@cheeseburgermonkey7104
I really like the illusion that rhombuses can look like an isometric projection of a collection of cubes Edit: Congratulations on 100k subs!!! You deserve millions though, I can't wait for that
@diribigal
Mathologer taught me about the arctic circle, but thank you for introducing me to other arctic curves and for discussing the generation strategy.
@oraziovescovi1922
DUDE! The craziest thing happened with this video! I had an exam today. Yesterday night I decided that "screw it, I'll stop studying now and I'll relax a bit - let's see what's on YouTube". I clicked on your video, and you talked about the Monte Carlo method I realized that is was a (niche) thing that the professor explained in class, but I didn't review: I opened my notes and reviewed it. Today at the exam, first question: "explain the Monte Carlo method, what it is and when it is used" my jaw dropped soooo thank you for helping me pass my exam! I wouldn't have answered that question if it wasn't for your video!
@tjreynolds685
One thing I noticed is that “removing a cube” is the same as rotating that “vertex” by 180°! This is only allowable when all three colors are intersecting at the “vertex”!
@galactic_goat_217
7:04 “a lot of the time, being aesthetic, or interesting, or beautiful, is the only thing you need to make learning about something worth it” holy crap, this is exactly why i like this channel without understanding most of the stuff in it.
@iwatchedthevideo7115
One of the best new science channels on YT. Love it!
@technopyrka5836
I may have not unterstood everything, but... I love your voice. It's so calm, so understanding, so... I just can't describe it
@TehMuNjA
I have a few questions about the sampling method: if each of your moves is some local change of the state its not clear why this should generate a uniform distribution, especially when starting from such a special place in the state space. surely at early times this random walk will only fill some corner of the whole set of possible states. so, is it that you have to take many samples over a long time to generate a representative sample? even just starting at a random-enough initial state would make it more believable to me. otherwise, i would think you need to make a truly random permutation of all possible states to get a uniform distribution rather than only transitions which only differ in one position. this is probably well understood in mcmc but wasnt clear to me from the video.
@the10thdoctor84
It reminds me a lot of a video from the french math youtuber Mickaël Launay called "La puissance organisatrice du hasard - Micmaths" ("The organizing power of randomness")
It's about how seamingly organized randomness can sometimes be.
And there is a specific part discussing the Aztec Diamond which reminds me a lot about how the liquid region of the rombuses is a circle but in the video in question the size of it was significant enough so the circle was blatantly obvious.
It's really interesting if you don't mind french subtitles or auto translated english ones.
@santoast24
Yesss yesss yessss more fun random math and physics to add to my repertoire of "Toast, How do you know this stuff????"
@ValkyRiver
3D version: a rhombic dodecahedron can be dissected into four rhombohedra (flattened cubes with rhombic faces). A large rhombic dodecahedron can be filled with many rhombohedra — the result is an isometric projection of a stack of 4D cubes (tesseracts).
@georgew.9663
I love the conclusion to this video, appreciating something nice is enough reason to do anything
@bray7299
one of my favorite courses I have taken was a grad course in monte carlo so always excited to see it brought up in interesting applications like this one!
@tms725
So ... This is kinda funny. YouTube's algorithm just randomly proposed this video out of nowhere. And while I don't work with this stuff in a long time, my thesis started on planar partitions - the thingies that @vye9431 pointed to - and whenever they could be mapped to quantum mechanics / condensed matter problems. Mainly, we used the planar partition (and rhombus tiling) equivalence to dimers on an hexagonal lattice. The latter problem has an equivalent system in quantum physics / condensed matter - double carbon bonds on a graphene sheet - and we wanted to see if there was a way to exploit this equivalence to study the quantum problem. In the end, the "quantum" version of these tilings has some interesting properties - like how you can recover something similar to the Arctic circle, but with some "ripple" effects. But the hexagonal shape of the full tiling add some really strong boundary conditions, so AFAIK you can't really use them to model a graphene sheet. And, well, maybe (surely) I'm not good enough on math to build the whole equivalence 😅. We ended up pivoting to doing numerical simulations on more "boring", periodic graphene sheets / tilings. But those have some mathematically interesting phase transition properties! Anyways, that was a fun walk down memory lane 🙂
@James2210
When you say lozenges I can't help but think of cough drops.
@larzanebra
You are the kind of youtuber who makes people enjoy math , thanks
@Blah64
I have no clue what I was supposed to learn from this, but the visuals were fun.
@alainpbat3903
Losanges is what a rhombus is called in french. Also, this is something we should send to cgp grey. Also, this reminds me of those IQ tests where you're supposed to determine the number of cubes with a 2D view.
@Meanslicer43
6:55 this is true even in other fields. engineers sometimes have Legos and other toy sets as quick stand ins for things. not often, but it's done all the same. it gives a person another perspective to a problem they had been considering.
@seanthebeast300