nostr:npub1tm3v7q8jk0pe5zwrl7w9tav09cttdwsu8hfhgd0x9rchdk60vupq088zk5 I doubt a clean proof is possible, because grids of size 8, 10, and 12 do admit solutions (see pics). The solutions for size 8 and 12 generalize to any multiple of 4. I'm not sure if the solution for size 10 generalizes.

cc nostr:npub1ecj3mfr9lzvx7wh6fmh59vz6eet324mdtdlp9qxzqvwuvpglwnxqv6fchy nostr:npub17z3zrlvtcp3fyc94vdqdk7y8ccjc7yay998z7wsvl9f0t7yqmjes3uhe6e nostr:npub16pn60c6d7458s56quf3e58ahjkwwwmcfm94vxtc09qq7q3srdw4szeruz4 nostr:npub1u83gudwdfwjngz5eqxkrnpvsuydvqwjxwz0majvehqrh62804hfq8yr2s5 wonder if you can find a non-computer proof that size 6 is impossible

nostr:npub17z3zrlvtcp3fyc94vdqdk7y8ccjc7yay998z7wsvl9f0t7yqmjes3uhe6e You can clear the fog of war once you get the Limited Principle of Omniscience; otherwise, you don't even know if there exist any enemies in a given area. (I only know what LPO is from reading Andrej Bauer's 'ominous' remark you showed me.)

nostr:npub1jacntdqvalt27vngj9hwhjyqzppeayq7hnm2xmf7747t84yz32as4czppv nostr:npub1g0uss0sjsgxwmhqxgnvlj0zv9ru89xwfyktkcjc0kgy8syxj79ss383vfw nostr:npub1zf4q6mpdh257g489fvz5p8f7njssa03q5xyyxdpnprm0agdeh6asmp3zta Thank you!! God I've been so busy these days, but life is good. It was nice to post a bit more today.

nostr:npub1f8e6w3kg6cptk4ljl09ua3vezr7gws4jcuwyvzdnpytsnlp2yd6savzu5u nostr:npub1ecj3mfr9lzvx7wh6fmh59vz6eet324mdtdlp9qxzqvwuvpglwnxqv6fchy nostr:npub1fsq0e7kgsgphs9zq9v82yrle7rs4xd28lurtmry4uu4psrmv4q2q5us56e One of the most absurd things I have witnessed is when people resort to sitcom levels of social maneuvering in order to *avoid* collaborating on a problem with someone else, or mentoring an interested student, because it would be "not nice" to just say "no go fuck yourself."

nostr:npub1ecj3mfr9lzvx7wh6fmh59vz6eet324mdtdlp9qxzqvwuvpglwnxqv6fchy nostr:npub1fsq0e7kgsgphs9zq9v82yrle7rs4xd28lurtmry4uu4psrmv4q2q5us56e

I once went to my advisor and said, "I feel like there's so much to learn, and I want to learn it, but I worry that it'll take me way too long before I start doing original research."

My advisor said, "Don't worry about taking time to learn. Once you become a postdoc, you'll never have time to learn again, so you should learn as much as possible while you can."

That response shocked me. On other occasions, I've heard professors with prestigious positions and named chairs complain that, due to their stature, they have lots of responsibilities and barely any time for their own research, let alone learning anything new.

I always wondered why someone would seek a higher position of authority if it takes away your time and ability to do the very thing which set you on this path in the first place. The answer, it seems, is that the system expects you to keep progressing, so you do.

I don't think this entirely explains your phenomenon, but maybe it's a part of it. Academia is so competitive and demanding that people are forced to choose between hubris and irrelevance.

nostr:npub1ecj3mfr9lzvx7wh6fmh59vz6eet324mdtdlp9qxzqvwuvpglwnxqv6fchy For the pedagogical point, I think most proofs should be presented like this:

1. Here's the conceptual idea.

2. Here's the plan for translating the idea into symbols.

3. Here's roughly how long the symbolic proof turns out to be.

Any proof which you cannot present in this way is one which you don't understand well enough to teach (or the field doesn't understand it and should think more about it).

nostr:npub175dlmjzxq6fgswh73qym7epwcll0dlrkpvcd479u9fc3yrzgxrqsjdwrtj Binary search is not appropriate for a gender-inclusive environment!!!

nostr:npub1pz6u0prt75nvmyfhgpngncrvq7xf7cs8f3xgnfd79j7uknj978mstj7c8z Thank you for tagging me. I like the character development that's been happening. Elephant Eater's worldview is totally consistent with her Word being False, permitting "P and not P" while eliminating any way to distinguish between them. Explosion of possibilities.

The first meeting of the Astronomer and the Computer is also poignant.

nostr:npub175dlmjzxq6fgswh73qym7epwcll0dlrkpvcd479u9fc3yrzgxrqsjdwrtj The general formula for solving cubic equations is extremely ugly, there's no way around it. The one for quartic equations is even worse. Both formulas are obtained by algebraic manipulations which resemble "completing the square" for quadratic equations.

There is no general formula for equations of degree > 4. (Abel's Impossibility Theorem.) So the fact that explicit formulas exist for degrees <= 4 should be considered a miracle, even if those formulas are ugly.

