, people have often misguidedly tried to interpret it as showing that we are the destination, the goal, the point of all that winnowing and competition, and our arrival on the scene was guaranteed by the mere holding of the tournament. This confusion has been fostered by evolution's friends and foes alike, and it is parallel to the confusion of the coin-toss tournament winner who basks in the misconsidered glory of the idea that since the tournament had to have a winner, and since he is the winner, the tourna­ment had to produce him as the winner. Evolution can be an algorithm, and evolution can have produced us by an algorithmic process, without its being true that evolution is an algorithm for producing us. The main con­clusion of Stephen Jay Gould's Wonderful Life: The Burgess Shale and the Nature of History (1989a) is that if we were to "wind the tape of life back" and play it again and again, the likelihood is infinitesimal of Us being the product on any other run through the evolutionary mill. This is undoubt­edly true (if by "Us" we mean the particular variety of Homo sapiens we are: hairless and upright, with five fingers on each of two hands, speaking English and French and playing tennis and chess). Evolution is not a process that was designed to produce us, but it does not follow from this that evolution is not an algorithmic process that has in fact produced us. (Chap­ter 10 will explore this issue in more detail.)

Evolutionary algorithms are manifestly interesting algorithms—interest­ing to us, at least—not because what they are guaranteed to do is interesting to us, but because what they are guaranteed to tend to do is interesting to us. They are like tournaments of skill in this regard. The power of an algo-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

rithm to yield something of interest or value is not at all limited to what the algorithm can be mathematically proven to yield in a foolproof way, and this is especially true of evolutionary algorithms. Most of the controversies about Darwinism, as we shall see, boil down to disagreements about just how powerful certain postulated evolutionary processes are—could they actu­ally do all this or all that in the time available? These are typically investi­gations into what an evolutionary algorithm might produce, or could produce, or is likely to produce, and only indirectly into what such an algorithm would inevitably produce. Darwin himself sets the stage in the wording of his summary, his idea is a claim about what "assuredly" the process of natural selection will "tend" to yield.

All algorithms are guaranteed to do whatever they do, but it need not be anything interesting; some algorithms are further guaranteed to tend (with probability p) to do something—which may or may not be interesting. But if what an algorithm is guaranteed to do doesn't have to be "interesting" in any way, how are we going to distinguish algorithms from other processes? Won't any process be an algorithm? Is the surf pounding on the beach an algorithmic process? Is the sun baking the clay of a dried-up riverbed an algorithmic process? The answer is that there may be features of these processes that are best appreciated if we consider them as algorithms! Consider, for instance, the question of why the grains of sand on a beach are so uniform in size. This is due to a natural sorting process that occurs thanks to the repetitive launching of the grains by the surf—alphabetical order on a grand scale, you might say. The pattern of cracks that appear in the sun-baked clay may be best explained by looking at chains of events that are not unlike the successive rounds in a tournament.

Or consider the process of annealing a piece of metal to temper it. What could be a more physical, less "computational" process than that? The blacksmith repeatedly heats the metal and then lets it cool, and somehow in the process it becomes much stronger. How? What kind of an explanation can we give for this magical transformation? Does the heat create special toughness atoms that coat the surface? Or does it suck subatomic glue out of the atmosphere that binds all the iron atoms together? No, nothing like that happens. The right level of explanation is the algorithmic level: As the metal cools from its molten state, the solidification starts in many different spots at the same time, creating crystals that grow together until the whole is solid. But the first time this happens, the arrangement of the individual crystal structures is suboptimal—weakly held together, and with lots of internal stresses and strains. Heating it up again—but not all the way to melting—partially breaks down these structures, so that, when they are permitted to cool the next time, the broken-up bits will adhere to the still-solid bits in a different arrangement. It can be proven mathematically that these rearrangements will tend to get better and better, approaching

 

 

 

 

 

 

 

 

 

 

 

 

 

