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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.







  • 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.




  • solrize@lemmy.mltoChess@lemmy.mlBeginner questions
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    22 days ago

    My buddy who was a 2300-ish player suggested the book “Chess The Easy Way” by Reuben Fine and I read it. It was written around the 1940s and is still a great book. “A Primer of Chess” by Capablanca is also great. And for total beginners, “Bobby Fischer Teaches Chess” is surprisingly helpful (it’s almost entirely about back-rank checkmates).

    Other than that, play a lot of slow OTB games. Don’t play speed chess. Check every move carefully to make sure it’s not a blunder. To do that, you have to spend time thinking at each move. That’s not compatible with speed chess. Ancient advice is to literally sit on your hands while deciding a move. That is to slow down the impulse to move before you have completely thought it out.











  • I’d DIY it (maybe with FreeNAS, about which I know nothing) instead of buying a proprietary NAS in a box. What’s the point of self-hosting if you’re going to be at the mercy of someone else’s software anyway? If you’re DIY’ing, there are 3.5" drive enclosures with soundproofing stuff in them that should keep the drive pretty quiet. Or if you can afford enough SSD’s for your storage requirements, then use those.