more meaning out of Alain Connes 2015 talk to physicists: Alain Connes - Temps et aléa du quantique

 In fact every type can occur and, for instance, very standard foliations such as the Anosov foliation of the unit sphere bundle of a compact Riemann surface of genus > 1 give a factor of
type III1.

 

 This is how Alain Connes ends his 2015 lecture to physicists.

 https://alainconnes.org/wp-content/uploads/book94bigpdf.pdf

slowly I decipher his talk! haha

 There is an overall motion. ...I always hesitated to give this talk. It's an intuitive idea. It's based on mathematics....the intuitive idea is that there are factorizations with infinite degrees of freedom that they generate their own time and of course it's related to thermodynamics...

I will first explain how quantum mechanics gives the right mathematical 

formalism for the notion of ``real variable". The thesis I will try to 

present next is that quantum phenomena have an intrinsic variability which 

is more fundamental than that of the "passage of time". The latter should 

then appear as emerging from quantum formalism and I will give the essential 

mathematical ingredients
who codify this emergence.

you take 2 x 2 matrices by 2 x 2 matrices and you repeat infinitely many times as type III 

factorization.  ... in other words these factors have periods, they have periods....