Started off by being put down as I walked down the escalator at Vauxhall by two people running up, something that I never do. There was a also a discarded box, then flat-packed and once containing tins Stella Artois. A touch dangerous in that if one's foot was to land on the thing one would probably lose one's footing, not a clever prospect half way down a longish escalator.
Once again (see reference 1), a little early and on this occasion made a start with a drop of Chablis at the 'Goat', rather less crowded inside than one might have thought from the crowd on the pavement, only a few of whom were smoking. Perhaps they did not care for the rather loud music inside.
From there into the Royal Institute, to the same lecture theatre and much the same sort of audience as last time, less the Royal Highness. I was a bit put out at first to find that the topology of the talk was nothing like the topology that I remembered, with the core of the talk being the apparently pervasive hyperbolic spaces, responsible for all kinds of nice computer generated pictures and seemingly some kind of a relation of fractals. But all was well in the end: I may not have understood much of the lecture, but it did make a nice trip down memory lane.
We were told of foldings, starting with the folding of a a square of paper into a torus, something I first learned of maybe fifty years ago from a chap called Whittaker, or Weary for short. And despite the remark about quality time below, I have given some quality time to pondering about why folding a piece of paper into a torus - which is very implausible - is mathematically interesting, while folding a ('T'-shaped) piece of paper into a cube, quite near a sphere topologically and which is possible, never mind plausible, is not. I think I have come to the right answer.
We were told of a theorem which said that there were exactly eight kinds of geometry, aka Thurston's geometrization conjecture. I was reminded of the central limit theorem, which I did once know something about, and which said, as far as I recall, that, with certain limits, any limit probability distribution is a sum of three standard distributions, two of which were the normal distribution and the poisson distribution. Which went some way to explaining why normal distributions were so normal.
Series also talked a little of the changing nature of mathematical proofs, which were becoming much more of a team effort, much more computer assisted. The computer could do a lot of the grunt work these days but there was a problem about whether one could trust the product of a computer. Did such product have the same status as a more traditional proof done with paper and pencil? With which one really could feel that one knew what was going on.
A lot of the illustrations used can be found by asking google for images about 'hyperbolic space'.
On the way back to the 'Goat' I found a pile of neatly taped packages of booklets on the pavement, waiting for the dustman. Picked one up, untaped it in the 'Goat' to find I was the proud owner of two sale catalogues from Bonhams, one from Sotheby's and a rather odd magazine called Spears. More on them in due course. Next move was to continue with the bottle of Chablis that had been opened for me earlier and taking it in 175ml doses, I was a bit cross to find some left at the end of the bottle and I suggested to the barmaid that perhaps she should put that some in my glass as she had clearly been giving me short measures. She smiled indulgently and refused. Is was not until I had got home that I realised that 4 times 175 does not make 750, a confusion over the size of a quarter bottle that I have had before. We also had a confusion about whether the word pistol came from Pistoia, with me firmly in the nay camp, vaguely remembering having checked this very point before. But this morning wikipedia tells me that while it probably does not, plenty of respectable people think that it does. OED thinks that it does. Memory playing tricks again. Perhaps the answer is that a word can have several derivations, a sort of convergent evolution, with all the derivations of a word lending support to its use.
Walked back up the 65 odd steps of the Vauxhall escalator, bothering on this occasion to move the flat-packed box, which had not moved from the position it had occupied earlier in the evening. Much quicker & easier to retrieve such a thing going up than going down.
Home to realise that I had never given much thought to what properties of a space make geometry, the sort that Euclid invented and which I did not touch after O-levels, possible. Fell asleep to the thought that geometry of this sort is clearly possible in what we now call Euclidean space but that I did not have a clue as to whether it was possible in other sorts of spaces. Must resist the temptation to investigate further. All too easy to burn up lots of quality time - a diminishing quantity these days - on such excursions.
The copyright of the image included above is owned by Jos Leys. Google will find plenty more of his work for you.
Reference 1: http://psmv2.blogspot.co.uk/2014/09/hadrons.html.
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