After the election
Memories of the Blair administration
So Blair got back in with a reduced majority. I
find myself trying to turn my thoughts to contemporary figures who are more
inspirational. For me, Andrew Wiles is possibly the most impressive figure of
recent times. When I was in my first year at university my friend Steve and I
crashed a course in Galois theory. Most people could probably take a pair of
compasses and a ruler and divide a given angle in two. Even though you probably
can't recall how to do this immediately, I bet you'd work it out quite quickly
if you tried. For centuries mathematicians wondered whether there was a similar
procedure for trisecting rather than bisecting any angle; they had a hunch,
through the repeated failure of bright guys trying, that you couldn't, but no
one could prove it. Then, I'm guessing in the eighteenth century, a young
French mathematician (Galois) proved that it couldn't be done. The proof uses
field theory and if you browsed a book on it (Emil Artin's is very elegant while
Ian Stewart's is much more readable) you'd wonder what it had to do with rulers
and compasses. Anyway, Steve and I did the course and learnt the proof, and I'd
be hard pushed to point to anything I've ever come across that is more
intellectually interesting. A minor variant on the same proof also shows that
you can't use ruler and compasses to construct a square having the same area as
a given circle, thus dispatching the equally ancient "squaring the circle"
question. Shortly after devising these proofs Galois died in a
duel.
Well most of you will know about Fermat's Last Theorem and how it resisted solution until the end of the twentieth century when Wiles, who had spent ten years thinking about nothing else, came up with a proof of insolubility for order >2. While this also used field theory the amount that you need to master is so vast that only a small number of people could even follow it. While this is hugely impressive, it's so far beyond what ordinary mortals can get to grips with that it's also something of an intellectual dead end for the non specialist, if you see what I mean. So I don't spend much of my life thinking about Andrew Wiles.
On the other hand, I do give the occasional processing cycle over to Gary Kasparov. While chess and maths seem very similar there are profound differences. For example, in chess you can play one great move after another every game but still lose them all on time; whereas to prove a theorem you have to be correct in an eternal, platonic sense, in chess you have to be effective. While maths is the higher and nobler discipline, when I get more time it's chess that I want to return to. And the differences between the two are reflected in the incommensurability of Wiles' and Kasparov's achievements. Get this: Kasparov, who recently announced his retirement, has been the world number one for twenty years!! When you think about the vast number of very bright people who give over their lives to this game it's astonishing that anyone can even remain champion from one year to the next; the existence of an empirical highly-gradated ladder of ability with one person at the pinnacle tells us something non-obvious about brains and people.
Kasparov bequeaths to us three legacies, being his games, his books and his use of computers, and these three are highly related. Stylistically, Kasparov could be thought of as "post-positional". While he obviously understands "strategic" or positional characteristics of the game (which were essentially known a century ago) as deeply as any other player it seems not to define his play as concretely as it does for many other players, such as Karpov, the previous world champion. This can be seen in his books, by which I really mean his series "My Great Predecessors" in which he analyses the games of all former champions. (I have these and want to get more time to read through them one day. Although when I played I was most influenced by Fischer, I'm most looking forward to reading what K has to say about Mikhail Tal.) While the books have plenty of text sections about personalities and the rest of it, the bulk is given over to analysis of games. There is tendency for such commentaries to tell a story that's thematic in nature - a kind of morality tale about the strengths and weaknesses of players and positions. K's analysis features little of this and a whole pile more analysis of concrete variations; these are not books to read on the Tube. This segs into his other legacy: Kasparov is the first real champion of the computer era. While being famous in the popular imagination for losing to Deep Blue, the extent to which he has embraced the use of computers and integrated them into his pre-match and intra-match analysis makes him virtually bionic. (And, for the record, last time I knew anything he was still whipping computers in competitive games.) At least some and probably a lot of the commentary that he gives in his books comes from analysis that he's worked at with a machine. This is interesting because he manages to assimilate it into his play over the board. Obviously other contemporary players do this too, making it all the more impressive that he has stayed on top for so long.
