fan of all things aerospace, also trying to learn about ai, low level software, hardware
I hope this email finds you lying there naked?
Is this what the Nintendo Switch 2 Camera is missing?
Today's wikipedia article is Chandrasekhar–Eddington dispute
https://en.wikipedia.org/wiki/Chandrasekhar%E2%80%93Eddington_dispute
smh US politics is full of gangs https://en.wikipedia.org/wiki/Special:PrefixIndex/Gang_of we need to CRACK DOWN, HARD!
Today's wikipedia article is Gang of Four (disambiguation)
Pixel graphics accidentally meets cryptography:
The function R_θ that rotates the plane by θ about the origin can also be written as the composition of three axis-aligned shears
y ← y + x tan (θ/2)
x ← x − y sin θ
y ← y + x tan (θ/2) # same constant, but with the modified x
(You can derive this by setting the rotation matrix equal to the product of three arbitrary shears in the y,x,y directions, and then doing algebra and trig identities to work out the constants.)
By rounding the addend in each step, we can make a function P_θ that maps integer x,y input to integer x,y output, and approximates R_θ in the sense that every pixel ends up within a bounded distance of its 'true' destination:
y ← y + round(x tan (θ/2))
x ← x − round(y sin θ)
y ← y + round(x tan (θ/2))
This function is bijective: no two input (x,y) pairs map to the same output, and every output has a preimage. Why? Because each step individually is bijective, due to mapping (A,B) to (A, B+f(A)) for some function f (where A,B are x,y, one way round or the other). If I receive the output (A, B+f(A)), I can compute the same f of the same A, and subtract it off again.
It doesn't matter that the function f itself might _not_ be bijective. (Some of them in this example certainly are not.) Bijectivity is guaranteed by the fact that the output pair still contains the input to f. So each of those three steps is bijective, and hence, their composition is too: you can undo all three steps one by one. (In fact, the inverse of P_θ is exactly P_{−θ}.)
This is also the structure of a Feistel network, which used to be the standard construction of block ciphers in the DES and Blowfish days. You'd divide the block into two halves L,R, and then repeatedly add (or XOR) a complicated function of one side into the other side, then switch roles. That structure guarantees the cipher as a whole is bijective, whether or not the complicated functions are. So you could make the functions as horrible as you liked without having to concentrate on two things at once.
http://www.jitterbuzz.com/indtol.html
14k words on 'the aristocrat of toasters'
from my link log —
Crossness pumping station: seduced by symmetry.
https://www.anthonybaines.co.uk/blog/2021/9/2/crossness-pumping-station-seduced-by-symmetry
saved 2025-05-15 https://dotat.at/:/C1Y0K.html
> The devil, having failed to get Jesus to accept an earthly crown, challenges John, the disciples, and Jesus to a fishing contest in the desert, accompanied by his own fishing demons. Jesus naturally wins.
from https://en.wikipedia.org/wiki/Pseudo-Evodius
Fun game: find a street preacher and try and narrow down their denomination, without interacting with them, as quicky as possible
@simon thought you might find https://mikecaulfield.substack.com/p/differences-in-link-hallucination interesting
The existence of top surgery and bottom surgery implies the existence of up surgery, down surgery, strange surgery and charm surgery
You need to explore this guy's website, a relic of 2002. He's a poly anarcho-capitalist PL theory professor who dislikes democracy, very amusing read
http://kilby.stanford.edu/~rvg/orientation.html
http://kilby.stanford.edu/~rvg/matrimony.html