 

the optimum or strongest total structure, provided the regime of heating and cooling has the right parameters. So powerful is this optimization pro­cedure that it has been used as the inspiration for an entirely general problem-solving technique in computer science—"simulated annealing," which has nothing to do with metals or heat, but is just a way of getting a computer program to build, disassemble, and rebuild a data structure (such as another program), over and over, blindly groping towards a better— indeed, an optimal—version (Kirkpatrick, Gelatt and Vecchi 1983)- This was one of the major insights leading to the development of "Boltzmann machines" and "Hopfield nets" and the other constraint-satisfaction schemes that are the basis for the Connectionist or "neural-net" architectures in Artificial Intelligence. (For overviews, see Smolensky 1983, Rumelhart 1989, Churchland and Sejnowski 1992, and, on a philosophical level, Den­nett 1987a, Paul Churchland 1989.)

If you want a deep understanding of how annealing works in metallurgy, you have to learn the physics of all the forces operating at the atomic level, of course, but notice that the basic idea of how annealing works (and particularly why it works) can be lifted clear of those details—after all, I just explained it in simple lay terms (and I don't know the physics!). The ex­planation of annealing can be put in substrate-neutral terminology: we should expect optimization of a certain sort to occur in any "material" that has components that get put together by a certain sort of building process and that can be disassembled in a sequenced way by changing a single global parameter, etc. That is what is common to the processes going on in the glowing steel bar and the humming supercomputer.

Darwin's ideas about the powers of natural selection can also be lifted out of their home base in biology. Indeed, as we have already noted, Darwin himself had few inklings (and what inklings he had turned out to be wrong) about how the microscopic processes of genetic inheritance were accom­plished. Not knowing any of the details about the physical substrate, he could nevertheless discern that if certain conditions were somehow met, certain effects would be wrought. This substrate neutrality has been crucial in permitting the basic Darwinian insights to float like a cork on the waves of subsequent research and controversy, for what has happened since Dar­win has a curious flip-flop in it. Darwin, as we noted in the preceding chapter, never hit upon the utterly necessary idea of a gene, but along came Mendel's concept to provide just the right structure for making mathemat­ical sense out of heredity (and solving Darwin's nasty problem of blending inheritance). And then, when DNA was identified as the actual physical vehicle of the genes, it looked at first (and still looks to many participants) as if Mendel's genes could be simply identified as particular hunks of DNA. But then complexities began to emerge; the more scientists have learned about the actual molecular biology of DNA and its role in reproduction, the

 

 

 

 

 

 

 

 

 

 

 

 

 

 

clearer it becomes that the Mendelian story is at best a vast oversimplifica­tion. Some would go so far as to say that we have recently learned that there really aren't any Mendelian genes! Having climbed Mendel's ladder, we must now throw it away. But of course no one wants to throw away such a valuable tool, still proving itself daily in hundreds of scientific and medical contexts. The solution is to bump Mendel up a level, and declare that he, like Darwin, captured an abstract truth about inheritance. We may, if we like, talk of virtual genes, considering them to have their reality distributed around in the concrete materials of the DNA. (There is much to be said in favor of this option, which I will discuss further in chapters 5 and 12.)

But then, to return to the question raised above, are there any limits at all on what may be considered an algorithmic process? I guess the answer is No; if you wanted to, you could treat any process at the abstract level as an algorithmic process. So what? Only some processes yield interesting results when you do treat them as algorithms, but we don't have to try to define "algorithm" in such a way as to include only the interesting ones (a tall philosophical order!). The problem will take care of itself, since nobody will waste time examining the algorithms that aren't interesting for one reason or another. It all depends on what needs explaining. If what strikes you as puzzling is the uniformity of the sand grains or the strength of the blade, an algorithmic explanation is what will satisfy your curiosity—and it will be the truth. Other interesting features of the same phenomena, or the pro­cesses that created them, might not yield to an algorithmic treatment.

