The Most Powerful Diagram in Mathematics
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- Опубліковано 9 чер 2024
- ⬣ LINKS ⬣
⬡ PATREON: / anotherroof
⬡ CHANNEL: / anotherroof
⬡ TWITCH: / anotherroof
⬡ WEBSITE: anotherroof.top
⬡ SUBREDDIT: / anotherroof
⬣ ABOUT ⬣
I have loved this diagram ever since I first saw it on the coffee cup of one of my lecturers / colleagues. But I was shocked to discover that its extraordinary properties weren’t very well-known! In this video, I build up some theory necessary to understand the MOG, then demonstrate how to use it.
⬣ TIMESTAMPS ⬣
00:00 - Intro
02:49 - Motivation
07:14 - Steiner Systems
18:23 - Three Big Questions
29:21 - S(5,8,24) and the MOG
44:47 - Outro
⬣ HINT ⬣
Why might S(2,3,10) be impossible to construct? Try and prove the following lemma: If S(t,k,n) exists, then S(t-1,k-1,n-1) exists. Then use the contrapositive of this statement together with what we know about the number of blocks. In fact, one can prove that: If S(t,k,n) exists, then S(t-m,k-m,n-m) exists for integer m such that t-m is non-negative.
⬣ INVESTIGATORS ⬣
Nothing for you here. Sorry!
⬣ REFERENCES ⬣
R. T. Curtis, A New Combinatorial Approach to M24. Math. Proc. Camb. Phil. Soc. (1976), 79, 25.
J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices, and Groups. Springer Science (1991).
⬣ CREDITS ⬣
Music by Danjel Zambo.
Pythagorean Theorem diagram:
upload.wikimedia.org/wikipedi...
Jakob Steiner:
upload.wikimedia.org/wikipedi...
Gino Fano:
en.wikipedia.org/wiki/Gino_Fano - Розваги
CORRECTIONS AND CLARIFICATIONS
1. But that rotation at 25:11 is 120 degrees! Yeah. It is. I don't know how that error slipped through. I am a mathematician, I promise!
2. But the octad containing at {4,9,10,13,21} in S(5,8,24) in the big list at 30:42 is {2,4,9,10,13,16,21,23} and the one you calculated at 34:24 is {1, 2, 4, 6, 9, 10, 13, 21}! This is correct -- the "big list" version of S(5,8,24) is a different labelling than that "standard MOG ordering", so they're isomorphic but different.
3. At 21:36 I jokingly defined isomorphic. I defined it as a noun though and it's actually an adjective.
4. 29:05 are there 27 sporadic groups? Some authors argue as much. The non-cyclic, non-alternating groups broadly fall into the groups of Lie type (of which there are several infinite families) and the 26 sporadic groups. Then there's the Tits group (named after Jacques Tits) which isn't strictly speaking a group of Lie type, so some authors lump it in with the sporadics. But because it is derived from a case of a non-simple lie type group, most mathematicians agree that it doesn't belong with the sporadics. I agree with this consensus and that it is best considered as the only simple member of an infinite list of groups. Maybe I'll make a video about it one day!
5. At 28:18 I claim L2(7) is isomorphic to L2(3). I misspoke and didn't catch this in the edit: it's not L2(3) but actually L3(2). What am I, a group theorist?!
6. But come on, is this *really* the most powerful diagram in mathematics? Well, clearly that sort of statement is bound to be a little subjective. But I actually believe what I say in the title. Most diagrams clear up what we *already know* by neatly presenting things. The MOG is the opposite: it sets out a complicated structure in such a neat way that we can use it to *learn more*. I know I don't go into all of that in this video, but that's what the next video is for!
I'll add more when they arise -- thanks for watching!
Thank for the hard work and organized explanation in simple language! That help us to view the elegance mathematic from a spectacular windows outside the great hall of Group theory. Great job!
Have you tried streaming on Kick? Twitch seems to be melting down.
This is a nitpick, but you labeled "isomorphic" as a noun.
@@pyros6139 Whoops! Well spotted. Damn.
Didn't you say at 29:05 that you'd clarify the fact that some people count 27 sporadic groups?
