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There is a great book which was out of print for a while, but which seems to be available as a Dover book, It's Called "Tilings and Patterns" by Grunbaum and Shephard.
On 16:09 you say "he contributed to a ground breaking discovery". Actually, he didn't contribute, he made the discovery. Let's give the genius all the credit he deserves, please. The other guys just proved he was right.
With you. They proved him right. Lots of work, for sure but he discovered it on his own with the exception of Dave's (?) contribution that pointed out every iteration of the shape was aperiodic
As Dave got his fair share of praise in the comments and the real world, I like to thank and praise the "trained" scientists for supporting Daves' finding and setting his name even first in the publication. I like it!
Team work. David submitted. The others performed confirmation, Hat. Back to David non mirroring, 2nd iteration, Turtle. Third, weekly periodic. Wiggle sides, Specter. Don't forget the whiny moaners. I don't what's behind Dave's skills, but he spent years honing it in play. Much like mathematicians, physicists, and chemists of old. I trust that computers haven't completely robbed us of more to come. Thanks to team Up and Atom for bringing us.
@@Lu-db1uf Maybe that Harvard prof who falsified data in their research on dishonesty. Not everyone in academia is humble and honest, although for the most part, they probably are.
No, I'm pretty sure you're just dense. Clearly hobbyist, as opposed to mathematician, in this context means someone not formally trained in mathematics.
The way he casually proceeds to discover more versions makes it apparent this discovery was not a fluke but a stroke of genius! So weird that a cut-up multi-hexagon didn’t prop up in an exhaustive search of some graduate’s geometric sim or something.
@@edwardk3 unsure where *you* are coming from... OP isn't comparing men to women, he didn't claim women can't be geniuses. Emmy Noeter, for instance, is an undisputed legend in Mathematics.
@@edwardk3 You jumping right into a feminist rant without regard for what was actually said shows where you are coming from. It isn't a good place either.
He is incredible! No matter how much people complained, he just busted out an even better solution until it was perfect. Even with all eyes on it, he still found improvements before anyone else! Incredible
@@VeganSemihCyprus33 A large collection of uncorroborated assertions, made worse by the use of music where none should be present. Good luck finding subscriber #582.
Dave is how old math dudes should look, IMHO. When it comes to 'formal' Dave lacks more than just training. Don't change Dave, you rock. Jade, you too rock, thanks for brightening my day with Dave, ha.
Dave is a case of someone reaching an abstract solution after a life of empirical work, actually pretty common for craftsmen, but he knew to contact the people who could distill it into formal knowledge A great example of reaching out to people with similar goals but different methods
Just to know. That's good enough for me. I don't need the flashing lights and neon signs. Fame is vanity, and so is fortune. To know... It doesn't matter if I get there first. Just simply to know. From there I can construct wisdom. And from wisdom I can shape those who come after me, so they can find it too. Life isn't a race. It's not a competition.
I love your point here. Sometimes there are people who learn & understand something - in spite of not having “appropriate” training. Their thoughtfulness can overcome their lack of experience, making them useful collaborators. We would do well to nurture such people.
@@BKNeifertKnowing is all well and good. But sharing opens windows of opportunity to people who will or can know more within different context. What might be mundane in your knowledge could very well be groundbreaking in others. Knowledge without sharing is always a waste of potential. It's not about fame. Other people put that on the knowledge and the person. Even if sought after or not. It's about outreach potential.
@@Lloocii When the LORD opens that door for me. One of my favorite stories, is Washington sitting in the Continental Congress. He's the only Founding Father with any experience as an officer, and he sits there, quietly, every day in his colors. He waits, waits, waits, and then is appointed his position by the congress unanimously. There's something shameful about pushing yourself and advancing your own goals. Rather, to humbly sit and wait for your peers to accept you, that's honorable.
One thing I love is that Dave is credited as lead author on the paper, even though the way the story played out he discovers the shape versus created the mathematical proof (eg inspiration was the lead over perspiration)
Dave made the discovery and the others confirmed it and ran with it. Others will always expand upon, generalize, and study the implications of a discovery. That takes using standard math theory, so anyone with that background can fill that role.
@@davidanderson_surrey_bc Dave contacted the others with his discovery which they confirmed with their mathematical proof, so they are not the lead authors by definition. Otherwise, the others had nothing.