Here, then, is Darwin's dangerous idea: the algorithmic level is the level that best accounts for the speed of the antelope, the wing of the eagle, the shape of the orchid, the diversity of species, and all the other occasions for wonder in the world of nature. It is hard to believe that something as mindless and mechanical as an algorithm could produce such wonderful things. No matter how impressive the products of an algorithm, the underlying process always consists of nothing but a set of individually mindless steps succeeding each other without the help of any intelligent supervision; they are "auto­matic" by definition: the workings of an automaton. They feed on each other, or on blind chance—coin-flips, if you like—and on nothing else. Most algorithms we are familiar with have rather modest products: they do long division or alphabetize lists or figure out the income of the Average Taxpayer. Fancier algorithms produce the dazzling computer-animated graphics we see every day on television, transforming faces, creating herds of imaginary ice-skating polar bears, simulating whole virtual worlds of entities never seen or imagined before. But the actual biosphere is much fancier still, by many orders of magnitude. Can it really be the outcome of nothing but a cascade of algorithmic processes feeding on chance? And if so, who designed that cascade? Nobody. It is itself the product of a blind, algorithmic process. As Darwin himself put it, in a letter to the geologist Charles Lyell shortly after

 

 

 

 

 

 

 

 

 

 

 

 

 

 

publication of Origin, "I would give absolutely nothing for the theory of Natural Selection, if it requires miraculous additions at any one stage of

descent.  If I were convinced that I required such additions to the theory

of natural selection, I would reject it as rubbish..." (F. Darwin 1911, vol. 2, pp. 6-7).

According to Darwin, then, evolution is an algorithmic process. Putting it this way is still controversial. One of the tugs-of-war going on within evo­lutionary biology is between those who are relentlessly pushing, pushing, pushing towards an algorithmic treatment, and those who, for various sub­merged reasons, are resisting this trend. It is rather as if there were metal­lurgists around who were disappointed by the algorithmic explanation of annealing. "You mean that's all there is to it? No submicroscopic Superglue specially created by the heating and cooling process?" Darwin has con­vinced all the scientists that evolution, like annealing, works. His radical vision of how and why it works is still somewhat embattled, largely because those who resist can dimly see that their skirmish is part of a larger cam­paign. If the game is lost in evolutionary biology, where will it all end?

Chapter 2: Darwin conclusively demonstrated that, contrary to ancient tradition, species are not eternal and immutable; they evolve. The origin of new species was shown to be the result of "descent with modification." Less conclusively, Darwin introduced an idea of how this evolutionary process took place: via a mindless, mechanical—algorithmic—process he called "natural selection." This idea, that all the fruits of evolution can be ex­plained as the products of an algorithmic process, is Darwin's dangerous idea.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CHAPTER FIVE (last two sections omitted)

The Possible and the Actual

1. Grades of Possibility?

However many ways there may be of being alive, it is certain that there are vastly more ways of being dead, or rather not alive.

—Richard Dawkjns 1986a, p. 9

Any particular non-existent form of life may owe its absence to one of two reasons. One is negative selection. The other is that the necessary mutations have never appeared.

—Mark Ridley 1985, p. 56

Take, for instance, the possible fat man in that doorway; and, again, the possible bald man in that doorway. Are they the same possible man, or two possible men? How do we decide? How many possible men are there in that doorway? Are there more possible thin ones than fat ones? How many of them are alike? Or would their being alike make them one? Are no two possible things alike? Is this the same as saying that it is impossible for two things to be alike? Or, finally, is the concept of identity simply inapplicable to unactualized possibles?

