Oxford dons are expected to have glittering conversations at high table, and we had a good one today.

One of the fellows mentioned a psychologists’ theory that an infant first understands the number 2, then later the number 3, then later the number 4, before finally figuring out the general notion of number.  However, she said, she and her husband hadn’t been able to detect stages 3 or 4 in their own little boy.

I mentioned the physicists’ theory of the period-doubling transition to chaos.  This involves an infinite succession of orbits, each one 4.669… times shorter than the last (Feigenbaum’s constant).  Maybe the little one went through all the number stages, but too fast to observe?

It was David Wallace who wrapped up the interchange with a philosophers’ twist.  If an infant masters the number 2 in one week, the number 3 in the next half-week, the number 4 in the next quarter-week, and so on, why then, in a fortnight he’ll have mastered all the numbers, an infinite collection of specific notions in finite time!  Who needs the general concept?

[14 April 2016]