:0 amazing resources, thank you!
06.03.2026 14:59
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:0 amazing resources, thank you!
Where did you learn about this? I learned about it by deep diving on the chebyshev polynomials wiki page and finding some self published books 😆 which was not a great way (but it was fun)
There have to be more disquieting facts you can hand pick related to the cyclotomic polynomials Phi and the polynomials with real roots Psi, with IIRC x^{\varphi(n)/2} \Psi_n(x+1/x)=\Phi_n(x).
I don't know much of what to properly call Psi. varphi is the totient function.
😅 and then if I compare to the original I can see clearly that I know nothing about playing guitar
www.youtube.com/watch?v=w1vV...
Been practicing "Mais Quand?" by Erik Mongraine. Haven't learned the best part yet but if you haven't heard the song before you might not notice that I omitted it :P
But it is a mathematically inevitable consequence of the Einstein field equations. A singularity develops.
But in a funny way, you can never observe the singularity and then bring that information back out ("no naked singularities"). So how are you going to do an experiment to demonstrate there's a singularity? You really can't, you get spaghettified and hawking-radiated out a bajillion years later.
This is part of what Penrose and Hawking are famous for! Singularities are guaranteed en.wikipedia.org/wiki/Penrose...
I can't remember where I read good non-technical accounts of this... Probably Susskind's Black Hole Wars. Hawking's autobiography is good but I can't remember if it discusses this.
(oops, also you need vanishing diffusion term to get the sharp cusps)
The KPZ equation is very cool. In the simple case with no noise term, its solution is patched downwards pointing parabolas. I'd like to get a pic where those sharp cusps develop over time but where you can still see some effect of noise like in this pic, but I can't find the right params atm.
You would NEVER catch me up at 4:30am numerically integrating the KPZ equation to draw stromatolites.
Well... maybe.
Mathematica source code: www.wolframcloud.com/obj/011068c9...
me at the function
"Doctor... It's my chat... They keep saying 'Lyra' to every constellation, they think it's the funniest thing ever but then when Lyra actually comes up they say 'Bootes'. I'm trying to be supportive I really am."
Lyra!!!
Always a pleasure, especially the amazing discussions of sequels to pirate based games!
:( have a good soup!
My advice: flea
Oh thank god
@pooltoy.live 👍
posting about linear algebra at 2:30am type beat (apologies to @yungbishop.bsky.social )
If you like that, you might like this challenge codegolf.stackexchange.com/q/214638/53884 based on OEIS sequence oeis.org/A337517 (the number of distinct resistances that can be produced from a circuit with exactly n unit resistors.)
Oh awesome! Might try my hand. I used some of the code from oeis.org/A048211 which is slightly different. Actually a(5) is the first different number, so I wonder what the unique circuit with 5 resistors that obtains a new value (not obtainable by series and parallel circuits) looks like.
Inspired by x.com/shapoco/stat...
circuits in textual form: pastebin.com/Dh80i9KD
I used slow mathematica code, you have to go to 14 resistors before you can do better than 22/7. I basically just check N cases where N is taken from oeis.org/A000084
If you're given only twelve 1 ohm resistors but you need a circuit with an equivalent resistance of pi (approximated as closely as possible), and you have to use all of the resistors (no shorting or leaving them out), here the ways to get 22/7 ohms (which is the best you can do). #math #circuits
IMMENSELY EXCITED.
Oh, did someone mention Valheim? I can be normal about Valheim. I'm being normal about Valheim right now.
Dastardly.
