While editing the new number theory page at Wikipedia, I realised that (a) the page needed more pictures; (b) it isn’t trivial to come up with relevant pictures for all areas of number theory. What would be a natural physical representation of a prime number?
Fortunately, there is something I first heard about as a side note in a math talk a few years ago. Well before the advent of digital computers, there were, of course, analog computing devices — and some of them were used in number theory. In particular, Lehmer (the father; I think the son and the daughter-in-law also got involved) built actual, physical sieves; these look nothing like a sieve in a kitchen or a mine — rather, these are machines full of bicycle chains, holes, beams of light and electrified brushes, used for factoring and solving some diophantine equations.
I went to the Comédie Française the other day to see something by Racine. For whatever reason, I was expecting a great deal of declamation — rather traditional acting, good for language practice. Instead, the acting was thoroughly naturalistic (and top-notch as such, of course); we could have been watching a very late nineteenth-century work – Racine as Ibsen. Of course this made it much easier to react directly to the work as a play. The only problem is that the acoustics became non-trivial, especially if you were perched high up in a five-euros seat (as I was); the actors spoke in low voices when their characters would naturally do so — and I felt as though eavesdropping on Titus’s and Berenice’s private conversations from an opposite balcony three stories up.
At least I felt vaguely productive while engaging in the equivalent of post-film activities later – since this involved boning up on the original text rather than looking up the IMDB entry.