When Riemann wrote his essay on the foundations of geometry, he was incredibly careful. He said his ideas might not apply in the very small. Why? He said that the notion of a solid body of a ray of light doesn't make sense in the very small. So he was incredibly smart. His idea, I have never been able to understand his intuition...But however he wrote down explicitly that the geometry of space, of spacetime, should be encapsulated, should be given by the forces which hold the space together. Now it turns out this is exactly what we give here.Alain Connes lecture on spectral [frequency] invariance and noncommutative logic
Unitary Invariance is Spectral [noncommutative frequency multiplication].
What Connes is admitting is that "solid bodies" or "things" - aka matter - comes from the noncommutative mass of light (spirit or shen).
So he says it is a force of frequency - this is what I called the "Fundamental Force" in 1996 - my first monograph starting to delve into noncommutative logic.
Why should Nature require some noncommutativity for the algebra? This is very strange. For most people noncommutativity is a nuisance. You see because all of algebraic geometry is done with commutative variables. Let me try to convince you again, that this is a misgiving. OK?
Our view of the spacetime is only an approximation, not the finite points, it's not good for inflation. But the inverse space of spinors is finite dimensional. Their spectrum is SO DENSE that it appears continuous but it is not continuous.
His [Riemann's] intuition was everything was based on light traces and solid bodies. And solid bodies do not make sense in the very small, neither do light traces as photons, because a photon is a particle....
One day I understood the following: That we are born in quantum mechanics. We can not deny that... Quantum mechanics has been verified. The superposition principle has been verified. The spin system is really a sphere. This has been verified. This has been checked so many times. That we can not say that Nature is classical. No. Nature is quantum. Nature is very quantum. From this quantum stuff, we have to understand our vision, our very classical, because of natural selection way of seeing things can emerge. It's very very difficult of course.
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