How a Hobbyist Created An Infinite Pattern That Never Repeats
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- Опубліковано 7 чер 2024
- Has the Einstein Problem finally been solved? For decades, mathematicians, logicians and professional puzzlers have tried to find the existence of a single tile that by itself scales to infinity without ever repeating it's pattern. Was 2023 the year this illusive shape was found...
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#maths #science #einstein #puzzle #breakthrough
Chapters:
0:00 Can A Single Shape Infinitely Tile?
0:52 Regular Tessellating Polygons
3:45 Introducing Irregular Shapes To The Problem
4:23 Non-Periodic and Aperiodic Tiling
5:56 Wang Tiles
7:16 Penrose Tiles
8:35 David Smith and the Aperiodic Monotile, The Hat
10:45 The 'Impossible' Shape - The Spectre
11:59 5 Fold Symmetry In The Real World. Dan Shechtman & Quasicrystals
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Want a dino tile? 🦖 Drop me a comment below! I'll announce the winners at the end of next weeks video
Errata:
- A clip of a spinning heptagon from a cut scene made it in, in place of a spinning hexagon - I will be forever embarrassed of this mistake - sorry.
Dinos please!
Dino please
Dino, please! 🦖🦕
dino please!!!
Sounds like strange matter.
2:02 Ah yes, the famous six-sided pentagon ;)
3:08 and the famous seven-sided hexagon, too.
Fun video, thanks for making it.
Thanks Destin! 🙏
Just wanted to point out, as a graphic artist and Civilization 6 fanatic, the shape you used when talking about a shape with six sides (at 3:10), in fact, had seven sides.
Was gonna comment this, glad somebody else noticed too😂
Ahhh, nightmare! Thanks for the catch
Same thing at 2:02, the Pentagon is a hexagon (at least the hexagon is a hexagon tho)
@@DrBenMiles Don't be too sad; Leave a mistake like that in the video 'accidentally,' and more people (like me) get upset enough about it to leave a comment and boost your channel stats. ;)
I’m just glad, as a physics hobbyist, that a hobbyist was able to make waves
For real, the scientist gets a nobel prize for a semi repeating problem but a hobbyist figures it out and is called ... A hobbyist
@@scootndute579 Well, in astronomy, they're called "amateurs", and they're well known for occasionally figuring things out. Lots of astronomy stuff was first observed by amateurs. Maybe not so surprising when you consider that modern amateur telescopes are usually better than what Galileo used, plus there's photography now ... and how many objects are flying around even just in our own solar system.
You’re somewhat incorrect in your statement of the problem, there are lots of shapes that can tile aperiodically, the problem was to find a shape that can tile aperiodically but cannot tile periodically.
The definition given of aperiodic was no periodic. So, given base level reasoning any aperiodic shape will be not periodic. Any periodic shape will not be aperiodic. So, I'm not so sure you're correct in your statement at all.
At 0:48 he briefly shows an aperiodic tiling with a tile that CAN be tiled periodically.
The previous comment is correct.
@@brostein6when was that definition given?
@aDifferentJT in the video. Also a base understanding of how prefixes work.
@IPWCsInTheory that would make the tiling periodic.
The sad story of Pauling's denigration of Shechtman and his work simply reinforces for me how supremely arrogant and cliquish the scientific community can be, and how easily one can be cast out of it, lose their funding, and the resulting ability to pay their mortgages, car installments, and their childrens' college tuition, if they don't tow the party line.
There’s a quote, don’t remember the exact quote or who it’s contributed to, but it says that half of what we know about science is wrong, we just don’t know which half.
I have a hard time taking anyone seriously who says “that’s not possible”. History is filled with examples of how humanity was certain about how the world and universe works, but later we found out it was flawed, or even completely wrong.
@@badgerchillsky535 Along those lines, speaking of quotes, one of my favorites is _"The moment a scientist declares 'the science is settled,' he ceases to be a scientist, and becomes an evangelist."_
@@badgerchillsky535 The worst offender to me is by far medical science. Medical science study is overwhelmingly done exclusively on white men and then its just assumed that any findings can be translated and adjusted for women and people of other races.
You mean race isn't skin deep and that biological sex isn't irrelevant? Sounds like someone needs more diversity and inclusion reeducation.