You are in the same tier as Mathologer, Numberphile, 3b1b, and StandupMaths. Truly S tier math content here. I find your topics as clear as 3b1b and yet more abstract. I think you achieve this from embracing longer form content.
Except for being annoying.
3b1b is more about information visualisation in my opinion.
Where has this channel been my whole life?? Excellent presentation: rooted in application, elegant in explanation, and the perfect amount of comedy :D
Binge watch time!!! 🎉
💯
Ikr
@@brianbouchard1899u might even still be able to watch the whole catalog tbh now I think
I found my Inner Nerd here.. 🤓 😂
*Mathematicians hate him!* Learn how he cracked the code with this *one weird diagram!*
Hahaha
29:46 Julius and Augustus didn't shove their months into the middle of the year.
It _is_ true that there used to be 10 months, but the two months added were January and February, by Numa Pompilius, to the _end_ of the year.
It's _also_ true that Julius was the one to mess up the calendar. Janus was the Roman god of gates and doorways, and Julius thought it would be fitting for the "doorway" to the new year to be January 1st, rather than March 1st/25th/Christmas.
July and August weren't new months, they were just re-named old months, "Quintilis" and "Sextilis".
Also worth noting that in "messing up" the calendar, Julius Caesar made it actually a ton more regular than it had been before.
Before, the calendar required manual correction, and was so messed up that he once won a naval battle by knowing that it was actually fall when the calendar said it was winter. (He was also the one in charge of manually correcting it, so this was his fault.)
yes! it's pretty weird so many people get this wrong
Thanks for adding this for those interested! 🙂
In my defence, I never claimed they put them in the middle of the year. It's also not clear *who* arranged the months as such (I can find sources claiming that they were always added to the beginning, and some agreeing that they were added to the end and moved later.) The point is that January and February ended up at the beginning which ruined the sequencing, so my remark "you monsters!" refers to whoever made the decision to have them at the start!
sextillis would have been the goofiest month name
gah u beat me to it i was gonna comment that
6:15 I like this style... i imagine it is quite difficult do edit, but I like it none the less.
It makes the Video more light hearted amongst all the serious mathematics.
I found S(3,4,8) in an interesting intuitive way I think.
Consider a cube with vertices labeled 1-8 (or however I guess). Every face is four vertices which are all coplanar, meaning that any three of the vertices on a given face can define a unique plane, and are only contained in that one plane. It might help to imagine the right triangle that those points form. 6 faces describe our first 6 blocks. Next, every edge also forms a plane with the edge opposite of it. There are 2 of these diagonal planes formed from edges along each of x,y,&z directions, so 6 more. First 12 blocks done.
Then I realized I was missing some. The last two blocks are a little sneaky, but having seen the circle “line” from S(2,3,7), and after holding a rubix cube for a couple minutes, I found them.
Start from a face and choose a diagonal on that face. Now on the opposite face, combine it with the diagonal that goes in the other direction. Those 4 points form a tetrahedron on the inside of the cube, and while they are not coplanar, they also do not collide with any of the planes we’ve described already. Any three of the points in the tetrahedron form an equilateral triangle, and thus are distinct from all of the right triangles forming rectangular blocks that we’ve described already. We have 2 choices for that first diagonal, and so we have 2 more blocks, bringing us to the final total 14.
I spent a few minutes convincing myself that any 3 vertices on a cube are either contained in a plane (which does include a fourth vertex), OR is contained in one of those tetrahedrons. Thus 14 is the number or blocks. Yay!
(edits for clarity)
Come on, no one commented. Bravo🎉
bruh
The moment I saw the Fano plane in the patreon plug my mind jumped to octonions, and I was thinking "huh, that's cool, octonions kinda rock and I'm excited to learn how they link to this stuff." 17 minutes in my mind has been blown several times already.
(octonions do kinda rock though)
It’s like peeling back the layers of an octonion
I've become so addicted to your videos. They are just pure quality maths i never got in school growng up. I actually feel myself gaining better perspective on the world with each video.
Love ya man, thanks for your work here.
The Steiner Diagram of S(2,3,7) is also isomorphic to the multiplicity graph of the octonion basis elements.
