Veritasium - 2020-09-30
Simple rules of geometry meant that 5-fold symmetry was impossible as were crystals without a periodic structure. This turns out to be wrong. Thanks to LastPass for sponsoring a portion of this video. Click here to start using LastPass: https://ve42.co/LPs Huge thanks to Prof. Paul Steinhardt for the interview on this topic. Check out his book ‘The Second Kind of Impossible’ If you'd like to learn more about Penrose tilings, go check out "Penrose Tiles to Trapdoor Ciphers" by Martin Gardener, which helped my research for this video. Filmed by Gene Nagata (Potato Jet on YouTube) Animations by Iván Tello and Jonny Hyman Editing, Coloring, Music & Audio mastering by Jonny Hyman Prague scenes filmed in 2012. Special thanks to Raquel Nuno for helping with the tilings! Additional Music from Epidemic Sound
One of the most interesting classes I ever had
it's not a class
Actually that you never had, if you had it in classes you probably would actually like school
Bruh
yes
Yea
Hats off for the editor, most mind-blowing animation I've ever seen
Animations by Iván Tello and Jonny Hyman, video was also edited by Hyman
I love when math people describe stuff as “the most five-ish” which makes absolutely no sense but makes a ton of sense at the same time
Did anyone bothered to look at these patterns through the "lens" of Fourier Transform? The outcomes would be interesting to say the least, since the Fourier analysis is good at detecting periodicities in signals. A pattern that doesn't repeat to infinity would have very interesting spectral properties. Perhaps something to explore in a new video?
If it repeats, the golden ratio is not irrational right
Do it yourself.
@Ibrahim I'm not following. What do you mean?
@Christian Reno Good advice buddy.
Also, the Penrose structures can yield interesting cryptographics results, since the distance can't be calculated (beyond certain distances) and yet have a fixed shape once a certain set is known. It can also be used for quasi random generation in procedural generation for gaming worlds. (The latter is my favourite)
I feel like i learnt alot while learning nothing at the same time
I feel more smart but still dumb
@Athan Mutia It’s not useless information, it’s just useless to you.
I can't agree more
Just like school
Me too I’m stoned lmfao
Im a textile print and pattern designer and professor who teaches symmetries and tessellations but im not a mathematician. I just learned something new, thanks a lot!
An interesting, very well done and inspiring video. In the background of periodic and non-periodic paving of an infinite surface with a small number of samples, an analogy can be seen not only with the rational in relation to irrational numbers, but also with the "world of outcomes" in relation to the "world of possibilities".
Also a fun trick to do when a few of these patterns are shown simultaneously is by squinting your eyes until the edges of the area are perfectly in line. You'll see that all the matching patterns show up as normal, but the parts where they're different you see almost flashing zig-zag lines.
Penrose tiling also appears in the middle of Helsinki in Finland. A large walking street is covered in the pattern spreading up to a hundred meters. It was selected over various "regular" patterns. Really cool!
This reminds me of an old saying we have here: "Everyone said that it was impossible. Then someone came who didn't know that and just did it."
LMAO!
oh also the saying with bees "According to all known laws of aviation, there is no way a bee should be able to fly. It's wings are too small to get its fat little body off the ground. The bee, of course, flies anyway, because bees don't care what humans think is impossible."
impossible's a myth.
@Get on the cross and don’t look back a guy in the video is just talking about a cool pattern tf does cool flying book of rings have to do with this
@Derp Atel like that one thing were I have a chance to walk through a wall.
The regular hexagon is my favorite shape because of its tiling, I think its beautiful. This video is just full of mathematical reasons to give my friends for why the regular hexagon is the best 2D shape.
Hexagons are the bestagons
"what exists because we just can't percieve because it's considered impossible?" is such a beautiful and impactful question. how much have we dismissed because we couldn't believe it could exist? how much have we overlooked?
I love the way he explains everything it's so interesting if it was a part of my textbook I wouldn't have find it that interesting
Mind blown. Also, I now have an inexplicable urge to tile something in a Penrose pattern.
