Saturday, February 02, 2008

Bad science: Cubic litres!

I enjoy Ben Goldacre's Bad Science column in Saturday's Guardian. Today's included this

I know I'm wrong to care. On the BBC news site "crews were hopeful the 20m cubic litres of water could be held back and not breach the dam wall". And that'll be a struggle, since "cubic litres" are a nine-dimensional measuring system, so the hyperdimensional water could breach the dam in almost any one of the five other dimensions you haven't noticed yet.

I just love the idea of the water by-passing the dam in the extra dimensions. I have always felt that really a universe with only three spacial dimensions was just right. From "Flat Land" [W] we know how noisy it would be in one dimension (sound intensity does not decay with distance), and in two dimensions we could not tie our shoe laces, and a body could have only one oriface to the gut serving both purposes. An in four dimensions shoe laces would also be a problem as any curve embedded in four dimensions is unknotted. In a strange way the higher dimensional spaces are pretty boring places. All the lovely regular polytopes in three and four dimensions. Then from dimension five all the way out to Hilbert space there are just the three. Well there is a more interesting story for exotic differentiable structures on n-spheres but I am not sure what influence that would have on the life of nine-dimensional beings.

It reminds me of a story told by Sir Christopher Zeeman

At 2am on the Sunday morning I was sitting on the lavatory contemplating my theorem, when suddenly it hit me that I use the same proof to unknot n-dimensional spheres in (n + 3)-dimensions, for all n. Once I had seen that, I was able to reduce the original proof in 5-dimensions down to ten lines, which I published as a one-page paper in the Bulletin of the AMS.

Do we have any of that six-dimensional spherical pasta for lunch? Funny how it never seems to get knotted? Oh and pour me a cubic litre of hyper-beer.