—Wiliard Van Orman Quine 1953, p. 4

There seem to be at least four different kinds or grades of possibility: logical, physical, biological, and historical, nested in that order. The most lenient is mere logical possibility, which according to philosophical tradition is simply a matter of being describable without contradiction. Super-

man, who flies faster than the speed of light, is logically possible, but Duperraan, who flies faster than the speed of light without moving anywhere, is not even logically possible. Superman, however, is not physically possible, since a law of physics proclaims that nothing can move faster than the speed of light. There is no dearth of difficulties with this superficially straightforward distinction. How do we distinguish fundamental physical laws from logical laws? Is it physically or logically impossible to travel backwards in time, for instance? How could we tell for sure whether a description that is apparently coherent—such as the story in the film Back to the Future—is subtly self-contradictory or merely denies a very fundamental ( but not logically necessary) assumption of physics? There is also no dearth of philosophy dealing with these difficulties, so we will just acknowledge them and pass on to the next grade.

Superman flies by simply leaping into the air and striking a gallant midair pose, a talent which is certainly physically impossible. Is a flying horse physically possible? The standard model from mythology would never get off the ground—a fact from physics (aerodynamics), not biology—but a horse with suitable wingspan could presumably stay aloft. It might have to be a tiny horse, something aeronautical engineers might calculate from considerations of weight-strength ratios, the density of air, and so forth. But now we are descending into the third grade of possibility, biological possibility, for once we begin considering the strength of bones, and the pay-load requirements for keeping the flapping machinery going, we concern ourselves with development and growth, metabolism, and other clearly biological phenomena. Still, the verdict may appear to be that of course flying horses are biologically possible, since bats are actual. Maybe even full-sized flying horses are possible, since there once were pteranodons and other flying creatures approaching that size. There is nothing to beat actuality, present or past, for clinching possibility. Whatever is or has been actual is obviously possible. Or is it?

The lessons of actuality are hard to read. Could such flying horses really be viable? Would they perhaps need to be carnivorous to store enough energy and carry it aloft? Perhaps—in spite of fruit-eating bats—only a carnivorous horse could get off the ground. Is a carnivorous horse possible? Perhaps a carnivorous horse would be biologically possible if it could evolve, but would such a diet shift be accessible from where horses would have to start? And, short of radical constructive surgery, could a horse-descendant have both front legs and wings? Bats, after all, make wings of their arms. Is there any possible evolutionary history of skeletal revision that would yield a six-limbed mammal?

This brings us to our fourth grade of possibility, historical possibility. There might have been a time, in the very distant past, when the possibility of six-limbed mammals on Earth had not yet been foreclosed, but it mieht

also be true that once our four-finned fishy ancestors got selected for moving onto the land, the basic four-limbed architecture was so deeply anchored in our developmental routines that alteration at this time is no longer possible. But even that distinction may not be sharp-edged. Is such an alteration in fundamental building-plan flat impossible, or just highly unlikely, so resistant to change that only an astronomically improbable sequence of selective blows could drive it into existence? It seems there might be two kinds or grades of biological impossibility: violation of a biological law of nature (if there are any), and "mere" biohistorical consignment to oblivion.

Historical impossibility is simply a matter of opportunities passed up. There was a time when many of us worried about the possibility of President Barry Goldwater, but it didn't happen, and after 1964, the odds against such a thing's ever happening lengthened reassuringly. When lottery tickets are put on sale, this creates an opportunity for you: you may choose to buy one, provided you act by a certain date. If you buy one, this creates a further opportunity for you—the opportunity to win—but soon it slides into the past, and it is no longer possible for you to win those millions of dollars. Is this everyday vision we have of opportunities—real opportunities—an illusion? In what sense could you have won? Does it make a diflFerence if the winning lottery number is chosen after you buy your ticket, or do you still have an opportunity to win, a real opportunity, if the winning number is sealed in a vault before the tickets are put on sale (Dennett 1984)? Is there ever really any opportunity at all? Could anything happen other than what actually happens? This dread hypothesis, the idea that only the actual is possible, has been called actualism (Ayers 1968). It is generally ignored, for good reasons, but these reasons are seldom discussed. (Dennett 1984, and Lewis 1986, pp. 36-38, offer good reasons for dismissing actualism.)