Fun fact: the symbol groupings in each square of the MOG also define a Steiner system on their own for S(3,4,16). For example, the square where all four symbols in a column are the same can define the blocks (1,5,9,13), (2,6,10,14), (3,7,11,15) and (4,8,12,16), and each triplet appears exactly once (as you showed in the 2-2-1 case, when you fit a triplet into the square there's a unique way to finish it with a fourth element)
Man, Steinerverse 2: Part 1 was amazing! How dare you leave us on a cliffhanger while only introducing the coolest characters at the very end though? Anyway, the visuals were revolutionary and you left me more confident than ever that Part 2 will be one of the all-time greats! ♾️🕷️
Hahaha.
This was perhaps the most amazing mathematical journey that I’ve been through. Even though it seems so completely unhinged. Coming from an engineering background and only now diving into “real” mathematics the existence of such objects amaze me. And the way you explained and motivated all (and your clear passion) made it that much more special. Can’t wait for part two. Thank you Alex
literally one of the best math youtubers out there i can literally watch an entire one of your hour long videos so easily.
You earned a subscriber. I was on the edge of my seat the entire video, hooked onto every single word, and I hated the cliffhanger, but you can be sure I'll be back. I love this. MORE!
I love the phisicality of your explanation, and the fade during the titles is so smooth. Keep it up!
1:08 pausing to comment. Holy shit that intro has me so hooked. Instant subscribe, thanks for making this. Okay, continuing to watch
A video about Hyperreal numbers as a follow up to the defining every number ever video would be awesome!
That woukd be cool!
You’ve becoming my favorite math channel. Incredible work, these videos are amazing!
Love it Another Roof. Every video has been an absolute banger. Sincerely, thank you.
You do a great job of walking through the whole concept and then the specific example. It REALLY helps. Thank you!
If you take the digits of the binary positive integers with 3 digits to be the x, y, and z coordinates on a graph, they are the coordinates of the corners of a cube. Was very satisfying when you ended up drawing this cube at 5:48 :)
Just saw the same thing, and only 16 minutes later, it appears. 😀
15:55 "how did I know these things" -- god I was so certain the next line was going to be "well thats thanks to this videos sponser, Brilliant. Brilliant is an online ... "
Hahaha! This gave me a good laugh. Thanks as always for stopping by 🙂
This is bt so far the best find I've made in youtube. Pure gold content, really.
I'm not able to fully understand everything bc I'm sill young but, oh my, you're incredible at teaching. Not only understandable communication but also very entertaining. Hope to see this channel breaking barries and educating millions of people
holy shit... I can't tell you how long I've been waiting for this video to exist. ever since I learned about this group (primarily in the context of sphere packing), all the bizarre junctions it forms across fields of study, and how it apparently relates to the Monster group - despite being comprehensible (however minimally) to mere mortals - I've wanted to know more. but, as you sort of allude to, Wikipedia leaves a lot to be desired amid the sea of notation. this is an excellent video, and the diagram at the center of it is a work of art. thank you so much
I love how the word "Monster" just spuriously popped up near the video with no explanation. Bwahaha!
Turning this incredibly lengthy and complicated process into a simple _and funny_ matching shapes puzzle really is nothing short of a miracle
I gotta say, it's refreshing to see more varied content on here. I know every math/science youtuber wants to tackle subjects that are interesting and not too complicated to explain, but that usually means they circle around the same topics. The truth is, if you allow yourself to make longer videos, you can talk about any obscure subject in any textbook. But it's super challenging all the same, so I really appreciate videos like this.
Anyway, subbed and liked. I particularly liked your joke on 19:20. 'I know what you are wondering! how long and intellectual is his face?' lol
Soooo, there are so many gears turning in my head now because the first thing that came to mind was a treatise on building a tic-tac-toe computer using tinker toys. One of the ways they went about building it was to construct a vertical ladder-like framework that would trip a move indicator when a reader would meet a block of a certain pattern; it would otherwise fall through. However, a ladder of all possible combinations of moves would make too man rungs on the ladder to be tenable for use, so they had to cut the number down in some way. They ended up working out the reflection and rotation of each possibility and eliminating any matches that came up as they were generating it. They ended up with 48 unique board configurations for game play. That treatise helped pushed me into electronic engineering and math and this video is reinforcing that push even more.
In short, thanks for the rekindling!
The quality of your writing and topic selection has improved; sub earned, and bravo.