@@donaldkasper8346I agree, even though the others might have invested more time building the proof, that assumption is actually irrelevant. And this might not even be true, perhaps Dave was only able to discover this, because he has been experimenting with shapes all his life. :-)
Given who solved the Poincaré conjecture, Dave seems to me like exactly the sort of person who would solve this kind of problem. Sometimes you need a somewhat eccentric person with a lot of time, passion and little to no connection to academia to come up with something novel.
Can you imagine those mathmaticians while working on the first proof? “Alright guys, this is big. We’ve possibly got an Ein Stein tile, we need to spend all our time with this. This is a mathematic breakthrou-“ *phone rings* “Dave? What is it? We’re working on proving your tile!” “I’ve found another one.” … … … “What?” “I’ve found another one.” Dave is a goddamn legend!
@@607 Something that academia is often loathe to talk about is falling into rigid thinking. They can often have the answers right in front of them, but because of built in biases due to education/training, they fail to see them until something or someone brings them to their attention. They get trapped in a "This is the way!" thinking process until jarred out of it. Another way to think about it that they tend to spend most of their time working on more practical shapes and applications. Ask them to design new wing shapes for a heavy hauler plane, a hyper fast supersonic plane, and a high efficiency wing for a solar powered plane for a world record attempt, and they can probably get you proto-type designs in a few hours. When you ask them for a non-standard shape that is not in any currently applicable endeavor, they have to first break out of the methods of thinking that make creating the wing designs easy before they can see those new shapes. Is this true of EVERY mathematician/academic? Absolutely not. However, the ones that can think in both manners easily are the minority. Additionally, sometimes they can be attacked for advancing an idea that is outside the norm because it can change how other areas have to be contextualized. This can make some academics mad, especially those that have built careers bolstering the current paradigm.
@@tmac2744 Your anti-academia bias is showing. The simplest answer is that the first tile was emailed to the academics on November 20, 2022. The second tile was emailed on December 6, 2022. The academics spent that time analyzing the first tile, to confirm mathematically that it was aperiodic. They were looking at the 'how', not the 'what'. That's quite reasonable, as that is their expertise, not Dave's. Dave's lack of formal training precluded him from working on the 'how', so he simply continued looking at the 'what'. And as a result, he found another shape quickly, before the academics had finished analyzing the first. He was running down the road while they were checking the road for its structural soundness. Both are laudable pursuits. Now as to the spectre, the third shape(the proto-spectre), Dave only noticed it based off of Joseph's model that morphed between the hat and the turtle. It was the academic expression of the relationship between the two discovered shapes that allowed Dave to discover the third shape. However, it still wasn't perfectly aperoidic either. But the academics now could apply their training to adjust the sides with the 'wiggles', which is a lot more complicated than was laid out here. While you're pointing out the 'oh the academics are too rigid, they don't have vision', you miss that the non-academic Dave used his unique ability to 'see' shapes to give clues to the academics to then discover more, and their ability to represent the new discoveries both mathematically and to morph those shapes with computer rendering then allowed Dave to think up a new shape, which they then modified, to create a final, perfect aperiodic shape. There were two halves to this equation: The intuitive driving the curiosity and discovery, and the logical driving the proof of what is there, and demonstration of the limitations of it as well.
The amazing thing is that David Smith was not the first amateur mathematician to make a series of breakthroughs in tiling theory. In the 1970s, amateur mathematician Marjorie Rice discovered four different, previously unknown pentagonal tilings on the plane (among many other findings involving tilings). In 1999, one of those pentagonal tilings was made into actual floor tiles and used to tile the foyer of the headquarters of the Mathematics Association of America, in Washington DC.
"Moneyball" doesn't tell the story of Bill James, the man you are thinking of. The movie tells the story of how the Oakland A's achieved great success with his ideas though. @@beaviselpastafarian5039
He can imagine things - its very important - the One-Stein thought experiment :) - btw he also looks as if he was skateboarding, driving hoover and smoking his lungs for the last 40 years :)
So many times we see complex mathematics being used to make a finding that doesn't look very useful in real world...until it does and then it changes the world. Hats off to scientists and mathematicians!
couldn't an infinite amount of these shapes be created by just shifting the lines a little bit here and over there?? Or is that the concept itself...?? This shape is an infinite number of shapes... ??
