A well-known mathematician said once that it would take a million years to understand prime numbers well, if ever. One should have asked him what he aspired to understand about prime numbers that could take that long. As far as I know, no mathematician has even asked the question why the prime numbers, being at the core of arithmetic, do not seem to have any importance in Nature —when yet the Riemann zeta function, so intimately linked to their structure, seems to be reflected in many different kinds of physical systems.
Continuar leyendo «NAME, CONSCIOUSNESS AND NUMBER»Etiqueta: Riemann zeta function
IRONY AND TRAGEDY IN THE RIEMANN HYPOTHESIS
Did you know this secret? The worst is that beauty is not only terrible, but also a mystery. God and the Devil fight in it, and their battlefield is the heart of man.
Fiódor Dostoyevski
Mei Xiaochun published a paper 3 years ago in which he claimed that the Riemann hypothesis does not even make sense because there are already four serious inconsistencies in the 1859 text to begin with. In a later paper, he uses a standard method to prove that the Riemann zeta function does not have a single non-trivial zero. Zero zeros. Needless to recall that, according to the prevailing mathematical opinion, have been calculated billions of them.
Mei Xiaochun is not overcomplicating matters. The inconsistencies he talks about are very basic, they infringe even the very Cauchy-Riemann equations that are at the basis of complex analysis. I am not a mathematician and prefer to defer my judgment on the relevance of his arguments, but I think that, at the very least, they deserve an answer; though we are unlikely to find it anywhere. If some mathematician deigned to answer, surely he would say something like that the analytical continuation has principles that the author seems to ignore, but no one ignores that creating new principles out of convenience is the most elegant way of not having them.
Continuar leyendo «IRONY AND TRAGEDY IN THE RIEMANN HYPOTHESIS»METANOIA, CONTINUUM AND QUATERNITY
This is a translation of the final chapter of the essay “Espíritu del Cuaternario” (Quaternary Spirit)
After so many considerations on science we need to return to a more general perspective.
It was probably as a reaction against the intrinsic idealism of the trinitarian symbol that a number of thinkers of diverse orientation turned in the twentieth century, and especially after the post-war period, towards quaternary schemes as symbols of totality. Jung was maybe the first perceiving the need for this shift, followed later by such well-known authors as Heidegger with his earth-heaven-celestials-mortals quaternity, or the Schumacher of the magnificent «Guide for the Perplexed» with his fourfold field of knowledge: inner self, inner world, outer self, outer world, opposed two by two as determinants of experience, appearance, communication and science.
Continuar leyendo «METANOIA, CONTINUUM AND QUATERNITY»INFORMATION THEORY AND THE ZETA FUNCTION
It has been said that if the Riemann hypothesis were solved, all the keys to cryptography and cybersecurity could be broken; no one has specified how that could lead to faster factorization methods, but at least it reminds us of the close relationship between a hitherto intractable problem, cryptography and information theory.
Such speculations are only based on the fact that the Riemann zeta function establishes a connection between prime numbers and the zeros of an infinitely differentiable function that provides the most powerful method for exploring this field, prime numbers being the basis of classical cryptography. But we have already seen that the zeta is way more than this.
Continuar leyendo «INFORMATION THEORY AND THE ZETA FUNCTION»THE LITTLE FINGER STRATEGY
There is a technological war, but whoever thinks it is only technological has already lost it. Now China seems to have taken the lead over the United States in the fight for control of communication channels, and many would celebrate it were it not for the fact that this 5G is only intensifying what already was a huge wave overflow.
Not only do we oppose the indiscriminate deployment of technologies but, in a now distant article, we even suggested another line of biophysical research to evaluate the impact of electromagnetic radiation on humans and other living beings [1]. It is clear that the big corporations promoting this deployment are only concerned about market shares, but who says that in a few years they will not be sued for damages?
Continuar leyendo «THE LITTLE FINGER STRATEGY»From monopoles to polarity
Polarity was always an essential component of natural philosophy and even of plain thought, but the advent of the theory of electric charge replaced a living idea with a mere convention.
Regarding the universal spherical vortex, we mentioned earlier Dirac’s monopole hypothesis. Dirac conjectured the existence of a magnetic monopole just for the sake of symmetry: if there are electric monopoles, why can not exist magnetic monopoles too?
Mazilu, following E. Katz, suggest quietly that there is no need to complete this symmetry, since we already have a higher order symmetry: the magnetic poles appear separated by portions of matter, and the electric poles only appear separated by portions of space. This is in full accordance with the interpretation of electromagnetic waves as a statistical average of what occurs between space and matter.
Continuar leyendo «From monopoles to polarity»