I paused the video to hash out the S(3,4,8) Steiner set myself, with the added rubric of designing a class-based team co-op game out of a pool of varied attributes. Most fun I've had in a long time, and now I have a small TF2 clone in my back pocket to boot.
Image files like wbm, pnm, mif are really flexible and amazing for viewing pixel patterns when you encode the color data to Base64, again and again... .
Everything becomes a Math splendor to behold.
For anyone interested, the sporadic group that is the automorfism group of (5,8,24) is M₂₄, one of the five sporadic Matheu groups.
The Steiner system of (5,6,12) has automorfism group M₁₂, another sporadic Matheu group.
The other sporadic Matheu groups (M₁₁, M₂₂ and M₂₃) can be obtained be simply fixing one of the elements of the group with a Matheu number one higher.
These are also the automorfisms of Steiner systems of (4,5,11), (3,6,22), and (4,7,23).
You can make these Steiner systems from (5,6,12) and (5,8,24), since you can just lower every number on the Steiner system and it will still work.
15:02 I like how everything below the 1-row in the first 7 columns of S(3,4,8) is the same S(2,3,7) as in the previous solution
fantastic. I was having issues following along until I played this a 2x speed and it made it easier to understand
43:12 I was lucky enough to have John Conway as a lecturer at Cambridge. His lectures (on "Foundations of Mathematics") were inspirational.
Incredible. I've said this many times before but one of my biggest regrets was that I never got to meet him. We worked in the same field and during my PhD I had at least one chance to go to a conference he was at, but for whatever reason I couldn't go. I would have loved to have met him!
@@AnotherRoof He taught me Algebra 3 at Cambridge. Best lecturer ever. But then years later through a sequence of lucky events I got to know him when he was at Princeton, and even collaborate with him on writing a little paper. Truly an honour. Feature Conway more in this Channel to see your subs sky-rocket imho :)
I would like to point out at 19 minutes and 13 seconds a moment of humility and creating an opportunity for potential to grow. Thank you friend for creating engaging educational material!
I minored in math in college, and ended up doing business math (actuary, so a bit more complicated). I always had the love of numbers, but business tends to be 'practical'. Glad I can now take my time to wade through higher level material. Thanks.
26:36 this made me realise how in English having "no choice" often means having "one choice", interesting quirk of natural language
Nice observation! I'm still amazed that as kids we can pick up natural languages so effortlessly given all their quirks such as this one. The problem of course is that in the given contexts, those two occurrences of "choice" mean different things (namely, something like "required decision" and "available option" respectively).
Whaaaat this is awesome! I've never heard of this stuff before. I can't wait for part two!
u r perfect. you address the most sensitive aspects of the topic. your language (visual encoding) is rich and powerful and puts the most important to the most visible places.
Awesome video tutorials and even better instructional tools, highly educative and unique in his level of clarity. I enjoyed it immensely. Congratulations. PS. I'm not a nerd, just too attracted to knowledge.
When you said you were going to explore I suddenly got scared because I knew the whole vid was 45 min long and I didn't know where in the vid we were... then you said "uin the next video" and I breathed a sigh of relief! The pacing of your explanations is impeccable and I thought that you might need to rush if it was still in this one, happy to see that you didn't, and I can't wait to peek behind the curtain of the magical MOG
"But that's BORING!"
Literally every mathematicians core motivation.
Just wanted to mention that besides the interesting topic itself, your presentation is top-notch. I very much like the analog - style presentation and human pesence. Language is clear and speed is only _sometimes_ too fast to follow. Glad there is a pause button ;c) Video composition and editing is also flawless, which shows by it never being noticeable. I am definitely in for the next video...
0:51 This, in my opinion, is an amazing sales pitch.
A really nice introduction to some interesting topics. Looking forward to the next video.
This is an absolute brilliant video! Bravo!
Rob Curtis is actually publishing a new book on this very subject later in the summer: look out for "The art of working with M24" published by CUP. It's also worth noting that whilst the diagram is where it originally came from and you'll find it in Rob's PhD thesis, but the more modern approach via the hexacode really is much faster to do - you'll find it described in Chapter 10 of Conway and Sloane.