Me: Gives this pattern to the guy tiling my kitchen
Tile guy: Sweats profusely
When a mistake doesn't become apparent for another 4 hours of tiliing
🤣🤣🤣
stolen comment bro
@Zhong Ping that's why you use matching rules on the vertices and not just on the edges
LOL
I really appreciate this video. It took many of the things thst I have known for a long time and really put a great picture on how everything went together. You remind me of my favorite teacher. God bless you.
To me its insane how an almost random theory, sprouting from Keplers incorrect assumption about the nature of the universe, led to the creation of new electronic pieces and materials. No matter how you slice it, math has practical use in everyday life. All these numbers and equations that we learn in school arent just number, they're just a small fragment of a much larger picture of tactile, everyday objects and phenomenon. I know its hard to explain and I'm getting a little philosophical. But its crazy how a never-repeating pattern can have such practical uses, and tie into so many other mathematical phenomenon such as the golden ratio, snowflakes, and crystals.
This channel is exceptional. I've watched it for years but I saw the most recent "blackhole" one and it blew me away. But when this particular one started describing things to do with "phi" etc I got a shiver down my spine.
Through certain psychoactive substances during my youth, I was given, let's say - "a download" and "visions" of the universe being 'fractal' in nature.. I had no idea what a Fractal was until much later in my life. And watching this presenter slide those patterns on top of each other, then seeing the "matter" slowly emerge was very indicative of it.
I wonder what the old Hippy's would make of Quasicrystals? I think they'd greet an old friend :)
I saw this exact pattern during a DMT trip, never thought I'd see it again!
Isn't it weird how this could be a lecture in some school and we'd all be falling asleep, but this guy managed to make it so interesting that 3m people decided to watch it?
As a teacher, you don't have the time to put in as much effort into a few minutes of content than a video does. Producing something like this takes weeks. Including scripting, filming, visualizing and editing.
14 million now
Now it's 14 m
3am people?
Oh nvm you meant 3 million i was watching this at 2 am
I must say, videos like this ALWAYS haunt me! I begin thinking so hard that it hurts my head; going based on THIS.. So does this mean no two pictures taken will ever be the same? Based on everything being impossible to replicate? Say an image of two people, doing the same thing in the same place? .. Does that make sense to anyone else?
I’m downloading this video so perhaps when I’m next time drunk I might pick up more. 😁
The graphic pictures of geometric shapes made seeing your descriptions so much more interesting/amazing and I kept feeling like I was experiencing eureka moments. Those two pieces of acetate revealing deeper patterns close and far blew my mind. Thank you for creating this complicated video/topic more accessible for all.
If each part of the pattern appears an infinite number of times on any pattern how is it impossible to force it to repeat?
What I find interesting about Kepler's original pentagonal pattern is that it reminded me very much of Islamic tiling and the artform that comes with it, and how all patterns come down to 3, 4 and 5-fold patterns (pls correct me if I'm wrong. It's been forever since i studied it LOL)
Hmm idk but seems very similar
My mind was blown several times through the course of this video, well done.
lol.. I said the same thing.. Glad I'm not the only one.
I've been watching this guy's videos; they used to be quite interesting but nowhere near the mind-blowing quality of this one. One thing I know for sure: This guy just keeps getting smarter and smarter, and that makes me happy.
does knowing this make your life any better though?
@Vijaz555 I don't hop on youtube with the expectation that every video is going to "boost" my life. On the contrary, youtube is a big time waster. I would say this does fascinate me as I have heard of quasicrystals before but did not quite understand them. So yeah made my day a bit better.
There is a theory that Penrose tilings are actually just a 2D slice of of a periodic structure in 5 dimensions
One of your lessons that undeniably cracked a paradigm or two in this head! 🤔
Something interesting that Derek touches on but doesn't go into too much detail here is why it is that there are only 3 ways to tile a plane with regular polygons (the square, triangle, and hexagon) and why there are only 5 regular polyhedra. The reason for both of these ideas are intimately intertwined, and are shockingly purely arithmetic consequence of a simple geometric formula.