These familiar and prima facie reliable ideas about possibility can be summed up in a diagram, but every boundary in it is embattled. As Quine's questions suggest, there is something fishy about casual catalogues of merely possible objects, but since science cannot even express—let alone confirm—the sorts of explanations we crave without drawing such a distinction, there is little chance that we can simply renounce all such talk. When biologists wonder whether a horned bird—or even a giraffe with stripes instead of blotches—is possible, the questions they are addressing epitomize what we want biology to discover for us. Alerted by Quine, we can be struck by the dubious metaphysical implications of Richard Dawkins' vivid claim that there are many more ways of being dead than of being alive, but manifestly he is getting at something important. We should try to find a way of recasting such claims in a metaphysically more modest and less contentious framework—and Darwin's starting in the middle gives us just the foothold we need. First we can deal with the relation between historical and

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biological possibility, and then perhaps it will suggest some payoffs for how to make sense of the grander varieties.1

2. The Library of Mendel

The Argentine poet Jorge Luis Borges is not typically classified as a philosopher, but in his short stories he has given philosophy some of its most valuable thought experiments, most of them gathered in the stunning collection Labyrinths (1962). Among the best is the fantasy—actually, it is more a philosophical reflection than a narrative—that describes the Library of Babel. For us, the Library of Babel will be an anchoring vision for helping to answer very difficult questions about the scope of biological possibility, so we will pause to explore it at some length. Borges tells of the forlorn explorations and speculations of some people who find themselves living in

1. Back in 1982, Francois Jacob, the Nobel laureate biologist, published a book entitled The Possible and the Actual, and I rushed to read it, expecting it to be an eye-opening essay on how biologists should think about some of these conundrums about possibility. To my disappointment, the book had very little to say on this topic. It is a fine book, and has a great title, but the two don't go together, in my humble opinion. The book I was eager to read hasn't yet been written, apparently, so I'll have to try to write part of it myself, in this chapter.

a vast storehouse of books, structured like a honeycomb, composed of thousands (or millions or billions) of hexagonal air shafts surrounded by balconies lined with shelves. Standing at a railing and looking up or down, one sees no top or bottom to these shafts. Nobody has ever found a shaft that isn't surrounded by six neighboring shafts. They wonder: is the warehouse infinite? Eventually, they decide that it is not, but it might as well be, for it seems that on its shelves—in no order, alas—lie all the possible books.

Suppose that each book is 500 pages long, and each page consists of 40 lines of 50 spaces, so there are two thousand character-spaces per page. Each space either is blank, or has a character printed on it, chosen from a set of 100 (the upper- and lowercase letters of English and other European languages, plus the blank and punctuation marks).2 Somewhere in the Library of Babel is a volume consisting entirely of blank pages, and another volume is all question marks, but the vast majority consist of typographical gibberish; no rules of spelling or grammar, to say nothing of sense, prohibit the inclusion of a volume. Five hundred pages times 2,000 characters per page gives 1,000,000 character-spaces per book, so there are ioo1000000 books in the library of Babel. Since it is estimated3 that there are only 10040 (give or take a few) particles (protons, neutrons, and electrons) in the region of the universe we can observe, the Library of Babel is not remotely a physically possible object, but, thanks to the strict rules with which Borges constructed it in his imagination, we can think about it clearly.

Is this truly the set of all possible books? Obviously not—since they are restricted to being printed from "only" 100 different characters, excluding, we may suppose, the characters of Greek, Russian, Chinese, Japanese, and Arabic, thereby overlooking many of the most important actual books. Of course, the Library does contain superb translations of all these actual books into English, French, German, Italian,..., as well as uncountable trillions of shoddy translations of each book. Books of more than 500 pages are there,

2.  Borges chose slightly different figures: books 410 pages long, with 40 lines of 80 characters each. The total number of characters per book is close enough to mine (1,312,000 versus 1,000,000) to make no difference. I chose my rounder numbers for ease of handling. Borges chose a character set with only 25 members, which is enough for uppercase Spanish (with a blank, a comma, and a period as the only punctuation), but not for English. I chose the more commodious 100 to make room without any doubt for the upper- and lowercase letters and punctuation of all the Roman-alphabet languages.