Damn, i swear that Dave has a nice mathematician mind! Even if he only considers himself as an artist. Well done Dave, you just got immortal in maths ❤
@@nielskorpel8860 Half true. I didn't invent them but I discovered the hat and turtle after constructing them. I also recognised that the polygon in the middle of Joseph's evolutionary timeline could possibly tile without mirroring.
@@nielskorpel8860 This ties into (or tiles into) the age-old philosophical question about whether mathematics is discovered or invented. It's entirely plausible that such shapes have been used at some point for some purpose in our vast history, but the aperiodic tiling property was apparently overlooked until now. 😉
I love how Dave didn't just strike gold once, but three times and counting. It points to a way of thinking that isn't available to most mathematicians - and it seems to come relatively easily to Dave.
No its called having too much time on his hands, mathematicians dont spend their free time (and definitely not the job time they get paid for) to look for solutions to useless meme shit like this....
@@SeaShrimp You're a bitter soul. Here's a guy helping mathematicians to further their understanding of complex geometry, and all you've got is resentment and insults. You're a sad case - but I suspect you already know that.
@@SeaShrimp Literally just watch the video. It talks about mathematicians spending their free time looking for solutions to this problem This is not very sigma of you Shrimpy Simpy.
i could’ve drawn this a million times as a kid and never even thought of it being ground breaking. So could have anyone. This definitely isn’t the first time it’s ever been drawn, it’s first time it’s been drawn in this context. Which kind of begs the question, what other things have been “discovered”, but in the wrong context and was just discarded?
This is so fascinating. I would never have thought that new mathematical discoveries could be made by mere mortals at this point. I was certain that would be a “a computer calculated the aperiodic monotile” video. Go Dave!
The way I understand it, a computer was involved, but I have no reason to doubt that Dave wrote the code, so Dave deserves the credit. Dave's program 1) tried to prove that the tile couldn't tile, by trying all ways to put tiles together with no gaps or overlaps, the point being to prove that every way fails. But with this hat tile, the program managed to keep going successfully, surrounding the first tile with 16 rings of tiles. No non-tilable shape previously discovered can be surrounded by any more than 6 rings of other tiles. 2) tried to find a way to tile it regularly, by putting some tiles together to make a bigger block that can tile by just shifting. But with this hat tile, the program tried all ways to put up to 64 tiles together, with no success. The previous record for a tilable shape is I think one that needs a 20-tile block. So all credit to Dave for finding that this shape is interesting.
Actually, Dave was using my software to explore his ideas. My Polyform Puzzle Solver is for designing and solving packing puzzles. It is a pretty good program, but not at all suitable for the things he wanted to do, which is why he got Craig involved whose software was. I got thanked in the paper, which was a big surprise as I was not aware of their research until the paper was made public.
@@jaapsch2 That is very cool! A collaboration between talented programmers and insightful individuals, then. I can only ever hope to be the former, but I fear I’m neither 😅
that is so wild. go from none to Dave saying "hey maybe this hat?" to "oh by the way, found this turtle?" the moment she said there was a connection between the two figured it was going to prove more but didn't expect a continuum afterward. i would've been impressed with that until the mention of the reflection was different (thinking of the z and s and the L and J in Tetris). this wiggly thing (OMG!) totally impressed!
I love stories of people with weird abilities. Without any formal training, this guy seems to have brain that’s somehow wired to find aperiodic tiles. It just goes to show how amazing the human race is!
I disagree. He just took the time to look into it, because he enjoyed it. If I understand correctly, he's been working with tilings for fun for many years, so it makes sense that he got a feeling for them. :)
I could not agree more. There are many problems in math where most mathematicians (most probably rightly) think that only highly trained professional mathematicians will be able to make any significant contribution (e.g. Collatz). Here, this was/is different and this is makes the whole story very sympathetic. There was a lot of training and, as you call it, weird abilities but not from somewhere mathematicians would have expected.
Interesting how David named the Undisputable Einstein Tile "Spectre" and amazing that a non-mathematician came up with all of them just by working with geometrical shapes. How picky and petty that mirror images were balked at, but Dave did it anyway, giving them what they demanded. I don't think I'd want to tile any floors or walls with it, except for maybe a framed display commemoration for its creation and creator, but Dave solved a 50-year mathematical question which provides possibilities for science, engineering and technology. One possibility could be Run Flat Tires for vehicles. They exist, but this could make them better. Maybe a Graphene organization for cell phone touch screens. I enjoyed your video and the story of development. Thanks
This story proves how modern 'academia', while amazing, can also act as a cage and box where confined and incomplete thinking exists. Dave was not in that cage. What a guy!
