I first encountered Jorges Luis Borges’ story, The Library of Babel, as a student in the early 1960s, and it blew my mind. It describes a mysterious library, organised as a presumably infinite collection of connected hexagonal rooms, whose walls are filled with uniform volumes containing random text. Everything that could ever be written in every language is in there somewhere, but the wretched librarians who patrol the rooms are lucky to see two consecutive intelligible words in their whole lifetime, which may be short, since jumping down the infinite stairwells is a popular way out.
An allegory, even a satire, about society and communication, the story raises philosophical and mathematical questions that could provide a lifetime of amusement. The library must contain all our literary works (and our advertising, and our telephone directories) including Borges’ story itself, translated into every language on this planet and others. It must also contain all these with one letter changed, one word wrong, or two, or three – you get the picture. And by what criteria would you decide they were “wrong”?
It’s awfully tempting at this point to write a column about the blogosphere as our modern Library of Babel, but with enormous self control I’ll resist and pursue a different tack. I’ve recently been reading up about the human visual system and the way the brain handles imagery for a book I’m preparing, and one day I suddenly wondered what would be the visual equivalent of Borges’ library: the Photogallery of Babel, if you like. This turns out to be as interesting as the original, but different in rather revealing ways.
First of all, we have to decide on the uniform format for pictures in the gallery and, while I could choose a JPEG file of some size, I prefer instead the biological option of “one human retina full”. The retina is a finite array containing around 126,000,000 rod and cone cells, and for our gallery format their output would be sampled at some finite resolution – 32 bits would do, since that approximates photorealistic colour. Each picture in the gallery would therefore be a bitmap of around 4 billion bits, and the gallery would contain every possible 4Gb image.
I see the pictures as being hung on the white walls of a spiralling ramp, rather like the New York Guggenheim but taller. Not infinitely high, though, because there’d actually be a finite number of pictures, around 101,000,000,000 to be exact – its ten-to-the-billion floors would stretch some way out of the solar system, making planning permission tricky. This gallery would contain everything that it’s possible to see, or to imagine. The only problem is that every picture you’d see in your lifetime would look like an almost identical reddish-bluish-greenish fog, in which you might discern some faintly recognisable object.
Borges’ library wasn’t actually infinite, either, because he specified that each book was 410 pages with 40 lines of 80 characters, from an alphabet of 25 symbols including space and punctuation: that’s 251,312,000 unique books. However, the question of what language those characters represent complicates things: Kevin Kelly has suggested that every single book, however random looking, could be made intelligible if you discovered the correct language or encoding. Is this true of pictures, too? Actually, it is – you could choose a random gallery picture, take a copy of the Mona Lisa, then use morphing software to turn the former into the latter.