Darwin's Dangerous Idea (20 page)

course, the Library does contain superb translations of all these actual books
Moby Dick
is in the Library of Babel, of course, but so are 100,000,000

into English, French, German, Italian,..., as well as uncountable trillions of mutant impostors that differ from the canonical
Moby Dick
by a
single
shoddy translations of each book. Books of more than 500 pages are there, 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, 2. Borges chose slightly different figures: books 410 pages long, with 40 lines of 80

any sentence of English, of whatever length, can be broken down into 500-page chunks, characters each. The total number of characters per book is close enough to mine each of which is somewhere in the library! How is this possible? Some books may get (1,312,000 versus 1,000,000) to make no difference. 1 chose my rounder numbers for used more than once. The most profligate case is the easiest to understand: since there ease of handling. Borges chose a character set with only 25 members, which is enough are volumes that each contain a single character and are otherwise blank, repeated use of for uppercase Spanish (with a blank, a comma, and a period as the only punctuation ), but these 100 volumes will create any text of any length. As Quine points out in his infor-not for English. I chose the more commodious 100 to make room without any doubt for mative and amusing essay "Universal Library" (in Quine 1987), if you avail yourself of the upper- and lowercase letters and punctuation of all the Roman-alphabet languages.

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 3. Stephen Hawking (1988, p. 129) insists on putting it this way: "There are something volumes, in one of which is printed a 0 and in the other of which appears a 1! (Quine also like ten million million million million million million million million million million points out that the psychologist Theodor Fechner propounded the fantasy of the univer-million million million (1 with eighty zeroes after it) particles in the region of the sal library long before Borges.)

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

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

cubic centimeters.

110 THE POSSIBLE AND THE ACTUAL

The Library of Mendel
111

typographical error. That's not yet a Vast number, but the total rises swiftly created for himself if he'd tried to arrange them in alphabetical order in his when we add the variants that differ by 2 or 10 or 1,000 typos. Even a honeycomb. Since there are only a hundred different alphabetic characters (in volume with 1,000 typos—2 per page on average—would be unmistakably our version), we can treat some specific sequence of them as Alphabetical recognizable as
Moby Dick,
and there are Vastly many of those volumes. It Order—e.g., a, A, b, B, c, C ... z, Z, ? , ; , „ . , ! , ) , ( , % , . . . a, a, e´, è, e,... Then wouldn't matter which of these volumes you found, if you could only find we can put all the books beginning with the same character on the same
floor.

one of them. They would almost all be just about equally wonderful reading, Now our library is only 100 stories high, shorter than the World Trade and all tell the same story, except for truly negligible—almost indiscrim-Center. We can divide each floor into 100
corridors,
each of which we line inable—differences. Not quite all of them, however. Sometimes a single with the books whose second character is the same, one corridor for each typo, in a crucial position, can be fatal. Peter De Vries, another philosoph-character, in alphabetical order. On each corridor, we can place 100
shelves,
ically delicious writer of fiction, once published a novel6 that began: 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"

"Call me, Ishmael."

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 Oh, what a single comma can do! Or consider the many mutants that begin: shelf, one drawer for each fourth-letter position. That way, each shelf can be

"Ball me Ishmael __ "

only, say, 100 feet long. But now the file drawers are awfully deep, and will In Borges' story, the books are not shelved in any order, but even if we run into the backs of the file drawers in the neighboring corridor, so ... but found them scrupulously alphabetized, we would have insoluble problems we've run out of dimensions in which to line up the books. We need a finding
the
book we were looking for (for instance, the "essential" version of million-dimensional space to store all the books neatly, and all we have is
Moby Dick).
Imagine traveling by spaceship through the
Moby Dick
galaxy three dimensions: up-down, left-right, and front-back. So we will just have to of the Library of Babel. This galaxy is in itself Vastly larger than the whole pretend we can imagine a multidimensional space, each dimension running physical universe, so, no matter what direction you go in, for centuries on

"at right angles" to all the others. We can conceive of such hyperspaces, as end, even if you travel at the speed of light, all you see are virtually they are called, even if we can't visualize them. Scientists use them all the indistinguishable copies of
Moby Dick
—you will never ever reach anything time to organize the expression of their theories. The geometry of such that looks like anything else.
David Copperfield
is unimaginably distant in spaces (whether or not they count as only imaginary) is well behaved and this space, even though we know that there is a path—a shortest path, well explored by mathematicians. We can confidently speak about locations, ignoring the kazillions of others—leading from one great book to the other paths, trajectories, volumes (hypervol-umes), distances, and directions in by single typographical changes. (If you found yourself on this path, you these logical spaces.

would find it almost impossible to tell, by local inspection, which direction to We are now prepared to consider a variation on Borges' theme, which I go to move towards
David Copperfield,
even if you had texts of both target will call the
Library of Mendel.
This Library contains "all possible ge-books in hand.)

nomes"—DNA sequences. Richard Dawkins describes a similar space, which In other words, this
logical
space is so Vast that many of our usual ideas he calls "Biomorph Land," in
The Blind Watchmaker
(1986a). His discussion about location, about searching and finding and other such mundane and is the inspiration for mine, and our two accounts are entirely compatible, but practical activities, have no straightforward application. Borges put the books I want to stress some points he chose to pass over lightly.

on the shelves in random order, a nice touch from which he drew several If we consider the Library of Mendel to be composed of
descriptions
of delectable reflections, but look at the problems he would have 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 6.
The Yale of Laughter
(1953). (It goes on: "Feel absolutely free to. Call me any hour 500-page permutations of these four letters are already in the Library of 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 Babel. Typical genomes are much longer than ordinary books, however.