This is easily the best exposition of the hierarchy argument. I've seen several videos on the aperiodic monotile but you're the first one to really help me grasp that part. Thank you!
Kudos to Myers, Kaplan and Strauss for being humble and down to earth enough to work with David Smith and not dismissing him as a "crank". Academia is full of professors that would, or worse, just steal the idea and claim it as their own discovery.
Dave, probably: "Why spend your time aperiodic tiling your bathroom when you could spend it planting these lovely aliums and then chilling amongst them?"
I love how you can tell that tile guy's brain is wired in a *completely* different way from everyone else's. Like he is not "doing math" as anyone would understand the term but he's still running laps around people who made careers of "doing math" about this problem.
No. He took a geometrical but non-mathematical approach to the problem. When he found a solution he asked mathematicians for help with the maths. Dave did the visualisation, the mathematicians did the maths. All are worthy of credit for their contributions.
@@upandatom amazing interview with the einstein guy with no formal training however defined wow wow wow wild stuff who knows how people get inspired by other people considered living or dead even wow wow wow wow yeah the true einstein tile however defined now found indeed wow wow wow🧩♾♾♾♾♾☮️💟😍😘🥰🌈🗽🤯🤯🤯🤩🤩🤩🎬🎬🎬🤖🤖🤖🥳🥳🥳…
I can tie my shoelaces with just one hand! I use my left-hand. Of course, my right-hand is just a reflection of my left-hand, so it would be wrong to say that I use two hands to tie my shoelaces. I just use my left-hand and its reflection.
Massive credit to that Dave guy. I'm really glad this video touched on the fact that the scientific community will grab hold of this, because that was my very first thought. This is only the beginning.
Thank you for reporting on this. Kudos to David Smith on never giving up! When people had complaints about one tile, he came up with more shapes until he shut them up for good. Way to go!
For those who wonder why the L tile does not qualify as an aperiodic shape: it is because you can tile it in a periodic way too. For example, you can put two rotated L shapes on top of each other to form a rectangle and tile it. The shape they propose cannot be tiled in any periodic way.
Thank you! I spent the whole video wondering why we were shown an aperiodic pattern with a single tile but it didn't qualify as a monotile, and didn't have the mathematical literacy to look up the answer myself.
Dave has an amazing visual way of thinking. It is a gift and it is a gift that is very useful in many fields not just in mathematics and bathroom floor tiling.
This is inspiring stuff. I have a long background in Computer Science and Applied Mathematics, which sees my recreational focus gravitate towards patterns, symmetry, etc in Art, Logic, Music and Science. I’ve just recently (at age 62) gotten into drawing. I love transcribing renditions of geometric objects, whether they be simple, have rotational, reflectional or translational symmetry, and then to try creating tilings. This includes 2d drawings of “impossible 3d shapes” and sacred / Islamic geometry (shapes which are constructed using only a compass and a straight edge) and many other sources of inspiration. Watching the animations in this video gave me chills running up and down my spine in waves, exacerbated by the current ambient room temperature of 9°C at 1:30 am. [I should have something something warmer to wear!] So THANK YOU Up and Atom for your continuing high quality and interesting content. My salutations to Dave and his collaborators for original, imaginative and spontaneous creativity at the pinnacle of excellence. And an incredible effort by all of you in combining talents to produce this masterpiece. I really am impressed!!! Also I am really cold and should get under my blankets in bed!
There are some areas of STEM where you can contribute even without a formal background; where curiosity, lots of experimentation, an encyclopedic knowledge of the subject and a keen eye can carry you pretty far. My warm congratulations to Dave for spotting not one, not two, but three solutions to a half-century-old problem. Not that the three other collaborators don't also deserve credit for the rigourous proof, an essential part of the full solution. But this is the type of problem where coming up with a good conjecture is the most difficult part, not proving it. It was mainly Dave's insight and observation (and hard work, presumably) that cracked this one. So yeah... congrats to all, but Dave's the man! :P
It’s creativity through and through. Lots of people consider it the antithesis to formal science/math. He posited the solution before solving the problem.