The reflections in chemistry is called chirality! I'm loving this channel
This is so cool. Thank you for sharing! I studied a course with the Open University in the 90s called 'Graphs Networks and Design (MT365)' which covers a lot of the stuff you mention here. It was an excellent course. I really recommend it to anyone who wants to study these topics in more detail.
I wasn't expecting to find this on UA-cam! If it's what I think it is (I've only seen the first minute so far, but it looks like it
ma be) then it takes me back to my Cambridge post grad dissertation in 87/88
It's all coming flooding back. Miracles? Steiner systems? Remembering the heartache of trying to render MOG in Plain TeX (I never learned LaTeX at the time though it seems a no brainer in hindsight)
@@gavintillman1884 Haha this is amazing! I've written a lot in LaTeX and I think I'd still find it a headache to display the MOG. And yeah, I thought the MOG was a super well-known thing in the mathematical community but it seems it's pretty niche, and I was compelled to make a video(s) on it!
@@AnotherRoof i certainly wasn’t expecting to see it described as the most important diagram in maths, although I was aware of its importance in coding, sphere packing, simple groups etc
Just got to the end - was so please to stumble across this, especially as a) I wasn't particularly looking for it, UA-cam's algorithm obviously deemed I might be interested and b) it looks like it's only been up a few hours!
@@gavintillman1884 Thanks so much for watching! Praise be to The Algorithm.
i busted a neuron watching this.
I did the S(3,4,8) exactly like you did. I've never felt so accomplished in my life.
12:30 I notice that the lines each contain three numbers that bitwse-exclusive-or together to make zero (or equivalently, any two XOR to make the other one). I recognise this from seeing a similar diagram in a definition of Octonions.
XOR is also called "nim-sum" in game theory.
It's also a finite projective plane. Or a set of cards for a miniature version of IRL card game Dobble.
29:50 For quite some time, March was the 1st month of the year. Ever wondered why leap days are on the second month? It’s because it used to be the last month, where it makes way more sense.
I would have lead into the applications section by explaining that applications is just another good example of re framing a problem that helps people understand it. The context that a problem is presented in can really lend a lot to your understanding of it.
Entertaining and educational. Really great presentation.
This is such great content. Damn, I love this diagram. it's like magic
"what if we rotate it sixty degrees?"
Rotates it hundred and twenty degrees...
Great explanation. Using different colors on the sliding shape at the end would have made it easier to see which numbers were being added to the octad.
I like that your background is basically just acoustic foam. Hexagons are Bestagons ❤
They're actually roof shingles 😅But I agree about the joy of hexagons!
Can't wait for part 2, the Monster will rear it's bizzare head again
Thanks for sharing information!
12:31 This diagram looks the same as Octonion multiplication! Wikipedia says it’s the “Octonion Fano Plane”. I wonder how the diagrams are related?
Edit: Having watched further into the video, the diagram here is also a Fano Plane. Still not sure how they're related though.
this channel is gold
25:11 ...rotate the whole thing 60 degrees.
120 degrees, but who's counting. Oh... you were.
Yeah massive goof from me there! 😅
i love your videos; youre so underrated
this is a really incredible video!!! have been hankering to do some hobby maths and this is the sort of stuff i love!!! was just wondering if you would know of a good place to find a digital version of the mog diagram that you're using? i've been doing some searching but every photo seems to be very low-resolution :(
2:39 cheeky bit hahahaha first time seeing this channel and you've got my attention
29:50 technically, no more months were added. July and August were merely renamed. The discrepancy between months and their names originates in the fact that the Romans did not count January and February as part of the year, since effectively no work (military, farming, etc.) was done there. Hence they began counting at March, when armies were convened again (which is also why it is named after Mars, the god of war) and would continue operating until December, the tenth month.
Amazing that UA-cam brought me here! I've been working on a system of groups that I was trying to list all the permutations of based of certain characteristics and I do believe it is or is similar to a Steiner system. S (2,9,15)
Thanks to your video I might make some progress on my problem!
30:43
30th in 5 column. It take me actually more time to count precisely its position than finding it.
Finding take ~5seconds with lucky assumption to look first in every big group of 4s and then look for easily distinguishable "9, 10" in rows of similar characters. Happily 13 was just next and then I just checked for 21 and yeah.
