So, you may ask yourself why the last post about axiomatization? Well, because it shows some forms of generalizations that can be made… If you look at a quantum field theory and at a sigma model you will see that string theory is the generalization of QM in 2 dimensions… Simple quantum mechanics is 0-dimensional. Line quantum mechanics or quantum field theory is 1-dimensional quantum mechanics and string theory is 2-dimensional quantum mechanics. Now, for some very odd reasons string theorists consider that the only possible generalization is geometrical (or topological) and certainly only dimensional… But think again, what is the axiomatization of quantum mechanics? And what is the axiomatization of path integral quantization? Are you sure you cannot compensate a dimensional generalization by other mechanisms? Because I am certainly not that sure! We live probably in the “age of dimensional generalization of geometry” but if mathematics had stopped at that we would have no group theory, no sheafs, cohomologies, stacks, spaces, modules, rings, topoi etc. strings are JUST A WAY of looking at reality and certainly not the best…

# axiomatization?

Advertisements