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

Taking the current estimate of 3 X 109 nucleotides in the human genome, the Others have taken up the game: in the state of nature, mutant-Hobbes tells us, one finds exhaustive description of a single human genome—such as your own—

"the wife of man, solitary, poore, nasty, brutish, and short." Or consider the question: "Am would take approximately 3,000 of the 500-page volumes in the Library of I my brothe/'s keeper?"

112 THE POSSIBLE AND THE ACTUAL

The Complex Relation Between Genome and Organism
113

Babel (keeping print size the same).7 The description of the genome for a splicing laboratory, and, once constructed, would have an indefinite shelf horse (flying or not) or a cabbage or an octopus would be composed of the life, like a book in a library. But not every such sequence in the Library of same letters, A, C, G, and T, and certainly not much longer, so we can Mendel corresponds to a viable organism. Most DNA sequences—the Vast suppose, arbitrarily, that the Library of Mendel consists of all the DNA majority—are surely gibberish, recipes for nothing living at all. That is what strings described in all the 3,000-volume boxed sets consisting entirely of Dawkins means, of course, when he says there are many more ways of being those four characters. This will capture enough of the "possible" genomes to dead (or not alive) than ways of being alive. But what kind of a fact is this, serve any serious theoretical purpose.

and why should it be so?

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 (ap-3. THE COMPLEX RELATION BETWEEN GENOME AND

parent) possibility of alternative genetic alphabets—based on different chemical constituents, for instance. We are
still
beginning in the middle, ORGANISM

making sure we understand today's local, earthly circumstances before casting our nets wider. So any conclusions we come to regarding what is possible If we are going to try to make progress by boldly oversimplifying, we should relative
to this
Library of Mendel may have to be reconsidered when we try at least alert ourselves to some of the complications we are temporarily to apply them to some broader notion of possibility. This is actually a strength setting aside. I see three main sorts of complexity we should acknowledge rather than a weakness of our tactic, since we can keep close tabs on exactly and keep an eye on as we proceed, even if we are once again postponing what sort of modest, circumscribed possibility we are talking about.

their full discussion.

One of the important features of DNA is that all the permutations of The first concerns the "reading" of the "recipe." The Library of Babel sequences of Adenine, Cytosine, Guanine, and Thymine are about equally presupposed readers: the people who inhabited the Library. Without them, the stable, chemically. All could be constructed, in principle, in the gene-very idea of the collection of volumes would make no sense at all; their pages might as well be smeared with jam or worse. If we are to make any sense of the Library of Mendel, we must also presuppose something analogous to readers, for without readers DNA sequences don't
specify
anything at all—not 7. The comparison of a human genome with the volumes in the galaxy of
Moby Dick
blue eyes or wings or anything else. Deconstructionists will tell you that no
readily
explains something that occasionally baffles people about the Human Genome two readers of a text will come up with the same reading, and something Project. How can scientists speak of sequencing (copying down)
the
human genome if similar is undoubtedly true when we consider the relationship between a 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 genome and the embryonic environment—the chemical mi-croenvironment fingerprints, no two actual human genomes are exactly alike, even those of identical twins as well as the surrounding support conditions—in which it has its (the chance of typos creeping in is always present, even in the cells of a single individ-informational effects. The immediate effect of the "reading" of DNA during ual). Human DNA is readily distinguishable from the DNA of any other species, even that the creation of a new organism is the fabrication of many different proteins of the chimpanzee, which is over 90 percent the same at every locus. Every actual human out of amino acids (which have to be on hand in the vicinity, of course, ready 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 to be linked together). There are Vastly many possible proteins, but which there is plenty of room for no two human genomes to be alike. You have two versions of become actual depends on the DNA text. These proteins get created in strict each of your genes, one from your mother and one from your father. They passed on to sequence, and in amounts determined by the "words"— triplets of you exactly half of their own genes, randomly selected from those they received from nucleotides—as they are "read." So, for a DNA sequence to specify what it is 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 supposed to specify, there must be an elaborate reader-constructor, well which grandparent provides either of your genes. But their genomes nevertheless differ stocked with amino-acid building blocks.8 But that is just a small part of the at many thousands of loci, and in those slots, which genes you get is a matter of chance—a process. Once the proteins get created, they have to be coin-toss built into the machinery for forming your parents' contributions to your DNA.