That diagram is really useful for humans, but I wonder if it can be computerized. I might write a Python program for this some time and find out. (2-2-1 cases sound like a headache though)
The diagram doesn't need to be computerized. As he said in the video, a basic search knocks this out pretty quick. The point of the diagram is just because humans are much slower at searching lists.
@@SgtSupaman The fact that a computer can do this search quickly doesn't mean it couldn't leverage something very much like this diagram to do it even *more* quickly, which could be useful in practice if you're doing a very large number of these operations. If you're smart about it you can reduce the amount of required memory so much that it fits in L1 cache, which would dramatically reduce runtime, since runtime is generally dominated by memory movement and not CPU operations.
The most straightforward traditional way to solve this kind of problem quickly would normally be a perfect hash table, where you construct a hash function that takes every possible 5-tuple and produces distinct keys into a lookup table (no collisions guaranteed, although there may be blank entries). Each table entry could be just 16 bits (2 bytes), that's enough for 5 bits for each of the 3 remaining values. If you sort the 5-tuple using an optimized 5-item sorting algorithm, you can narrow it down to 42504 keys. Leaving some room to avoid collisions, that's gonna be about 100KB of memory for the table. That sure ain't gonna fit in L1 cache.
But if you base it on the diagram: I imagine for each color and for each position having a single 64-bit word bitmask indicating all the tableaus having that color in that position. Then it's a simple matter to use bitwise AND to intersect them, followed by ffz (find first zero) to convert that into an index so you can look up the other indexes having the same color in a small table. Now the total RAM requirement shrinks to something like 4 * 35 * 4 = 560 bytes for the masks, plus 4*35*4 = 560 for lookup table for the remaining values, 1120 bytes in all. And that would easily fit in L1 cache. So it could be dramatically faster, if the computational overhead is not prohibitive. Would have to measure it.
I love how 15:41 the chart looks like reflection around center line with inverse
Wow, that was so intriguing and enlightening.
Also, the mog panel you presented is really beautiful and I want to have it in my room, where can we have/pront kt ? Thank you for your amazing videos
That was crazy good. Thanks!
I just learned this, at all exact models in Steiner , combs, spheres, codes, groups, , it's basically logic gate inputs , to the ratio of outputs, and with the combinatorics 1024, the triangle is the platonic solid, from platonic, Aristotle, philosophical, the moon, earth, sun, cos, sin, to decision in everyday personal life, or degree win or lose vegas style. So your 1-8 grid is a 3 bit code from a hex address from ram, ram, inverted 16hex dec, what your designing in the {2,3,7} is 3 of 1024 key string total combination, so distance in hamming is LRC in resistance color code, but really if you stand at any intersection and look at the 4 cross walks, traffic poles at the base , measure if there is a distance to the ground plane and the pole to the wall, of a business is built at that intersection, then imagine 3 D contour of a cube and a vegas die with dots representing those traffic poles, the business wall to the pole makes all the difference in depth, but if you had to calculate the bit correction in a medium of Air then without nothing more than memory go back to your mental calculator use the sliced version of a sphere or traffic pole positioning in 3D space and attached the 2D circle slice onto the die as the 3D cube drawn on 2D surface as the me tal projection of two pages or open book in from of you, with top left, top right center bottom forming 45 degree ray imaginary to define the points in reference to traffic poles and tye wall structure which becomes the open book and the die, or the error correction in Air, without using a calculator if none is on hand, yes basic arithmetic is involved while waiting for a bus. And I never doubted this was the reason, just like I know the war is not on Germany anymore it's here in the 3D world of facts, none can erase the past let alone wish to return to it. Films about war, cryptography, economy, Schrodinger's Box, quantum , requires string theory to unknot the audience commutative using mental projection, or holographic. As Descartes or Movies, Depth, camera movement, and game scripting {237ly} as a vehicle to a degree and independence. Because the reality and the quantum don't come together until nature and nurture or realize undecided vs indecisive lead to career mistakes.
I love how he roasts himself in the first chapter.
