Tuesday, November 02, 2010
A wobble
Quite taken aback the other day. As I point out from time to time, I have been an atheist all my life. No truck, at least on my own account, with Allah, Jehovah, Jesus or the Virgin Mary. Then, quietly minding my own business, reading about a Russian called Florensky. Or rather, of mixed Armenian-Russian stock from Tiflis, the same Tiflis where Uncle Joe went to school, at very roughly the same time. It seems that this Florensky was a very talented chap, good at mathematics and all kinds of other things. But that when he was in his early 20's he saw the light and after various trials and torments became a priest in the Russian Orthodox church. Something that was not that unusual at the time for intellectuals not attracted by the Social Democrats or violence. And all of a sudden, between mouthfuls of bread and butter (it being breakfast time), I suddenly thought that maybe there was something other than the physical world of gluons, glue sticks and Newcastle Brown. Maybe Euclid's fourth postulate has some ethereal existence, other than on ancient papyrii? OK, so not as bad as seeing the Angel Gabriel peeping out from behind a cloud but tendencies in that direction. A road to Damascus moment. Or perhaps a Eureka moment.
Then, a day or so later, prompted to read Penrose on the road to reality by getting stuck in Yau on the shape of inner space, to find that he spends some pages in chapter 1 on this very point. Penrose, like many immature and mature mathematicians before him, looks to me as if he is wobbling a bit. That he thinks that there is something out there other than gluons & etc. Clearly time for some quality time.
Start off with horses. Is there a concept of horse out there? I am reasonably happy that there is not. There is a collection of animals out there, bit fuzzy around the edges, the members of which we call horses. Many of us have bits of code in the brain which enable us to decide whether or not a particular animal is a member of this collection. Most of the time we agree on the point. And the DNA of members of this collection is so arranged that they find it hard to breed exogamously. But there is no need for a concept called horse to be knocking around the ether. In fact, I can see all kinds of maintenance problems, the sort of thing you really would need the Angel Gabriel for, if you did have such a thing.
Then there are the Mandelbrot sets to which Penrose alludes. How could things of such beauty and intricacy not exist? They are certainly not the product of any human imagination. Reflecting, I think I can see this one off as well. There are all kinds of things in the mathematical world of astonishing complexity and craft. But I am happy for them to be the product of the basic machinery with which we are all endowed. If you crank the handle in the right way, out pop the Mandelbrot sets. There is no need for them to have any kind of prior or special existence and we can talk about them because we all have the same kind of basic machinery.
In the same way, one might score an amazing break in snooker. A break the like of which has never been seen before. But we are content for that amazing break to be called into being by the fairly elementary rules of snooker and a gifted player. We see no need for that break to have some special existence, despite its being as wonderful to a snooker person as a Mandelbrot set is to a mathematical person. But I shall give some more thought to how they are different.
In the meantime, it suffices for such things to be implicit in the world in which we live. There is no need for everything to be explicit. And anyway, if everything was explicit, think how boring the world would be. One only has to think of pornography.
In the margins of all this, wondered why a lot of books these days are something between A5 and A4 in size. Whatever happened to standardisation? Were the chaps in Brussels asleep on the job?
And then off to Headley Heath, a place to which we have not been for quite a while. Lots of autumn colour scattered across the hills. Pleased to see that the chain saw gang have not (yet) infiltrated whatever National Trust sub-committee runs the place. We saw just one tree which had been chopped down. An apparently hale and hearty mature beech. The excuse may have been that there was a fair bit of fungus settled into the base of the trunk and the trusties may have been nervous about the tree falling on a squirrel or something. But that apart, very little evidence of management. No swathes of woodland clear felled to make room for volunteers to play with cows. To be fair, we did see one cow and there were some elaborate wooden gates. But the place was not a mess of electric fences and cow droppings.
# posted by Jim @ 8:03 AM 