Thats because white men are the ones who end up paying for 99% if meds.
Dinos please!
…though if you'd asked me what my favourite aperiodic tiling was, before the Hat discovery, it was Penrose's kites and darts, then the Hats and Spectres took pole positions when they were discovered, and then, a couple of weeks ago, I found out about the Trilobite and Crab tiling, and I quickly fell in love with its simplicity in construction, and how close it dances with looking like it should tile the plane.
Shout out to the heptagon stepping in as the hexagon's understudy at 3:07. Pulled off a convincing performance!
😅 I'm crushingly embarrassed that slipped through
My four year old identified a shape (incorrectly) as a heptagon the other day. I was just shocked he knew that word.
As a dyslexic, math has always been a massive struggle, and I had no idea what you were saying, but I am still fascinated by math and especially quantum physics. As an artist, I see shapes in everything, and that dinosaur is cool. Who says they went extinct, they are in math.
Many species of dinosaurs went extinct, but there are still dinosaurs around. We call them "birds". You might say that they have ... _changed shape._
They are also called lizards, gators, komodo dragons, etc. They just got smaller.
@@troywhite6039Nope. Lizards etc. share a common ancestor with dinosaurs, but they're basically "cousins" of dinosaurs, not descendants. Birds, on the other hand, are direct descendants of the dinosaurs.
@@margretrosenberg420 Yeah, and that's a scary thought, you can't even use the "Just need to run faster than the slowest of us" trick since those darn birds just peck everywhere randomly.
3:09 describing rotating a hexagon. But is that a 7 sided tile?
9:44 It absolutely counts as one. We are tiling the plane --- the ordinary, familiar Euclidean plane. Reflections, just like translations and rotations, are isometries of the plane. So tiles that are reflections of each other are congruent, and so are instances of the same tile shape.
I love both these stories! thank you for bringing them to us!
Excellent, as ever! 😊😊
Thank you! 😊😊
The deserved a subscribe! All I could think of was how to incorporated this in a remodel.
I first heard the term quasicrystal back in Feb '87 at a presentation at the Cornell Space Sciences building. I remember it well.
That example at the end, of a scientist to afraid to publish a proof because the "scientific" community can be so harsh with people with new ideas, that tells it all. It's the main problem in science, most of people just repeat what is deemed "true" before them and are ready to stone anyone with a new idea. Just ask John Bell ...
That's not the main problem in science. The main problem is modern science is just how damn corrupted it is. Something like this should be criticised. A theory holding up even under scrutiny or even if it doesn't, it leading to new knowledge and insights... that's what science should be about. Sadly modern science is all about propaganda and indoctrination for large part. Doing research often requires funding and governments and major companies won't fund if they think the results work against them or if they don't deem something important enough.
@@thenonexistinghero
True, corruption is the other big problem. But even without corruption, prejudices would block any progress if it was not for some motivated genius.
But problems in Physics are more and more complicated and it requires the help of so many different fellows to prove your theory right, that it's impossible to get there if you have a "fantastic" hypothesis.
@@thenonexistinghero😂😂sure bud
@@colatf2 Good to know you're a mindless foo.
@@colatf2 ???????
Wow. It amazes me how some humans are able to figure out things that would never arise from my brain. I’m literally a kitten playing with a string compared to the thinker statue eternally thinking
You underestimate yourself.
"Always remember that you are totally unique, just like everybody else." (Sorry, I know it's a quote, I just don't know who first said it.)
We all excel at something; if we're very lucky we manage to figure out what before we waste our lives trying to be someone we aren't.
My brain crashed while listening to this video. Rebooting my brain now. I will keep watching this video until my brain stops rebooting. 👍
I love learning things that only 10% of my brain 'gets', hoping that the other 90% catches up eventually!!!
@7:55 Interesting, "...projection of a five dimensional space with fivefold symmetry onto a 2D plane..." . One should name Penrose- Tiles "Penta-Rose"-Tiles.
@3:07 you showed a heptagon while talking about a hexagon. Was that intentional?
