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Joined 3 years ago
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Cake day: June 22nd, 2023

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  • By coherent I assume you mean consistent. Yes an inconsistent theory isn’t considered useful in mathematics. In philosophical logic there’s an idea of “paraconsistency” that means something like “inconsistent but only slightly” but I think it’s not used much in math.

    Russell’s fix to Frege’s inconsistent system was quite complicated, much more than just adding an axiom disallowing certain types of sets. ZFC handles it differently too, by saying you can only create new sets by following certain rules designed to keep things consistent. Frege’s system let you do whatever you wanted and it went sideways quickly, as Russel found.


  • The KM3NeT experiment has recently observed a neutrino with an energy around 100,PeV, and IceCube has detected five neutrinos with energies above 1,PeV. While there are no known astrophysical sources, exploding primordial black holes could have produced these high-energy neutrinos. For Schwarzschild black holes this interpretation results in tensions between the burst rates inferred from the KM3NeT and IceCube observations, with indirect constraints from the extragalactic gamma ray background and with the non-observation of an associated gamma ray signal at LHAASO. In this letter we show that if there is a population of primordial black holes charged under a new dark 𝑢⁡(1) symmetry which spend most of their time in a quasi-extremal state, the neutrino emission at 1,PeV may be more suppressed than at 100,PeV. The burst rates implied by the KM3NeT and IceCube observations and the indirect constraints can then all be consistent at 1⁢𝜎, and no associated gamma-ray signal was expected at LHAASO. Furthermore, these black holes could constitute all of the observed dark matter in the universe.

    Neat. The story has been getting around though IDK how convincing anyone finds it.










  • I don’t know the unicode situation with ed. It is pretty minimal. There is also GNU Nano which I’ve never learned how to use. Ed is a line based editor, not screen oriented. I’ve programmed with it (back in the day) but these days I use Emacs for everything except minimal tweaks.








  • There is an MO thread about this:

    https://mathoverflow.net/questions/90876/what-would-be-some-major-consequences-of-the-inconsistency-of-zfc

    Basically “our mathematical system” for mathematicians usually (though not always) refers to so-called ZFC set theory. This is an extremely powerful theory that goes far beyond what is needed for everyday mathematics, but it straightforwardly encodes most ordinary mathematical theorems and proofs. Some people do have doubts about its consistency. Maybe some inconsistency in fact could turn up, likely in the far-out technical fringes of the theory. If that invalidates some niche areas of set theory but doesn’t affect the more conventional parts of math, then presumably the problem would get fixed up and things would keep going about like before. On the other hand, if the inconsistency went deeper and was harder to escape from, there would be considerable disruption in math.

    See Henry Cohn’s answer in the MO thread for the longer take that the above paragraph is cribbed from.