Some of Fields medalist Alain Connes‘ revolutionary ideas shed light on how to understand the ‘zoo’ of elementary particles thrown up by accelerators like the LHC. If Connes is right, the key to the fundamental nature of matter lies in graffiti carved on a bridge in Dublin in 1843.
The graffiti was carved by this man William Rowan Hamilton on Brougham bridge as the ebullient mathematician was passing on a walk with his wife. According to a plaque there, it read:
i^2=j^2=k^2=ijk=-1
I am in Dublin later this week and will be taking my camera.
So how does this answer the mysteries of the Universe? According to Alain Connes in his chapter of the multiauthored volume On Space and Time, spacetime indeed has ‘extra dimensions’ but these extra dimensions are not those of any usual kind geometry (curled up or whatever as in string theory) but something far more imaginative; they are given by a symbolic algebra defined by two copies of this graffiti.
Connes is a Fields medalist, which is like a Nobel Prize for mathematicians (who were left out in the will of Alfred Nobel. Incidentally, there is no merit to the popular myth that this was because of an affair between his wife and a mathematician; he never married). So what that means is that the actual mathematics behind his theory is very deep and very advanced; I’ll only be touching on the easier parts in this post.
Well, lets get the maths over with. The main idea we need is that geometry is algebra.
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