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]
I got my first pair of varifocals a few months ago. When I put them on I felt I was swimming in a sea of blur and I was tempted to abandon the experiment. Nathaniel said, don’t worry, in a few days you’ll be used to them and the world will look good again.
He was right. My brain adjusted comprehensively and my new eyesight quickly became the new normal. On a glorious walk along the South Downs Way yesterday, for example, I almost never noticed that the focussed fraction of my field of vision is half what it was a year ago.
Your first thought may be pleasure at how easily our brains adjust, but your second should be one of horror. How diabolically our brains disguise our declining powers! My visual input is half what it was a year ago, and I don’t notice. It’s probably a tenth what it was when I as a teenager, and I don’t notice that either. It’s a safe bet the power of my thought has diminished too. As the engine slows down, occasionally there are puzzling artifacts out there in the periphery, but for the most part, we don’t notice.
[11 April 2016]
Every adult knows that the matter of God is a serious one, quite unrelated to the case of Santa Claus, who is a harmless invention for children.
Kate and I saw a millennium-scale version of this disparity on display this week in hall after hall of the Prado. Half the paintings of the Renaissance seem to depict stories of the Christian holy family and the saints, and the other half, stories of Greek and Roman gods and mortals. In the first category, we have for example Fra Angelico’s beautiful “Annunciation”, which shows Mary being dazzled by a sunbeam of gold, symbolic of God impregnating her. This led to the birth of Jesus, who was both god and man. In the second category, we have Titian’s beautiful “Danaë and the shower of gold”, which shows Danaë being dazzled by a cascade of gold coins, symbolic of Zeus impregnating her. This led to the birth of Perseus, who was half god and half man.
I doubt one Prado visitor in a hundred notices how indistinguishable the Christian and Greek/Roman stories would be to the proverbial Martian. Even then, to make the parallel feels boorish and simplistic. One is tempted to think, well, that’s very clever, but of course, the two cases are completely different. Everyone knows those Greek and Roman stories are just stories! When in doubt of your doubt: remember Fra Angelico’s Mary and Titian’s Danaë.
[3 April 2016]