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So that not only the geometry is induced, but that the manifold itself - including dimensionality is also induced.

Could the things we know, spacetime, laws of physics, and the particle phenomenology be explained in terms of interacting/communicating self-organizing "statistical" manifolds, and what is the logic of that construction?

There are mathematicians doing alot of stuff on this, but they rarely have the perspective of a physicist, although it might be a "physicists toolbox".

Could such a path be the road to the new logic we may or may not need?

Ideas or pointers anyone?

/Fredrik