For your specific equation, I don't see any trick which would give a nicer formula. What do you need it for? For many applications, an approximate algorithm like Taylor expansion or Newton's method would be just as good as an explicit formula.

nostr:npub17dye8wm0l9w9qdsmvxw078ednfzaa9sw7xngsgwetvj8slv98mesn6yf4p cc nostr:npub1ecj3mfr9lzvx7wh6fmh59vz6eet324mdtdlp9qxzqvwuvpglwnxqv6fchy

nostr:npub1g0uss0sjsgxwmhqxgnvlj0zv9ru89xwfyktkcjc0kgy8syxj79ss383vfw When there is blood left on your own hands, there will be no doctors left to wash them

nostr:npub1ecj3mfr9lzvx7wh6fmh59vz6eet324mdtdlp9qxzqvwuvpglwnxqv6fchy nostr:npub1g0uss0sjsgxwmhqxgnvlj0zv9ru89xwfyktkcjc0kgy8syxj79ss383vfw nostr:npub1u5tpktgc8gv8jw22cyjyh5gy5nr07v88hmrvtut7zkr06q0py6fs30xmf3 It’s the logic of how you sometimes try a USB plug both ways and it doesn’t work, but then you try a third time and it works

nostr:npub1u5tpktgc8gv8jw22cyjyh5gy5nr07v88hmrvtut7zkr06q0py6fs30xmf3 nostr:npub1g0uss0sjsgxwmhqxgnvlj0zv9ru89xwfyktkcjc0kgy8syxj79ss383vfw No, science is discovered, not invented, and you have clearly never done either

nostr:npub1ecj3mfr9lzvx7wh6fmh59vz6eet324mdtdlp9qxzqvwuvpglwnxqv6fchy nostr:npub1g0uss0sjsgxwmhqxgnvlj0zv9ru89xwfyktkcjc0kgy8syxj79ss383vfw nostr:npub1u5tpktgc8gv8jw22cyjyh5gy5nr07v88hmrvtut7zkr06q0py6fs30xmf3 you have my sympathy there ... thankfully I’ve escaped this torture somehow

nostr:npub1ecj3mfr9lzvx7wh6fmh59vz6eet324mdtdlp9qxzqvwuvpglwnxqv6fchy nostr:npub1g0uss0sjsgxwmhqxgnvlj0zv9ru89xwfyktkcjc0kgy8syxj79ss383vfw I haven’t watched many science films (for obvious reasons), but I would rank Primer above Oppenheimer objectively speaking.

I do think Oppenheimer has a huge advantage if you see it in a theater, because it uses loud bomb noises to great effect. But it’s disjointed in an interesting way which makes it feel like there’s not much of a plot - or the plot is only a background to a bomb that is building itself. Primer is the opposite of all of this.

I also enjoyed The Zero Theorem (not really a science film) and The Man Who Knew Infinity, but I would put both below Oppenheimer.

nostr:npub1g0uss0sjsgxwmhqxgnvlj0zv9ru89xwfyktkcjc0kgy8syxj79ss383vfw The renaissance masters dissected humans to gain medical and artistic knowledge. Newton stuck a needle deep between his eye and eye socket to see how it changed his eye’s lens. It’s chuuni to say it, but I think science has always had a kernel of disregard for human life, and modern attempts to clean up its image only paper it over. Dr. Frankenstein was called the “Modern Prometheus” too

nostr:npub1ecj3mfr9lzvx7wh6fmh59vz6eet324mdtdlp9qxzqvwuvpglwnxqv6fchy nostr:npub1g0uss0sjsgxwmhqxgnvlj0zv9ru89xwfyktkcjc0kgy8syxj79ss383vfw nostr:npub1u5tpktgc8gv8jw22cyjyh5gy5nr07v88hmrvtut7zkr06q0py6fs30xmf3 Depending on your definition of “alien species” I can perhaps give one example already: Doron Zeilberger believes (apprently sincerely) that even large integers do not exist. What exists, in his view, is the ring Z/nZ for some n (larger than what is physically possible to compute).

Less flippantly, I take your point. Mathematics as a whole is quite arbitrary, which also makes it feel more freeing in a way, but also more depressing because the “dialectical forces” which drive its development tend to come from people and fashions rather than fundamental reality. The rules of logic seem universal to me (inb4 constructivism).

nostr:npub1w4jud2zhl9ztd5pycpzsq9nf07c3vcguavtrc6jypvtd6qealy9sl8cead nostr:npub1u83gudwdfwjngz5eqxkrnpvsuydvqwjxwz0majvehqrh62804hfq8yr2s5 nostr:npub1g0uss0sjsgxwmhqxgnvlj0zv9ru89xwfyktkcjc0kgy8syxj79ss383vfw You might be right. I see this idea being floated under the guise of “tactical” versus “strategic” nukes.

nostr:npub1u83gudwdfwjngz5eqxkrnpvsuydvqwjxwz0majvehqrh62804hfq8yr2s5 nostr:npub1g0uss0sjsgxwmhqxgnvlj0zv9ru89xwfyktkcjc0kgy8syxj79ss383vfw I find the Soviet “Dead Hand” system fascinating

nostr:npub1g0uss0sjsgxwmhqxgnvlj0zv9ru89xwfyktkcjc0kgy8syxj79ss383vfw Before the Trinity test, there was a concern thar nuclear fission was so powerful that it could ignite the whole atmosphere. Theory predicted it was very unlikely, but that was all. When those scientists at Los Alamos did the test, they knew full well that there was a slim chance they would end the world right then and there. But they pushed the button anyways.

So I think there are two sides to this coin. They had to be willing to reduce the world to ashes in order to usher us in to this strange new era of nuclear peace.

This is another thing which the movie portrays well. At least, it rightfully emphasizes it.

One thing that didn’t make the cut, but I wish it did, was how Fermi dropped some shredded paper during the blast and watched how far the wind blew them in order to estimate the megaton yield.