The same thing is happening in some areas of maths too - the proof of the four colour theorem - that four colours suffice to colour any map - being a good example; but for me the inspirational stuff in maths remains the Wiles type of proof, inaccessible though it may be.
Don't know how interested you are in any of these topics, but hopefully you had a few minutes thinking about the highest levels of human achievement and could momentarily forget that we are led by men who have degraded the quality of political discourse, dismantled our historic institutions in the pursuit of their own vanity and seem to think that bombing civilian targets promotes world peace (and that lying about it later is ok).
Another little triumph of the day is that we have had our last malaria tablets for the rest of the year.
Well most of you will know about Fermat's Last Theorem and how it resisted solution until the end of the twentieth century when Wiles, who had spent ten years thinking about nothing else, came up with a proof of insolubility for order >2. While this also used field theory the amount that you need to master is so vast that only a small number of people could even follow it. While this is hugely impressive, it's so far beyond what ordinary mortals can get to grips with that it's also something of an intellectual dead end for the non specialist, if you see what I mean. So I don't spend much of my life thinking about Andrew Wiles.
On the other hand, I do give the occasional processing cycle over to Gary Kasparov. While chess and maths seem very similar there are profound differences. For example, in chess you can play one great move after another every game but still lose them all on time; whereas to prove a theorem you have to be correct in an eternal, platonic sense, in chess you have to be effective. While maths is the higher and nobler discipline, when I get more time it's chess that I want to return to. And the differences between the two are reflected in the incommensurability of Wiles' and Kasparov's achievements. Get this: Kasparov, who recently announced his retirement, has been the world number one for twenty years!! When you think about the vast number of very bright people who give over their lives to this game it's astonishing that anyone can even remain champion from one year to the next; the existence of an empirical highly-gradated ladder of ability with one person at the pinnacle tells us something non-obvious about brains and people.
Kasparov bequeaths to us three legacies, being his games, his books and his use of computers, and these three are highly related. Stylistically, Kasparov could be thought of as "post-positional". While he obviously understands "strategic" or positional characteristics of the game (which were essentially known a century ago) as deeply as any other player it seems not to define his play as concretely as it does for many other players, such as Karpov, the previous world champion. This can be seen in his books, by which I really mean his series "My Great Predecessors" in which he analyses the games of all former champions. (I have these and want to get more time to read through them one day. Although when I played I was most influenced by Fischer, I'm most looking forward to reading what K has to say about Mikhail Tal.) While the books have plenty of text sections about personalities and the rest of it, the bulk is given over to analysis of games. There is tendency for such commentaries to tell a story that's thematic in nature - a kind of morality tale about the strengths and weaknesses of players and positions. K's analysis features little of this and a whole pile more analysis of concrete variations; these are not books to read on the Tube. This segs into his other legacy: Kasparov is the first real champion of the computer era. While being famous in the popular imagination for losing to Deep Blue, the extent to which he has embraced the use of computers and integrated them into his pre-match and intra-match analysis makes him virtually bionic. (And, for the record, last time I knew anything he was still whipping computers in competitive games.) At least some and probably a lot of the commentary that he gives in his books comes from analysis that he's worked at with a machine. This is interesting because he manages to assimilate it into his play over the board. Obviously other contemporary players do this too, making it all the more impressive that he has stayed on top for so long.
The same thing is happening in some areas of maths too - the proof of the four colour theorem - that four colours suffice to colour any map - being a good example; but for me the inspirational stuff in maths remains the Wiles type of proof, inaccessible though it may be.
Don't know how interested you are in any of these topics, but hopefully you had a few minutes thinking about the highest levels of human achievement and could momentarily forget that we are led by men who have degraded the quality of political discourse, dismantled our historic institutions in the pursuit of their own vanity and seem to think that bombing civilian targets promotes world peace (and that lying about it later is ok).
Another little triumph of the day is that we have had our last malaria tablets for the rest of the year.
Posted: Fri - May 6, 2005 at 06:49 PM
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Published On: Feb 08, 2006 06:20 PM
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Published On: Feb 08, 2006 06:20 PM