3. Stephen Hawking (1988, p. 129) insists on putting it this way: "There are something like ten million million million million million million million million million million million million million (1 with eighty zeroes after it) particles in the region of the universe that we can observe." Denton (1985 ) provides the estimate of 1070 atoms in the observable universe. Eigen (1992, p. 10) calculates the volume of the universe as 1084 rnhir centimeters.

beginning in one volume and continuing without a break in some other volume or volumes.

It is amusing to think about some of the volumes that must be in the Library of Babel somewhere. One of them is the best, most accurate 500-page biography of you, from the moment of your birth until the moment of your death. Locating it, however, would be all but impossible (that slippery word), since the Library also contains kazillions of volumes that are magnificently accurate biographies of you up till your tenth, twentieth, thirtieth, fortieth ... birthday, and completely false about subsequent events of your life—in a kazillion different and diverting ways. But even finding one readable volume in this huge storehouse is unlikely in the extreme.

We need some terms for the quantities involved. The Library of Babel is not infinite, so the chance of finding anything interesting in it is not literally infinitesimal.4 These words exaggerate in a familiar way—we caught Darwin doing it in his summary, where he helped himself to an illicit "infinitely"— but we should avoid them. Unfortunately, all the standard metaphors— "astronomically large," "a needle in a haystack," "a drop in the ocean"—fall comically short. No actual astronomical quantity (such as the number of elementary particles in the universe, or the time since the Big Bang measured in nanoseconds) is even visible against the backdrop of these huge but finite numbers. If a readable volume in the Library were as easy to find as a particular drop in the ocean, we'd be in business! If you were dropped at random into the Library, your chance of ever encountering a volume with so much as a grammatical sentence in it would be so vanishingly small that we might do well to capitalize the term—"Vanishingly" small—and give it a mate, "Vastly," short for "Very-much-more-than-astronomically."5

Moby Dick is in the Library of Babel, of course, but so are 100,000,000 mutant impostors that differ from the canonical Moby Dick by a single

4.  The Library of Babel is finite, but, curiously enough, it contains all the grammatical sentences of English within its walls. But that's an infinite set, and the library is finite! Still, any sentence of English, of whatever length, can be broken down into 500-page chunks, each of which is somewhere in the library! How is this possible? Some books may get used more than once. The most profligate case is the easiest to understand: since there are volumes that each contain a single character and are otherwise blank, repeated use of these 100 volumes will create any text of any length. As Quine points out in his informative and amusing essay "Universal Library" (in Quine 1987), if you avail yourself of this strategy of re-using volumes, and translate everything into the ASCII code your word-processor uses, you can store the whole Library of Babel in two extremely slender volumes, in one of which is printed a 0 and in the other of which appears a 1! ( Quine also points out that the psychologist Theodor Fechner propounded the fantasy of the universal library long before Borges.)

5. Quine (1987) coins the term "hyperastronomic" for the same purpose.

typographical error. That's not yet a Vast number, but the total rises swiftly when we add the variants that differ by 2 or 10 or 1,000 typos. Even a volume with 1,000 typos—2 per page on average—would be unmistakably recognizable as Moby Dick, and there are Vastly many of those volumes. It wouldn't matter which of these volumes you found, if you could only find one of them. They would almost all be just about equally wonderful reading, and all tell the same story, except for truly negligible—almost indiscrim-inable—differences. Not quite all of them, however. Sometimes a single typo, in a crucial position, can be fatal. Peter De Vries, another philosophically delicious writer of fiction, once published a novel6 that began-.

