Is Science going too far from reality and life? The Connes RH Devil in Music-Mathematics: A conspiracy of Nature and Number

 

 Alain Connes in his Riemann Hypothesis talk mentions the Devil in mathematics

 The Riemann Hypothesis [RH] does not directly predict the exact values of prime numbers, but rather it makes a statement about the distribution of prime numbers by suggesting that the zeros of the Riemann zeta function, a complex function closely tied to prime numbers, are located in a specific pattern, which would reveal insights into how primes are spread out across the number line; essentially, it tells us more about the "spacing" of prime numbers rather than pinpointing their exact locations

The RH is "some kind of delirium" and "life on Earth is going to disappear" and "it's time to change his role on Earth" -  Connes is giving a hat-tip to this famous mathematician who became a hermit based on his view that science was wrong....and ecology was correct.

Does Connes realize the same truth? hahaha. He has a novel based on this concept but it's in French only. 

I will listen to more of Connes latest Riemann Hypothesis lectures - what was called the "conspiracy between nature and number, atom and arithmetic" by math professor Steve Strogatz - but that quote as a promo for the "Music of the Primes" book was removed!

 Connes' youtube channel

 https://www.youtube.com/watch?v=Zh9mVUq0ZQM

This video shows the winding of physical time in our habits, little by little creating our

 individual time much more structured and larger in size.

  I will describe in my talk two roles of prolate spheroidal functions in the spectral interpretation of zeros of the Riemann zeta function. 

 

 So Barry Mazur was first to recognize the knots/primes connection? Or maybe it was Lou Kauffman.

I actually was given inspiration from Professor Joseph Mazur, the math professor brother of Barry Mazur. Let's see if Joe Mazur is still around and writing?  

yes.  https://worldfinancialreview.com/category/columns/understanding-war/ 

Wow he's got a lot of political economy articles now.

So that aligns well with this "conspiracy" of true math being against "science." hahahaha.

 assuming RH, the self-adjoint operator whose spectrum is formed of the imaginary parts of non-trivial zeros of the Riemann zeta function. The coefficients of the expansion are explicit expressions involving Bernoulli and Euler numbers. We relate the divergent terms with the heat kernel expansion of the Dirac square root of the prolate wave operator

 Heat Expansion and Zeta 

 investigated in our joint work with Henri Moscovici.

 

 What you get is the action by multiplication. Of course people know music, they know this action extremely well.

 what you get is is a is the action by multiplication

the action of the multiplicative integers and cross

on zero infinity on the half line and the action by multiplication

of course i mean you know people know music they know this action extremely well because multiplication by two on frequencies is passing to the octave multiplication by three you know i mean up to an octave is transposition and so on and so forth so i mean this is something which is a very natural object which is the half line the half

 

 When you compute this space, these points form a noncommutative space...

 This is joint work with C. Consani. When contemplating the low lying zeros of the Riemann zeta function one is tempted to speculate that they may form the spectrum of an operator of the form 1/2+iD with D self-adjoint, and to search for the geometry provided by a spectral triple for which D is the Dirac operator. We give the construction, using prolate spheroidal functions, of a spectral triple which is a finite rank perturbation of the spectral triple of the circle of length L and admits a spectrum of 1/2+iD very similar to the low lying zeros of the Riemann zeta function. We justify conceptually this result and show that, for each eigenvalue, the coincidence is perfect for the special values of the length L of the circle for which the two natural ways of realizing the perturbation give the same eigenvalue. We test this fact numerically by reproducing the first thirty one zeros of the Riemann zeta function from our spectral side, and estimate the probability of having obtained this agreement at random, as a very small number whose first fifty decimal places are all zero. The theoretical concept which emerges is that of zeta cycle and our main result establishes its relation with the critical zeros of the Riemann zeta function and with the spectral realization of these zeros described in 1999 by the speaker.