RANDOM JOTTINGS

Dick Pountain/20 January 1999/Idealog 54

Two apparently unrelated cultural events this week turned my mind toward the concept of randomness. One event was seeing Darren Aronofsky's odd little movie "Pi", about a mathematical genius who is obsessed with the infinity of digits required to express the value of the irrational number pi. "Pi" is not a documentary but a stylish and slightly pretentious work of fiction, though it has similarities to the real-life story of oddball Chudnovsky Russian brothers who turned their New York apartment into a supercomputer in order to calculate a billion places of the decimal representation of pi. They used $70,000 worth of mail-order Intel PC motherboards - strung together into a  message-passing parallel architecture of their own design, with boards festooned around the walls like fairy-lights on a Christmas tree - to achieve computing speeds of up to 2 Gigaflops. Why did they do it? To see if they could find patterns in pi; the modern equivalent of the alchemists' search for the Philosopher's Stone.                 

The other event was the publication of the complete short stories of Jorge Luis Borges in new translation, including the "The Library of Babel". I first read this story while still at grammar school, and it struck me like a bolt of lightning - in fact nothing ever struck me so powerfully again until I discovered, many years later, Isaac Babel's "Red Cavalry" stories, on a completely different theme(the coincidence of names is rather uncanny though). 

Those who have read "The Library of Babel" must bear with me while I summarize its plot. The Library is, we guess (though no-one knows) an infinitely large structure, composed of bookshelves arranged in circular fashion around a central spiral staircase. Each shelf holds 64 identical volumes, each of 64 pages, and these pages are filled with totally random letter combinations. The library is inhabited by a race of librarians who spend their lives plodding from shelf to shelf, up and down stairs, reading the books and looking for passages that make sense. Occasionally a couple of them bump into one another and swap excited stories of having discovered two consecutive words of comprehensible Spanish, or an almost-correct phrase in English. None has ever read more than a short sentence of sense. But all of them know that somewhere in the library exist the complete works of Shakespeare; and of Raymond Chandler; perhaps even of Irvine Welsh; all the back issues of PC Pro; and all of these translated into all known human languages, and in many languages not yet invented; written both forwards and backwards. And all of these things also exist with one word wrong, or two words wrong, or.... Now and again a librarian hurls himself down the infinite stair-well, as you would.

Now I could use this story as a cheap metaphor for searching the web using Alta Vista, but I will resist that temptation. I'd rather concentrate on the connection with "Pi". The point is that pi contains the Library of Babel. Probably. Write out pi in decimal notation (or in hex if you're a true hacker), split it up into consecutive pairs of digits and interpret each pair as an ASCII character, and you have an infinitely long string of random characters. Individual words might look a bit long if 32 (the ASCII space character) occurs less frequently than it does in typical English, but you could easily fudge that by re-using those digit pairs that encode non-alpha characters. What I'm suggesting is that the Chudnovsky brothers are engaged on the same quest as Borges's librarians of Babel (they live on a top floor too) - nothing less than the quest for sense, or order, among the randomness of the universe.

I'd also suggest that, as with the Grail and the Philosopher's Stone, this quest is an illusion, engendered by the human species overdeveloped cerebral cortex, which often leads us to believe that because we can name something, it must exist. Order does indeed exist among the randomness, but it's not our thoughts that create it, it's our very life. Life - that is, the DNA-based life we know about - is a spectacularly effective mechanism for creating order out of randomly moving molecules, stringing them together into genes and proteins, and apparently flouting the 2nd Law of Thermodynamics in the process. Every living thing is in effect a rather large but meaningful volume in the Library of Babel.  

That's not to say there's no point in studying randomness. On the contrary, perhaps the most important and interesting field of purely intellectual endeavour (since philosophy and the social sciences disappeared up their post-modern fundaments) is algorithmic information theory, which does precisely that. Founded by Gregory Chaitin, a researcher at IBM, this branch of mathematical computer science seeks to measure how complex bit strings are by the amount of computation required to reproduce them. For example the infinite string 11111111... is very simple, because the algorithm "keep on writing 1s forever" will reproduce it. The string 12121212... is only a little more complex. At the other extreme some strings are so complex that they are already their own simplest representation, and pi is one of those; such strings provide our only satisfactory definition of what "random" actually means. Actually most of the possible strings are of this random nature (they are the Library), but more interesting are those very, very, very rare (though still infinite in number) strings that fall between these extremes: the ones take a large but finite amount of computation to reproduce, like "War and Peace", or "The Library of Babel", or indeed this column.