BTW I couldn't be bothered to rephrase @thomaskaldahl196's comment, so I'll just directly quote:
> Where has this channel been my whole life?? Excellent presentation: rooted in application, elegant in explanation, and the perfect amount of comedy :D
great! all your videos are great! my favorite has to be the one about the toast problem! lets see if this one will make me change my mind :)
edit: now that i watched the video, i think i will have to wait for the sequel to get my answer! :)
Glad you enjoyed! The toast problem video is the one I'm most proud of too.
a great explanation for something so messy. If the user is distracted, it is easy to lose track of the process.
This was very well explained and I’m glad I found this channel. I missed the part where he explained why he think this is the most powerful diagram in mathematics. If anybody knows the time stamped love to get it.
To be explored in later videos but see my pinned comment! And thanks for watching 🙂
That's the most complicated coffee shop wallpaper I've ever seen.
If I am not mistaken, the grey squares, the white squares, the circles and the dots are giving 34 as a sum, if you apply them on the magic 4x4 square.
Cool! I thought this was going to be a video on Commutative diagrams and the idea behind Category theory.
29:50 - Haha! Julius and Augustus really were monsters!
aaahhhhhh the rules are too crazy.... but you did a bang-up job with the visualisations. Kudos sir for this excellent channel!
He must be really good at Sudoku. Honestly great video, well explained with math a bit beyond most YT math videos but not too far either.
Excellent video! Thank you very much for your efforts.
If you ever update this video, I'd like to add some constructive criticism: When marking the "missing" color/shape matches, don't fill them in in the same manner as the original marking. By marking the missing points with an X or an O, it's much easier to see how they are *additional* points to be added to the solution set, rather than having to keep track of "what I've got so far" bookkeeping. I understand that if I'm doing it myself, I see the duplications, but I think the lightbulb moment might come earlier to someone just watching the video.
But a fantastic video nonetheless- if you ran a correlation between "group theory vs. boredom", you be on par with 3b1b.
Eagerly awaiting another post explaining some of the points you kinda handwaved over, like how were the arrangements of the numbers in the top right come to be? I MUST KNOW!
They didn't add two more months, first month of the year got switched from March to January a few hundred years ago
UA-cam thought it would be funny to play this video when I was sleeping. There I was laying bricks and an inspector would come up to me every now and then just shouting numbers and I wouldn't understand. I finally looked up at the inspector and she was cross-eyed
Hahahahahhaahahaha I am dying of laughter, maybe you should experiment with that, "hey guys, it turns out that if you play the video about kitchen appliance restoration you have the wildest dreams, but never play the one about alpine rodent taxonomy or you're in for a bad time!"
Non-mathematician, non-college grad here. Design background and interested in the value of improving communication of math and science (any subject) with great graphics.
As I try to kearn music theory, your Steiner sets, snd the classification of Isomorphic Steiner Sets SEEM to represent the numerous combination and tecombinations of noted in musical Chords - inversions, extensions and other such terms. This may help ease the mind's resistance to accept there is any sense to "messing up" chord notes, "tablature", and having reason to expect sonorous music result. I can see why Pthagoras became interested in explaining music with mathematics.
It seems like Error Correction codes are what remain needed in AI code, which otherwise seems to be statistical combinatorics, which may incidentally result in "solutions" that seem "correct". AI seems to be guessing similarities of patterns, based on physical properties if computers being faster than humans at number "crunching". AI really seems like an automation of yhe Clever Hans hoax - the arithmetic performing horse from college Psychology 101 - horse read subtle body cues and signals from it's human handler.
Are you going to submit a #SOME3 entry?
I don't think so. I feel like the spirit of the contest is to give a spotlight to new creators. I know I only have 27k subscribers so I'm not a "big youtuber" yet, but I feel like I already have a good start to my channel and wouldn't want steal the spotlight from someone who needs a boost. SoME2 gave me the boost I needed so I hope SoME3 does the same for others!
11:45 if you color in all cells, where you wrote numbers with that greyish chalk, you get a simple monochrom pixel-art of a 45° tiltet rocket.
do you have any plans for a second UA-cam channel where you post twitch highlights?
Ho boy, a very intriguing title.
Indeed
3:10
Voice was mentioned, Fourier Stans rejoice!
The triangle made from cardboard is so epic!
Epic!!, Instant sub
Welcome!
Is there a max value of N for which a given pair of t and k has a valid system? Are their pairs of t and K that habe no non trivial solutions?