The Optimism of Vast Numbers

Daniel C. Dennett takes from Jorge Luis Borges’ “Library of Babel” to explain how human DNA contains both differences and similarities. There is a bit in Intuition Pumps and Other Tools for Thinking where Dennett explores the variation within one book in said library:

Moby-Dick is in the Library of Babel, but so are 100,000,000 mutant impostors that differ from the canonical Moby-Dick by a single typographical error. That’s not yet a Vast number, but the total rises swiftly when we add the variants that differ by two or ten or a thousand typos. Even a volume with a thousand typos – two 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 only you could find one of them! Almost all of them would be equally wonderful reading, and all tell the same story, except for truly negligible – almost indiscriminable – differences”.

Imagine if it was a score of Mozart’s instead of Melville. With the variations done to a piece fitting for such practice, there would be 100,000,000 mutant impostors that vary from the canonical movement of a Mozart symphony by one change of pitch. Like with the typos, this number will rise once variants differ from a couple to thousand of pitch changes (taking into account what parts of the orchestra are edited and the mind numbing variations derived from that).

The result is something that Dennett labels as a Vast number: finite but seemingly infinite enough to not be exhausted any time soon. What should be noted is that this thought experiment is done with one piece. Could one even imagine the Vast number of all of the mutant impostors of every piece of music known? Definite but sure as hell time consuming.

Sure, there will be some variations that are wonky, just as in the Library of Babel there are versions of Moby-Dick that are barely the original amongst the surge of typos. A certain set of variations could present a new piece in of itself (along with its variations!). This process can go on and on.

How optimistic this thought experiment is. What music creation can be done is a Vast number: there will be a time when we will run out of musical ideas but it will not be any time soon (or late).

1 comment
  1. I love this idea! In some of my college classes we would talk about what the essence of a piece of music is. In other words, what are the defining features that make this piece THIS piece instead of another one? Because after awhile, like you point out, if you have too many variations then it becomes something different altogether. Of course, we never came to a definitive answer. Cool stuff!


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