"Call me, Ishmael."

Oh, what a single comma can do! Or consider the many mutants that begin: "Ball me Ishmael___"

In Borges' story, the books are not shelved in any order, but even if we found them scrupulously alphabetized, we would have insoluble problems finding the book we were looking for (for instance, the "essential" version of Moby Dick). Imagine traveling by spaceship through the Moby Dick galaxy of the Library of Babel. This galaxy is in itself Vastly larger than the whole physical universe, so, no matter what direction you go in, for centuries on end, even if you travel at the speed of light, all you see are virtually indistinguishable copies of Moby Dick—you will never ever reach anything that looks like anything else. David Copperfteld is unimaginably distant in this space, even though we know that there is a path—a shortest path, ignoring the kazillions of others—leading from one great book to the other by single typographical changes. (If you found yourself on this path, you would find it almost impossible to tell, by local inspection, which direction to go to move towards David Copperfleld, even if you had texts of both target books in hand.)

In other words, this logical space is so Vast that many of our usual ideas about location, about searching and finding and other such mundane and practical activities, have no straightforward application. Borges put the books on the shelves in random order, a nice touch from which he drew several delectable reflections, but look at the problems he would have

6. The Vale of Laughter (1953). (It goes on: "Feel absolutely free to. Call me any hour of the day or night...." ) De Vries also may have invented the game of seeing how large an effect (deleterious or not) you can achieve with a single typographical change. One

of the best: "Whose woods are these, I think I know; his house is in the Village though___"

Others have taken up the game: in the state of nature, mutant-Hobbes tells us, one finds "the wife of man, solitary, poore, nasty, brutish, and short." Or consider the question: "Am I my brother's keeper?"

created for himself if he'd tried to arrange them in alphabetical order in his honeycomb. Since there are only a hundred different alphabetic characters (in our version), we can treat some specific sequence of them as Alphabetical Order—e.g., a, A, b, B, c, C ... z, Z, ?, ;, „.,!,),(,%,... a, a, e, e, e,... Then we can put all the books beginning with the same character on the sameyfoor. Now our library is only 100 stories high, shorter than the World Trade Center. We can divide each floor into 100 corridors, each of which we line with the books whose second character is the same, one corridor for each character, in alphabetical order. On each corridor, we can place 100 shelves, one for each third-slot. Thus all the books that begin with "aardvarks love Mozart"—and how many there are!—are shelved on the same shelf (the "r" shelf) in the first corridor on the first floor. But that's a mighty long shelf, so perhaps we had better stack the books in file drawers at right angles to the shelf, one drawer for each fourth-letter position. That way, each shelf can be only, say, 100 feet long. But now the file drawers are awfully deep, and will run into die backs of the file drawers in the neighboring corridor, so ... but we've run out of dimensions in which to line up the books. We need a million-dimensional space to store all the books neatly, and all we have is three dimensions: up-down, left-right, and front-back. So we will just have to pretend we can imagine a multidimensional space, each dimension running "at right angles" to all the others. We can conceive of such hyperspaces, as they are called, even if we can't visualize them. Scientists use them ah" the time to organize the expression of their theories. The geometry of such spaces (whether or not they count as only imaginary) is well behaved and well explored by mathematicians. We can confidently speak about locations, paths, trajectories, volumes (hypervol-umes), distances, and directions in these logical spaces.

We are now prepared to consider a variation on Borges' theme, which I will call the Library of Mendel. This Library contains "all possible genomes"—DNA sequences. Richard Dawkins describes a similar space, which he calls "Biomorph Land," in The Blind Watchmaker (1986a). His discussion is the inspiration for mine, and our two accounts are entirely compatible, but I want to stress some points he chose to pass over lightly.

