Comments on: Monkeys and typewriters

By: Jon Awbrey

Jon Awbrey — Tue, 08 May 2012 16:01:53 +0000

I think it’s an echo of ancient ideas about “eternal return” that trace back to the dim mists of pre-history in both Eastern and Western cultures. The (probably apocryphal) Pythagorean “horror of irrationality”, the Platonic Year, the Chinese Remainder Theorem, and so on.

By: Peter Cameron

Peter Cameron — Tue, 08 May 2012 09:04:36 +0000

Yes, one of the puzzles is how this came to be a metaphor for infinity.

By: Jon Awbrey

Jon Awbrey — Mon, 07 May 2012 15:44:13 +0000

A two-level formal language consists of a set of “words” and a set of “sentences”, where a word is defined as a finite sequence of symbols from a finite alphabet, and a sentence is defined as a finite sequence of words. The finite-state structure of a two-level formal language can be captured in a couple of finite-state transition trees, one for the words and one for the sentences. Recording data about the frequencies of node traversals allows us to compute relative probabilities and local entropies and many other statistics of interest, and the resulting structures can be used to predict likely completions of word and sentence fragments. I spent a couple of my parallel lives in the 1980s developing an AI sort of program that combined faculties for data-driven empirical learning with faculties for concept-driven logical modeling. One of the things I learned along the way is that there appears to be a trade-off between these two modes of processing that makes it very difficult to integrate empiricist and rationalist faculties within a single intelligent agent. Explains a lot about the history of thought, I think. Here is a pointer to what documentation I have on line — • Theme One Program

By: Colin Reid

Colin Reid — Sat, 05 May 2012 18:25:36 +0000

I don’t know if I like the ‘infinite monkeys’ explanation for how infinity is special. For instance if you had a writing team consisting of Graham’s number of monkeys, it wouldn’t take very long for one of them to type out the complete works of Shakespeare. (Granted, it wouldn’t be certain in any specified time, but as soon as you give each monkey long enough to make the required number of key presses, it’s ‘beyond reasonable doubt’.) I see it more as an example of how combinatorics does better than most subjects at getting us to think of big numbers.