GM
Discussion
Good morning ☀️ ☕️
Koch curve incoming.
Looked it up. Cool. Ever heard of the Devils Staircase?
I have not, is that like an escalator onlyou each step randomly teleports you to a different step and you never reach the top? Or like, at the end of the movie The Believer where the kid blows himself up at a synagogue and finds himself on an infinite stairwell with his rabbi asking him to reconsider himself forever
Don't know the movie ref, sadly. Just kind of a fractal construction, similar to what you named, which yields a surprising function: continuous, differentiable almost everywhere (with derivative 0, ie flat), continuous, but not absolutely continuous
EW! so it goes up but is always flat? That's disgusting!
While we're on the subject, you may not be aware of what's possibly considered the most counter intuitive "paradox" in geometry
https://en.m.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
Oo.. I'm gonna have to read this later while I shit in the dark because my office things it's a different time.
TLDR you can take a unit sphere, chop into 5 (I think) disjoint pieces, and reassemble them with normal 3D motions (no bending, just isometries or whatever - basically moving or twisting allowed) and get two spheres with no holes. Construction relies on controversial (but highly useful and widely accepted) axiom of choice. Pieces are "infinitely sharp" lol
My son is going to be very dissapointed with what Im about to do to one of his playballs
Also, I'm obsessed with geometric concepts that can be used to show an infite circumferance on a finite volume. When people learn about such objects for the first time it's usually a strong reaction.
Satsmcd posted about that famous Horn surface (finite volume yet infinite surface area) recently. I suspect he may not be full retarded...
Gabriel's Horn ya. Which makes sense because if you want to blow a horn for the apoclypse from the spirit realm into meat space you'd probably need infinite length but also finite volume so that the sound is right.
You like Gabriel's horn? Infinite surface area and finite volume. It's the horn you can fill with water but never paint.
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GM 🫂☕
Gm
Where are you in the graph?
GM - clearly we’re not bullish enough!
A fractal, nice
GM 🫂💜🤙
No, a wise person knows everyone is retarded.
This is breaking my brain 🤣
Jesus
agreed
Huh
GM! ☕ 😎