If we consider the Library of Mendel to be composed of descriptions of genomes, then it is already just a proper part of the Library of Babel. The standard code for describing DNA consists of only four characters, A, C, G, and T (standing for Adenine, Cytosine, Guanine, and Thymine, the four kinds of nucleotides that compose the letters of the DNA alphabet). All the 500-page permutations of these four letters are already in the Library of Babel. Typical genomes are much longer than ordinary books, however. Taking the current estimate of 3 X 109 nucleotides in the human genome, the exhaustive description of a single human genome—such as your own— would take approximately 3,000 of the 500-page volumes in the Library of

Babel (keeping print size the same).7 The description of the genome for a horse (flying or not) or a cabbage or an octopus would be composed of the same letters, A, C, G, and T, and certainly not much longer, so we can suppose, arbitrarily, that the Library of Mendel consists of all the DNA strings described in all the 3,000-volume boxed sets consisting entirely of those four characters. This will capture enough of the "possible" genomes to serve any serious theoretical purpose.

I overstated the case in describing the Library of Mendel as containing "all possible" genomes, of course. Just as the Library of Babel ignored the Russian and Chinese languages, so the Library of Mendel ignores the (apparent) possibility of alternative genetic alphabets—based on different chemical constituents, for instance. We are still beginning in the middle, making sure we understand today's local, earthly circumstances before casting our nets wider. So any conclusions we come to regarding what is possible relative to this Library of Mendel may have to be reconsidered when we try to apply them to some broader notion of possibility. This is actually a strength rather than a weakness of our tactic, since we can keep close tabs on exactly what sort of modest, circumscribed possibility we are talking about.

One of the important features of DNA is that all the permutations of sequences of Adenine, Cytosine, Guanine, and Thymine are about equally stable, chemically. All could be constructed, in principle, in the gene-

7. The comparison of a human genome with the volumes in the galaxy of Moby Dick readily explains something that occasionally baffles people about the Human Genome Project. How can scientists speak of sequencing (copying down) the human genome if every human genome is different from every other in not just one but hundreds or thousands of places {loci, in the language of genetics)? like the proverbial snowflakes, or fingerprints, no two actual human genomes are exactly alike, even those of identical twins (the chance of typos creeping in is always present, even in the cells of a single individual). Human DNA is readily distinguishable from the DNA of any other species, even that of the chimpanzee, which is over 90 percent the same at every locus. Every actual human genome that has ever existed is contained within a galaxy of possible human genomes that is Vastly distant from the galaxies of other species' genomes, yet within the galaxy there is plenty of room for no two human genomes to be alike. You have two versions of each of your genes, one from your mother and one from your father. They passed on to you exactly half of their own genes, randomly selected from those they received from their parents, your grandparents, but since your grandparents were all members of Homo sapiens, their genomes agree at almost all loci, so it makes no difference most of the time which grandparent provides either of your genes. But their genomes nevertheless differ at many thousands of loci, and in those slots, which genes you get is a matter of chance—a coin-toss built into the machinery for forming your parents' contributions to your DNA. Moreover, mutations accumulate at the rate of about 100 per genome per generation in mammals. "That is, your children will have one hundred differences from you and your spouse in their genes as a result of random copying errors by your enzymes or as a result of mutations in your ovaries or testicles caused by cosmic rays" (Matt Ridley 1993,

splicing laboratory, and, once constructed, would have an indefinite shelf life, like a book in a library. But not every such sequence in the Library of Mendel corresponds to a viable organism. Most DNA sequences—the Vast majority—are surely gibberish, recipes for nothing living at all. That is what Dawkins means, of course, when he says there are many more ways of being dead (or not alive) than ways of being alive. But what kind of a fact is this, and why should it be so?

Chapter 5: Biological possibility is best seen in terms of accessibility (from some stipulated location) in the Library of Mendel, the logical space of all genomes. This concept of possibility treats the connectedness of the Tree of Life as a fundamental feature of biology, while leaving it open that there may also be biological laws that will also constrain accessibility.