Let us imagine a biofeedback machine where the three principles of mechanics are expressed in an alternative but quantitatively equivalent form, as in Weber’s force law (1846): instead of inertia, there is a zero sum of forces; instead of a constant force, the intensity of force depends on the environment; instead of simultaneity of action and reaction, there is a «retarded potential» and thus an internal, proper time of the system. The first remarkable difference between these principles and the more familiar ones is that they allow, to a certain extent, the interpolation of consciousness within its framework. The second is that it applies equally to point and extended bodies or events, rendering unnecessary crucial artifices supporting special relativity, general relativity, or quantum mechanics and making them incompatible with each other. The third is that it makes possible a conception of time different from those of physics and psychology.
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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»The Multi-specialist, Mechanology and Fourth-Person Knowledge
This is an interview given recently for Ivan Stepanyan’s science and technology blog:
Why do you think science is going through a particularly critical time right now?
The different sciences are used to have periodic crises in their models, but now, as a faithful reflection of what is happening in our societies, the accumulated problems have reached an extreme point.
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