The Fundamental Force of Noncommutative phase logic: Why Renormalization Failed and is now the Return of the Repressed as the Ecological Crisis of physics

Yeah - here's the deal - if you listen to what I wrote above - and I'll clarify it for you - Gregory Bateson was struggling with some deep paradoxes in Western logic and how they apply to science and ecology as a science. So he never solved the problems he was addressing but he did "engage" with the problems and so there is a lot to be learned from his deep engagement.
 
So you can "learn" from that book. Now for someone who has taken the learning to another level - I recommend Fields Medal math professor Alain Connes - again he is both addressing deep logical paradoxes in Western science AND he is proposing a solution. His solution is beyond what Gregory Bateson proposed. So Connes gives a good summary of his approach in a free pdf. I'll get it for you and I can quote from it a bit.
 
http://www.alainconnes.org/docs/2000.pdf
 
So we can start with this one.
So he talks about what Heisenberg inadvertently discovered doing his quantum physics - about the foundation of reality!
Then he tells a joke:
A physicist walks down mainstreet looking for a laundry. He sees a shop with signs in the window: Bakery, grocery, Laundrette....so he enters. HOWEVER the shop is owned by a mathematician so when the physicist asks, "when will the washing be ready?" The mathematician replies, "We don't clean clothes, we just sell signs."
So then he explains that for Relativity (and classical physics) the geometry is defined by REAL numbers but that does not work as the foundation of reality is quantum which, as Heisenberg discovered, is noncommutative phase logic.
 

  Quote

On the other hand the stretching of geometric thinking imposed by passing to noncommutative spaces forces one to rethink about most of our familiar notions.

 
Now that's a powerful statement - he's stating the mathematical logic is FORCING science to do a 180 in thinking. Thus far science has been based on commutative symmetric mathematical logic - that everyone learns with the Pythagorean Theorem, etc. (calculus), etc.

OK let's consider a different Connes pdf
http://www.alainconnes.org/docs/shortsurvey.pdf

Quote

The difficulty is not to add arbitrarily the adjective quantum to our geometric words but to develop far reaching extensions of the classical concepts, ranging from the simplest which is measurement theory, and to the most sophisticated which is geometry itself.

So he's talking about creating a completely new science by reworking our basic notions of what it means to "measure", etc.
So what emerges is that "space" or spatial measurements are malleable with time - and so time is not an outside external parameter (as has been assumed) thus far in Western science.
So he is using quantum physics based on noncommutative phase matrices - but the fundamental concept is the spectral triple - or three frequencies that create the spatial value - but the three frequencies are noncommutative (meaning if you reverse the order of the phase in the measurement as a time change then the spatial value changes).
But the key crucial factor here is that ONLY the noncommutative phase logic enables both a "continuous" infinitesimal line to coexist with a discrete real number value. Up till now science has not been able to solve this logical paradox - and that is the SAME logical paradox that Gregory Bateson was struggling to solve.

Quote

It is precisely this lack of commutativity between the line element [geometry] and the coordinates on a space that will provide the measurements of the distance.

So what is very funny about this - is that this logical paradox is found right in the Pythagorean Theorem but we, as Westerners are taught that there are "thousands" of proofs for the Pythagorean Theorem and no one should DARE question its truth. haha.
So in terms of physics - as Connes describes -

Quote

"a new perspective...which gives a clear mathematical interpretation to the renormalization procedure used by physicists to extract finite values from the divergent expressions....

So up till now physicists - and science in general - has been ignoring the divergent math as an "unobservable" and since it is "unobservable" - therefore it can be ignored - with supposedly no physical effects.

This then got passed on into economics as an "externality" of ecology and social justice.
So because we can cut off the divergence from the math equation - therefore we can just declare it unobservable and so it no longer has any physical effect.

But that was all a lie. So now the entropy of commutative symmetric logic has built up on Earth - the ecological destruction is now taking revenge - the unobservables are now returning as the "returned of the repressed."

The fact that, for a "renormalizable" theory, one can cure these infinities is a manifestation of the idea that the corresponding physical processes are insensitive to the virtual states that live above a certain energy scale.

 oops