anon (Shelljump)

I am going live on twitch: today's items: *steam workshop support *level editor programming *listening to polyrhythmic konakol music twitch.tv/hi____________…

A lot has happened since we last posted...

@mathladyhazel need to start using “behold” in proofs going forward

Contrapositives are for cowards.

@Anthony_Bonato if you remove the cusp its significantly less tedious

What happens to my curly brackets over the course of every one of my mathematics lectures

@MathMatize a vector space is a setting in which you can linearly combine shit and it behaves reasonably

@PhysInHistory A lot of good would happen if people realized that most skills/traits sit in a partial order and not a total order.

Who do you think is The Greatest Mathematicians of all Time ? ✍️

what do you mean by difficult? that could mean its alien or unintuitive, which is just another way of saying its not closely related enough to things you have a familiar grasp on. you solve that by slowly pushing your frontier of experience outward incrementally. ("abstract" is a special case of this) it could mean it contains too many components interacting at the same time. you solve that by treating subsystems as a single black box once you understand those parts separately. also a familiarity thing. it could mean, as in a proof, a need to fill in and connect n missing dots from beginning to end, where n is large. again you gain enough familiarity that the dots don't seem as invisible and then suddenly the number of ones you gotta fill in shrinks. all of those things have the same solution, namely sharpening your intuition through experience, and building good mental models. the application of that advice is separate in each case, but its still kind of the same thing each time. it doesn't seem like a talent or intelligence thing in my experience, its just familiarity with a given pattern type and the efficiency of your mental model for that pattern. Once again, Bill Thurston is the guy to read up on regarding this.

How do some math people manage to understand some truely difficult stuff?

@PhysInHistory yoneda lemma

Which is your favorite mathematical equation? ✍️

@juzcook this is one of my favorite levels top 10 for sure

This is absolutely insane. Mario can screenwrap in every direction, and specific arrow blocks that Mario touches move the camera around a huge map by a set number of tiles. Level by TheBiob

@TonyTheLion2500 so the group of deck transformations of the universal cover of X is the same as pi1(X), and you get a galois-theory sorta thing where the subgroups of pi1(X) fit together in a way that matches the way the covering spaces of X fit together

In topology, what is the purpose of a covering space?

@TonyTheLion2500 not really my subject but I think you can use the jet bundle to define PDEs on fiber bundles, no? you might be asking something deeper, idk.

What's the relation between PDE and Riemannian manifolds?

in the rationals 3, 3.1, 3.14, 3.141, ... does not converge but gets arbitrarily close together (the condition OP posted). One way to define a real number (e.g. pi) is as an equivalence class of such sequences which "would converge to the same thing if there weren't a hole there". #Construction_from_Cauchy_sequences" target="_blank" rel="nofollow noopener">en.wikipedia.org/wiki/Construct…

@MathMatize if you want to intimidate people just use \boxtimes for everything

tanh(x*k) is like a smooth sign(x) with an adjustable smoothness factor "k". The output still ranges from -1 to +1

off the top of my head: all of master courses springboards and shells swiss hotel swissotel missingno worldpeace tubular most of ferpy's levels (everywhere else specifically) most of sweetdudes levels most of tithered with some major exceptions "my qldc level" bramble levels from vip 3

Kaizo Mario Nerds! What are your favourite or most memorable kaizo levels? Why?

@TheSph3ricalCow @martinmbauer can you provide a code snippet integrating f(x) = 1 on irrationals 0 on rationals from 0 to 1? should be interesting since every float evaluates to 0 and it integrates to 1...

@martinmbauer Actually yes it is because:

No it isn’t. That’s the whole point

Thanks! Glad you liked the game!

My Top 12 Indie Games from PAX West 2024 hard-drive.net/news-games/my-…

Come check us out at booth 764!!!!

New Trailer! New Features! Come check out Inpulse at PAX 2024, now with many new worlds and mechanics. Builtin TAS controls, input diffing, and more! #PAX2024