Atiyah

Sir Michael Atiyah came out of left field and made sensational claims (proved the Riemann hypothesis, calculated the fine-structure constant) more characteristic of a vixra physicist. And indeed, his Riemann preprint has been uploaded to vixra, though I don't know if it came from him.

I started a forum thread on the physics of his claims. I have not succeeded in properly deciphering his procedure to produce the value of 1/α. The integer part is Eddington meets Bott, but no-one has been able to motivate the next few digits.

But one interesting thing came up in that thread. Atiyah speaks of an iterated process that he calls renormalization, and "Auto-Didact" remarked that it resembles something out of bifurcation theory. And as I have posted here previously, 1/α is approximately equal to 2π times the square of Feigenbaum's constant.

So if - against the odds - there is anything to Atiyah's baroque conceptions, I think it would involve the Feigenbaum connection. But for now, I expect nothing. It was stimulating, it stirred things up, but I think it's a blind alley.

Historical interlude

Yet another subgenre of parodic scholarship has made its first appearance on vixra. An author whose name is Korean for "true history" overturns existing theories of the "Hwan-Suomi hyperwar", a clash of ancient supercivilizations unknown to normies and mundanes, but known to the cognoscenti of 4chan's "History and Humanities" board. Suomi means Finland, but these were hyperborean True Finns, superior to any modern stock; while the Hwan were the ancestral Korean master race, known to us thanks to the Handan gogi, a 20th-century work of "nationalist pseudohistory" (so say the killjoys at RationalWiki). Sometimes, fiction really is stranger than truth.

Koide from S-duality

1) Crackpot idea of the day: "the bottom quark is S-dual to the rho meson".

Gorsky et al conjecture that holographic QCD has a "flavor S-duality" in which vector mesons are dual to baryons. This is to be realized in string theory by a web of 5-branes.

Quark-hadron duality shows a kind of continuity between properties of quarks and properties of hadrons.

And the mass of the rho meson has been estimated at sqrt(6) times the constituent quark mass; while in the simplest version of Rivero's waterfall, the bottom quark mass comes out as 2 . sqrt(6) . sqrt(6) times the constituent quark mass. Also, the Brannen mass scale of the Koide triple containing the bottom quark equals the mass of the proton, the prototypical baryon.

2) Vague bonus idea: Koide relations are an echo of this S-duality.

This just comes from Brannen and Sheppeard's discussion of the discrete Fourier transform, in the context of circulant matrices (they obtain Koide masses as eigenvalues of a circulant). One might start with the realization of geometric Langlands via S-duality, and then look for analogues over finite fields. Sheppeard has occasionally hinted at something like this.