He also called the hexagons heptagons earlier in the video... Maybe he just put the clips in the wrong spot... 🤔🧐
I think I stared at shapes moving across the screen for too many hours and became blind to them. Sorry all. Thanks for catching 😂
not my usual cup of tea, but fascinating and beautiful... thanks for explaining
My favorite drama is geometric drama.
It always comes full circle.
This is new to me, very cool content. I'm amazed that such a complex piece can be tiled, forget about never repeating. Is the universe deliberately weird, or is my brain just too simple?
There's a box game from Germany called "Walong" full of multiple colours of the same curved piece that may have been overlooked as a solution the inventor went straight to market as a type of child's toy rather than seek academic review, but it can be combined with itself extensively (not sure about infinite)
Review it, you and him can study it together and get recognition
I just tried searching on "Walong game" and Google kept hitting on something called "Wo Long: Fallen Dynasty." Can you provide a link?
would you be able to share the stl for the dinosaur? I'd like to print some myself to play around with.
Perfect information down a road less traveled. I think E8 theory and other assemblages of ideas will eventually reveal something wonderful.😃
Oooh! oooh! "DINOS PLEASE" As a Very amateur "hobbyist"? (I, poorly, sculpt), I find the story super compelling (and a little bit an indictment of academia), and I've since the late '70's-early '80's been Awestruck by what that man (M.C. Escher) could do with a pencil
What a lovely story, it put a smile on my face.
"DINOS PLEASE"! (If you have any more!) It was good hearing more about the human background of this discovery.
I finally understand the problem. Dr Ben is a great explainer.
3:07 eh... Doctor, that ain't a hexagon. :D
Ben Miles - when you were rotating the shape (at about 3:10) you said it had 6-fold symmetry - but you were rotating a heptagon!
Dino please! Renovating here and this has given me ideas...
late to finding this fascinating article. if not "dinos please", then perhaps just the 'stl' so that I could have some samples made for my college class in "Geometry and the Art of Design". we explore tessellations and even Penrose law suit against Kleenex tissue company for copyright infringement -
for using his tiling patterns on the quilted sheets. Hope we do not see a "repeat" with these monotiles!!
Is there an existing library of periodic shapes and how they have been escherized?
How can I find new shapes for this process?
Ever heard of Google, one of many search engines you can ask anything.
Everything when on psychedelics
Patterns envelop every surface.
Not just any patterns, but symmetrical -geometrical patterns.
The human brain is wonderful
7:01 The aperiodic sets of two tiles are not Wang tiles.
3:07
_Accidentally picks up the wrong one_
Dinos please! I have always loved this problem, and the solution is so incredible.
5:26 I don't understand. There are aperiodic tilings containing large sections that appear elsewhere --- indeed, where *any* section, no matter how large, appears in infinitely many places in the tiling.
My desire for a Dino has crystallized sixfold
Pauling's response was sad. Good lesson in appeals to authority I guess. Love to give my nephews some dino-spectres.
Fascinating video, can't help but feel there's probably cryptographic implications to this as well, though I'm not well versed enough in either field to say what they might be.
Lol, spinning a heptagon to demonstrate 6-fold symmetry. I thought I was going nuts.
My bad. Late night editing brain let that slip through
Spectrum might had reached a Fractal Shape, since Fractals are not repeating, it should follow the tendency.
But nobody checks, ironically, withe the Einstein explanation of Relativity example: 1 observer standing still and another on a moving train, turns on the light, and the observer calculates the time it takes the Light to traveler man when the Light hits to the man standing; there's a gap; is this gap Fractal? Would it contribute to such Fractal and non-repeqting pattern shape? Would it mean the University and everything in it, have such feature?
Most of the "non repeating" patterns look like they repeat infinitely to me... At least this new shape doesn't automatically appear to repeat at all like the rest do.
my admiration for mr 2 nobels just fell 4 notches.
03:07 - this shape has 7 edges and 7 corners. - dont call it a hexagon. ;-)
So how about 3 dimensional non repeating shapes?
Daniel Shechtman: I am a sole winner of a nobel prize too, cop that Linus Pauling!
it's easy to find a image of how to draw the einstein but I have found myself unable to find how the spectre is made. it's just curiosity but, can somebody point me to a simple source that shows how to draw those curves?
@ 2:02
2 hexagons?
I know they are the bestagons but still...
