Saturday, April 4, 2015
Borges, Plato, & Natural Selection
Tomas Luis Borges had an astonishing genius for channeling vast currents in the history of ideas into the narrow stream of a compelling story. One of his most frequently mentioned stories was “The Library of Babel”. It begins with these words:
The universe (which others call the Library) is composed of an indefinite and perhaps infinite number of hexagonal galleries, with vast air shafts between, surrounded by very low railings. From any of the hexagons one can see, interminably, the upper and lower floors. The distribution of the galleries is invariable. Twenty shelves, five long shelves per side, cover all the sides except two; their height, which is the distance from floor to ceiling, scarcely exceeds that of a normal bookcase. One of the free sides leads to a narrow hallway which opens onto another gallery, identical to the first and to all the rest.
If you haven’t read the story, I am about to do you the terrible disservice of spoiling the end. I can only offer the defense that many more people have read about the story than have actually read the story.
The library consists of a vast but not infinite set of books.
There are five shelves for each of the hexagon's walls; each shelf contains thirty-five books of uniform format; each book is of four hundred and ten pages; each page, of forty lines, each line, of some eighty letters which are black in color. There are also letters on the spine of each book; these letters do not indicate or prefigure what the pages will say… Second: The orthographical symbols are twenty-five in number.
The library consists of all the books that are logically possible, given the parameters just listed. To say that this library would be vast is meaningful only in the strictest mathematical sense. It would be, to say the least, astronomical in extent. Consider that in this library somewhere is a perfect copy of Shakespeare’s Richard III. There is also a copy of Dickey Three with alternative endings, including one in which the villain is rescued by the Mighty Morphin’ Power Rangers. There are perfectly accurate histories of the life of every single human being and indeed every single organism along with alternative histories. In one of them I am married to two Victoria’s Secret models.
Of course, all of the coherent reads will be only a drop in the bucket. Most of the books will be incoherent jumbles of nonsense. One of the books will consist of nothing but the word “word” over and over again.
This brilliant thought problem, in the form of a librarian’s musings on the bizarre world that he inhabits, is another version of the infamous infinite monkey theorem. Could a set of monkeys (say 100), typing randomly, eventually produce a copy of Richard III? According to the theorem, which I believe to be logically sound, the answer is “yes, given enough time”. However, the time required is unimaginably vast. Even to produce “Now is the winter of our discontent” would require more time, I recently calculated, than the age of the Kosmos itself. Along the way you would get a vast number of half finished, garbled, and alternative versions.
Darwin’s great idea was to explain how you could get Shakespeare himself out of processes just as random as our team of monkeys or Borges’ library. All you need is some device that persistently steers the primates in the right direction. If the monkeys keep typing now is the winter over and over again until they get the next letter right and then keep typing that… That is what natural selection does.
These reflections were set in motion by wonderful essay in Aeon. Andreas Wagner, professor in the Institute of Evolutionary Biology and Environmental Studies at the University of Zurich and at the Santa Fe Institute in New Mexico, argues that Darwinian evolution could not work without “nature’s library of Platonic forms.”
How do random DNA changes lead to innovation? Darwin’s concept of natural selection, although crucial to understand evolution, doesn’t help much. The thing is, selection can only spread innovations that already exist. The botanist Hugo de Vries said it best in 1905: ‘Natural selection can explain the survival of the fittest, but it cannot explain the arrival of the fittest.’…
A metaphor might help to clarify the problem. Imagine a giant library of books containing all possible sequences of letters in the alphabet. Such a library would be huge beyond imagination, and most of its texts would of course be pure gibberish. But some would contain islands of intelligibility – a word here, a Haiku there – in a sea of random letters. Still others would tell all stories real and imagined: not only Dickens’s Oliver Twist or Goethe’s Faust, but all possible novels and dramas, the biography of every single human, true and false histories of the world, of other worlds as yet unseen, and so on. Some texts would include descriptions of countless technological innovations, from the wheel to the steam engine to the transistor – including countless innovations yet to be imagined. But the chances of choosing such a valuable tome by chance are minuscule.
That giant library is, of course, Borges’ library, though Wagner doesn’t give credit here. He does present the same problem.
A protein is a volume in a library just like this, written in a 20-letter alphabet of amino acids. And while protein texts might not be as long as Tolstoy’s War and Peace, their total number is still astonishing. For example, a library of every possible amino acid string that is 500 letters long would contain more than 10600 texts – a one with 600 trailing zeros. That vastly outnumbers the atoms in the visible universe.
The library is a giant space of the possible, encoding all the proteins that could be useful to life. But here’s the thing: evolution can’t simply look up the chemicals it needs in a giant catalogue. No, it has to inch its way painstakingly along the stacks.
So how does natural selection find the next viable protein sequence? How does this mindless process find the path that arrives at viable minds?
For more than a decade, this endeavour has been a focus of my research at the University of Zurich and at the Santa Fe Institute in the US. We evolve molecules in the laboratory and record their journey through these libraries, together with any new and useful texts they find. We also map the locations of millions of molecules that nature’s populations have discovered in their billion-year journey. We use powerful computer simulations to explore those parts of a library that nature has not yet discovered. Through these efforts, we and others have found a system of organisation in these libraries that is as strange as it is perfect for guideless exploration.
One of its features is easily explained once we observe that neighbouring texts in nature’s library have similar letter sequences, and the closest texts – immediate neighbours – differ in just a single letter.
If natural selection had to pick at random from the possible protein sequences, no conceivable time would suffice for evolutionary processes. But it didn’t have to do that. The basic molecules on which natural selection works (at the molecular level) open up a large but not vast number of pathways. Many different directions are open, but only so many. A library of possible forms is on the same shelf and it is a big shelf, but manageable. Certain pathways prove very fruitful, and natural selection moves up and down them again and again. Many different combinations of genes work the same outcomes along a viable pathway.
The remarkable thing is, having so many different ways to say the same thing means that there are many more possible slips of the tongue. And with each slip of the tongue comes the possibility of saying something different. Just as the word GOLD emerges from a single letter change in MOLD, some neighbours of a text express new meanings. And as the browsers work their way through each synonym for some original text, different innovations become accessible. By creating safe paths through the library, genotype networks create the very possibility of innovation.
Let me put this point as strongly as I can. Without these pathways of synonymous texts, these sets of genes that express precisely the same function in ever-shifting sequences of letters, it would not be possible to keep finding new innovations via random mutation. Evolution would not work.
What Wagner thinks, if I read him right, is that the molecular material that natural selection began to work on from the very beginning of life on earth already contained a large but manageable set of forms. If it hadn’t, evolution could not have been possible. He recognizes this library of viable forms to be Platonic. That makes two of us.