According to the Euler characteristic, for any polyhedron the number of vertexes minus the number of edges plus the number of faces is equal to 2. For example, a cube has 8 verticies, 12 edges, and 6 faces, and 8-12+6 is 2. Also, note that for any polyhedron each face must have 3 or more edges, and 3 or more edges have to meet at every vertex. This point is really obvious if you try to build a 3d shape with 2 edges to a face or 2 edges to a vertex-- it just doesn't work.
Let's say you have a regular polyhedra with p edges per face, and q edges per vertice. In this case because every edge is shared by exactly 2 faces, and every edge is shared by exactly 2 vertices, pf=2e and qv=2e. If this is confusing, imagine a cube. A cube has 6 faces, and every face has 4 edges. But because every edge borders two faces, it has (6*4)/2=12 edges. The same math applies to the vertices.
You can rearrange the above to get f=(2e)/p and v=(2e)/q. But because of Euler's characteristic of polyhedrons, v-e+f=2. Simple substitution yields (2e/q)-e+(2e/p)=2. If you divide the previous equation by 2e and rearrange, you get (1/p) + (1/q) = (1/2) + (1/e). Now, if each face has 6 edges or more, it means that p ≥ 6, which means that q ≤ 3. However, that means that each vertex would have 2 or less edges, which is impossible. Thus p<6. And because each face must have at least 3 edges, p≥3, each face of a regular polyhedra must have exactly 3, 4, or 5 edges. For similar reasons, 3≤q<6, so each vertex of a regular polyhera must have exactly 3, 4, or 5 edges meeting at it. Checking these numbers against the formula shows that there are only 5 combinations of "edges per face" and "edges per vertex" that give a number greater than 1/2, which will be exactly the 5 regular polyhedra.
Now, that's cool. But what if we had a polyhedron with somehow an infinite number of edges? In this case, because e is infinite, 1/e becomes zero, and you're left with (1/p) + (1/q) = 1/2.
In this case, there are 3 possible answers. You can have {p,q}= {3,6}, {4,4}, or {6,3}. Let's take a look at p=3, q=6. In this case, it means that there are 3 edges per face, and 6 edges per vertex. The only way to draw this is to have 6 triangles around every vertex. And.... if you put 6 triangles around a single vertex, then the entire thing flattens out and the triangles tile the plane, creating your infinite number of edges. Similarly, {4,4} gives a plane of squares and {6,3} gives a plane of hexagons. Super, super, cool how it all works out.
Is this the reason why heptagons (regular 7-sided polygons) don't appear in nature?
The math nerd in me: wow, that's absolutely fascinating, id like to study it further
The art nerd in me: make a quilt
Amazing video! I learned alot this was really enjoyable.
Honestly, this is quite entertaining. I didn’t expect patterns to spark my interest today-
I agree
yeah and now im scared of the golden ratio
@Your funni Boi hhhj
Idk, my curiosity in patterns sparks up every now and then, usually at regular intervals. So judging by my previous behaviors, this was to be expected
I love how a video about tiles turned into essentially multiverse theory
This is the why I enjoy Star Trek and similar types of science fiction, ones that take the science relatively seriously but assume that someday we'll find a way beyond the barriers we perceive. Because all it takes is one person with an idea, and then a second person taking it in a different direction. And suddenly, the future is something no one had ever thought of.
Your explanation is amazing your are really amazing genius you must be amazing student you are a professor seriously because I saw your almost all videos for physics and math thank you for explaining this much good work
i love how this channel kind of leads on the path to describe our universe with constants and expands its beauty
“Well it’s infinite, so it’s gotta repeat at SOME point, right?”
Scientists: “lmao no”
how do we know pi is infinite
how do we know it doesn't ever repeat
if it's truly infinite then it has to repeat at some point
we cant prove it's infinite until we see the end, which is impossible if it's infinite
so basically There are little patterns that repeat but there can never be the same large pattern? I'm still confused. my limited amount of brain cells are dying.
@Miniclash wait but then phi repeats?
Scientists: Nah we make the rules here LMAO
Hats off for the editor, most mind-blowing animation I've ever seen
"The Infinite Pattern That Never Repeats"
The word 'pattern': Am I a joke to you?
