Quarter Life Crisis

The world according to Sven-S. Porst

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What are news?

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In the face of big media corporations we’ve accumulated enough paranoia by now to assume that they’ll feed us disinformation under the name of ‘news’ whenever it suits them. So the question arises what news are or who gets to decide what is newsworthy and what isn’t. According to the people owning companies like Fox the answer seems to be simple: He who owns the news station gets to decide what the news are. And at least in areas where their business is affected you can see how this is good business sense.

On the other hand, people tell me I shouldn’t be cynical all the time. So I’ve subscribed to the motto that we shouldn’t account to evilness things which could equally well explained by stupidity. In this case that would mean bad journalism – not in the sense of disinformation but in the sense of poor research. And also in the sense that every damn media outlet simply seems to copy everything from their colleagues or the news agencies without giving too much thought to it.

Of course I have an example in mind: Today there was an item in the world news on the Russian mathematician Grisha Perelman potentially having proved the Poincaré conjecture. The conjecture itself is a bit un-sexy and technical to state. First you’ll need to use the word homotopy which is usually explained using rubber bands or ropes and things like apples and doughnuts (Is there anything they can’t do?). You’ll end up with a statement that goes along the lines of “A compact n-manifold is homeomorphic to the n-dimensional sphere if and only if it is homotopy equivalent to the n-dimensional sphere.”

While that’s a reasonably nice statement, it’s probably hard to understand what it means and why it should be hard. Even more so, one could wonder why the general public should be interested in that. That’s of course due to the Clay Foundation’s one million dollar award for solving that problem. ‘Money sells’.

Is this the reason why the item was in the news today? Well, not quite. Simply because this isn’t exactly news. Perelman put the first relevant paper on the maths arXiv in November 2002. It’s very modest. You won’t find the word ‘Poincaré’ in there at all. It just states that it’s another step towards proving the ‘geometrisation conjecture’ which in turn implies the Poincaré conjecture as a byproduct.

By spring 2003 probably most mathematicians had heard that a paper exists which could prove the Poincaré conjecture. It was also said that the paper was quite hard and people were still trying to understand it properly. Everybody was quite optimistic, though, that this would do the trick. And, even the media noticed (because of the price of course) that something happened and there were articles in the press on the topic in April 2003 (as I noted here).

So did anything newsworthy happen since then? Well, um, not really. People have studied the paper further, there have been talks and workshops. I even saw a new book on the ‘Ricci flow’, the technique Perelman uses, in the library which is aimed at giving people the background to understand his work. Everybody is still very positive on this. The hero of this story though, seems to be rather quiet and hasn’t even asked for his prize money. Indeed, he doesn’t seem to be technically eligible for it as the prize requires you to publish in a journal while he just gave his work to the free preprint server. So there we’ve got the weirdo mathematician again who doesn’t even care for money. That’ll make interesting reading at least.

Still, this isn’t exactly new and – as far as I can tell – it’s not the reason for the articles. Those reasons were a statement by a professor at a conference reiterating all the known points and optimism. It looks like Reuters put out a short report on this. And then the mindless drones at the various papers and web sites copied it, copied it and added the weirdo mathematician story or copied it and really fleshed it out, even trying to explain some of the maths concepts.

While (ignoring the obligatory errors and misrepresentations for a while) this is all nice and dandy, it’s not news and shouldn’t be treated as such. This looks like a really strange chain of events triggered by a tiny remark and then blown up by the way mass media work. It hints that they don’t work very well.

On the other hand, this story could be told for entertainment! The story of the Poincaré conjecture is a century long but quite funny. There are many wrong ‘proofs’ on the way. Talks with the topic “Why the Poincaré conjecture is so hard” are given. Poincaré initially made the conjecture for dimension 3, but then it was generalised to any dimension. Interestingly enough, the statement had been proved for high dimensions a while ago, with the general proof working for dimension 5 and higher. And there was another proof for dimension 4. So only dimension 3 remained – the original conjecture.

Some problems that can be solved easily in high dimensions can be notoriously difficult in dimension three or four. That area is called ‘low dimensional topology’, a name which may be too modest for the difficulty of some its problems. A professor of mine used to say In dimensions below three there’s not enough space to get you into difficult situations and in dimensions higher than four you have enough space to simply avoid the difficult situations – it’s a bit like parallel parking (a small car): If the space is two metres or shorter, there’s no way you’re going to fit in; and if it’s five metres or more it’ll be easy; Those in between these lengths will be the tricky ones. (See another comment on that topic in the second half of this post.)

Looking at physics, where people consider three-dimensional space or four-dimensional ‘space-time’, gives a hint why there is particular interest in those extra-hard dimensions. To stretch the above analogy, this’d mean that in the real world most parking spaces are of the ‘tricky’ lengths.

But I digress – all I wanted to say is that the story of the Poincaré conjecture may make a good novel. And what’s happening now may be a good last chapter. What happens if someone understands Perelman’s work, fleshes it out and publishes it? Will he or she be elegible for the prize? (In the real world this seems to be the case, as the gazillions of trivial patents we hear of every day suggest.) This scenario on its own would probably make good fiction.

Links: Reuters, Spiegel Online, Guardian, BBC, Feedster, Slashdot

September 9, 2004, 0:20

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