Dinos please! I imagine they’re all taken, but is there an STL file?
3:08 heptagon masquerading as hexagon
I would be interested in learning how you prove that such a shape can tile a plane to infinity without repeating.
Not sure what is the application of this but I guess the Spectre shape can be made into cookies with least waste as opposed to circle shaped cookies (the most common). However, humans have been making square shaped cookies for a very long time and it won't produce any waste.
Darn, and here I thought it was a Spirograph video!
The sound that precedes Scientific Discovery isn’t “Eureka”, but “Huh, that’s interesting”
How easy is it to make custom porcelain tiles? These would be amazing for my bathroom o.o
2:00 That's a hexagon, not a pentagon.
“DINOS PLEASE”
Ah yes, when "experts" declare that something is impossible. I would have thought that in the 21st Century we would have gotten past that, but apparently not "Mr. 2 Nobel Prize Winner". The internet is one of the reasons that non-scientists are able to provide scientific breakthroughs, if the "experts" are willing to listen.
This is the kind of logic flat earthers use to justify their beliefs
I just got told that one of my ideas is impossible within the last week. Maybe I should publish.
Citation, please, of an expert declaring that an einstein is impossible. Mathematicians haven't said this --- rather, before Dave Smith's discovery, they said that the smallest number of tiles in any *known* aperiodic tile set is 2, and no einstein is *known*. Experts distinguish between what is true and what is known to be true. They are more modest about the state of human knowledge than you acknowledge.
2:00 those are both hexagons
dino tile please!
I read a book about this..its fascinating stuff. They went all the way to the coldest parts of Russia to get the meteorite to prove that these patterns can happen in nature.
I'm letting that hat shape be reflected, because I can barely tell the difference anyways.
Reflections are always allowed in tilings in the plane.
Dinos please
This reminded me of the envy free cake cutting challenge, another mathematical algorithm If I could get the dimensions of the specter tile accurate, I think it would be cool to make a driveway or garden path from a cement tile mold.
I see you using that heptagon when you said hexagon
3:08 thats a heptagon
Why are you rotating an heptagon to demonstrate the hexagon 6-fold symmetry?
2:00 you did 2 hexagons
But isn't the textbook definition of the word pattern "a repeated decorative design"?
I wonder how many discoveries are beeing keept in drawers due to ego of supperiors or colleauges?
If I'm not too late, Dinos please.
price of a stock over time are the 2 dimensions we all use..
So ... should we have defined a circle as 12 degrees (or whatever other name)? That's the one that evenly divides into 3, 4, and 6. We're just lucky that 360 is 12*30.
Weight of Pauling: he also was a vitamin C cook.
Rock star scientist ... Brian Cox? Brian May? Some other Brian?
Dinos please. Don’t know what I’ll do with it though. Maybe try and fossilise it. 😅
"DINOS PLEASE"
Now do it in non-Euclidean space.
Dinos please!
Great video! Dinos please!
3:07 wasn't a hexagon
There's a reason for the saying:
"Science advances from funeral to funeral"; our limited minds, can only adapt so much, to the weirdness of the Universe 😊
Dinos please!
If it’s not too late! Also, this is incredibly cool thank you for letting me learn something. Incredibly neat today.
A 2d representation of a 3d cube representing 2d logic and trinary logic
Anyone notice that he showed a 7 sided "hexagon"?...😅
Chirality makes different shapes in proteins, why not hats?
2:02 And where is the Pentagon? Your third figure shows 72 degree by definition? Wow. That is keen.
hexagon! *shows heptagon*
Dinos please! ❤
3:07 that's not a hexagon
Funny how you're talking about the hexagon at the 3:08 mark yet the geometric shape you're showing is the heptagon. On purpose to be sneaky or just a mere oversight?
It is very funny and sad, when you understand that we have a unified physics theory that predicted everything correctly for 20 years now and is ridiculed or just ignored by the masses of physicists.... Stoyan Sargs BSM-SG model has predicted most phenomena that modern physics is puzzled about
So excellent, so beautiful
With regards
omg yes please to the dinos
Dinos please?
cool video
My favorite 5 dimensional latus projected on two dimensions is you mom!
DINOS PLEASE!
Dino please!
Finally, the anti-fractal.