XD
I want an entire series of anything and everything that was discovered solely due to curiosity of the complexity of a snowflake.
This was utterly fascinating to me. Great video!
I’d like to point out this dude hated his professor so much, he looked at 20,000 squares just to prove him wrong
I’d like to point out this dude hated his professor so much, he looked at 20,000 squares just to prove him wrong
Me: Gives this pattern to the guy tiling my kitchen
Tile guy: Sweats profusely
I feel so bad for the person who originally wrote this comment, Hannah R. All she wanted to do was to write a funny comment but ended up with a bunch of idiots in the reply section arguing over what a joke is. Jeez, don't you guys have anything better to do???
@radioactivedarkness r/wooosh
Spite fuels invention just as much as necessity
Now I understand why I learn maths at school.......this is explaining the sentence people say everything is possible...I love this video I won't ever insult math again....u made me fall in love with maths
now I wanna see this as a part of an algorythm to procedrally generate game maps
Well, constantly seeing repeating patterns in the "non repeating patterns" makes this video rather confusing. For a non repeating pattern you should not be able to pick up a segment of tiles and be able to place them anywhere else across the plane.
It's not that the patterns don't recur, it's that they don't recur consistently.
If you take the distance between a section and where that section comes up again, you won't necessarily find the section if you go out by that distance.
The part about the parallel lines explains it well, it goes LSLSLSSLSLSLLSLS or whatever, you can find infinitely many segments of LSL or SLS or even LLSSLL but the pattern is not periodic.
Its like in the number pi - you can find any and all digits, or even phone numbers in it, and you can even find them infinitely many times, but does that mean the number is rational?
I absolutely love this video, and have been watching it multiple time, since it was release, but one question has been nagging me. Shouldn't it be possible to do with one type of tile? Well, it is (using the rhombic Penrose tiling), if you look to the third dimension, and use golden rhombi, as is also evident when looking at the projection of the Rhombic triacontahedron (one of my absolute favorites)
I have been doing some practical testing, and it seems to work out, but of course I cannot test in the infinite plane, and thus cannot say if the same rules and/or restrictions apply.
I would very much like to know. ;)
No, Felix the cat
If I recall correctly, this is an open problem called the Einstein problem.
This whole Golden Ratio is fascinating. It keeps popping up all over the place. I dig it.
I always think of Lateralus by Tool whenever I hear about the Golden Ratio. Love me some Lateralus.
@Get on the cross and don’t look back Even Jesus(peace be upon him) said, my help comes from THE lord, THE maker of heaven and earth.
This proves that Jesus is not God and at the same time God is one and only cause Jesus(pbuh) said, THE lord...that means a specific God....the one and only almighty.
@Arthur wayne that proves absolutely nothing
@Get on the cross and don’t look back so sad Jesus dies of ligma
These patterns are so pretty with such deep meaning. I would like to see them printed on clothing. Also tile work in homes. As art.
He stumbled on the true nature of reality at 12:15: "Where there is an uncountable infinity of different Universes, but just by looking at them, you could never tell them apart." Amazing!
This man's enthusiasm, individuality, and presentation is quite the treat. These are the types of teachers kids need to stay focused and excited.
Veritasium - 2020-10-06
Roger Penrose was just awarded the Nobel Prize for Physics! Not for this pattern but “for the discovery that black hole formation is a robust prediction of the general theory of relativity”
JULIUSCOOL - 2022-05-05
balls haha.
sanchikrr - 2022-05-09
Hey Derek, what if i tell you, there is only 1 book on this face of the earth, where the golden ratio can be applied, and you would be able to see tons of miracles of mathematical, scientific, philosophical, linguistic, and on and on?
Would u then try it out for yourself?
Dave Insuna - 2022-05-10
@XtreeM FaiL I believe that was ‘Penzias’ (and Wilson).
XtreeM FaiL - 2022-05-10
@Dave Insuna You're right. Someone already corrected me last year.
Letame Espianto - 2022-05-17
How did you managed the jump on 2:45 ?