Axiomatic Sheaf cohomology/Aural Objets Trouves

… Updates, updates… Well, right now I’ve learnt the axioms of axiomatic sheaf cohomology. Which is nice. The only problem is that everything is rather esoteric at the moment – apparently every fine torsionless resolution of the constant sheaf defines canonically a sheaf cohomology theory. Not only that, but later in the book, it proves that every sheaf cohomology theory is isomorphic for the same choice of the base principal ideal domain K (the sheaves are sheaves of K-modules). This seems nuts right now, but I guess it must be a little less crazy than it sounds. Actually a sheaf cohomology theory seems to be rather a big beastie and so if you pick K as the field of real numbers, the cohomology theory that you get must encapsulate all the classical cohomology theories like de Rham and Cech. Crazy eh?

On a lighter note, I found out about an awesome experimental music project called Milkcrate. The idea of the whole thing is to make, I guess, unconventional music. It’s awesome. The rules are essentially that all of the objects that you use have to be explicitly non-musical (egg cartons and yoghurt pots?) and they have to all fit inside a standard – presumably Australian – milkcrate. Oh, and it all has to be completed in 24 hours. It seems to me that this is bringing the idea of objets trouves to music in a whole new electronic way. Hurrah for the internet!



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