I wonder how many people also messed around with these tiles but never got to emailing an academic or never even knew it was in fact a mathematical goldmine
Great video! As a high school maths teacher, this is so inspiring to me. I will definitely be showing my students... Dave reminds me of all the brilliant, self sufficient hippies I know aren't willing to be cogs in the system. What an absolute legend
I'm dyscalculian. I'm unable to comprehend any form of maths that goes beyond simple counting and at the same time there is a high chance I will make lots of mistakes at addition or substraction already. So it's pretty safe to say maths has been the bane of my life. BUT I think it's really awesome how so many people spent so much time and effort into discovering a unique shape and share it with everyone.
Major props to Dave for scoring a trove of examples of this geometric phenomenon, i wonder if this is related to the theory of six-fold symmetry in planar geometry
I'm pretty sure Dave is quite remarkable and his achievement proves nothing about "normal" people. The fact that he doesn't present himself in a certain expected manner doesn't mean he's less of a genius.
He is one of those guys that has an exceptional natural pattern-matching ability. I wouldn't be surprised if he were on the high-functioning part of the spectrum. AKA not really a "normal" person. Recognizing what he had is the exceptional part. There are precious few people who can recognize a potentially great discovery that they stumble onto, trained or not. I bet more than one kindergartner has cut out that shape randomly.
The games ussually code the space into square tiles for simplicity. Computing the perfect allignment of pixels and shapes on the edges of tiles would make the game more laggy.
Most of the time such things are beyond my understanding, logic and intelligence. But here the subject is so well conveyed that I not only got an idea or feeling for the problem and the solution, but also thought that there must consequently exist many more tiles before it was mentioned here. Great job, thank you!
Love this story and nice follow up on the story. I gave a workshop about this at a mathematics camp for young students (12-14 years). Very inspiring topic to present. I let them play with penrose tiles, then the L shape and finally with the newly discovered tile. The last one I made two colors, so they would discover the need to put some upsidedown. Was great fun!
I really think dave deserves all if not most of the credit for these shapes. Dont get me wrong I know the other people helped prove and publish the findings but he really seems like the one who discovered the einstein shape to begin with. And the second one, and the third, and so on. And the "true" einstein tile that beat the moaners. "co discoverer of the einstein tile" next to the others names... I mean yeah they helped prove that it was and publish findings but.... Dave really did actually discover the shapes from what I can tell
He's listed as the first author. In academic community authors get listed in the order of their contribution. Being the 1st name on the list is huge honour. And when cited, in some cases it would go something like: D. Smith et al (2023)
I really loved this video! Not only did Jade given us a very simple explanation to what appears to be a complex proof, the storytelling was also great and made us all love Dave.
One of your best video ever and that's something! The in-person interviews, the storytelling, the explanations, the animated diagrams! Everything drips passion and effort. Thank you!
Isn’t it beautiful how art can go hand in hand with science? Imagine how much more potential there is when combining those two ways of seeing the world. ❤
A great video Jade. Nicely reduced the complexity of the proof so that everyone understands easily. And a nice chronology of explanation from aperiodic tiles 1964 to Penrose tiles to current hat turtle Daves's eye and the spectre. Keep doing more ..Thanks!
The flaw with “the math world” is the arrogance of mathematicians. Whenever there’s a problem that hasn’t been solved for some time, the old heads discourage the newbies from pursuing it because they just assumed that if it hasn’t been solved, that it’s unsolvable. I believe the reason it took 50 years was because people were told NOT to try to find the answer as there isn’t one, and you’d only be wasting your time.
Fascinating story of discovery! A problem that some of the greatest minds in math and physics could not solve but a bloke just playing around with shapes figured it out. Absolutely inspiring!!!!! Way to go Dave👍. Thanks for posting Jade your a Rock Star ⭐.
Amazing video! I remember hearing the buzz and excitement about this with the first discovery, and super nice to hear the mathematical proof behind it laid out and explained so clearly. Which is a testament to your teaching ability, since proofs seem to always be the hardest thing for people to wrap their heads around. And the animations in this video are wonderful too. Great work!
It is such a great success story. Pros sometimes lump all weird hobbyists into the crackpot category because there are so many of them (crackpots). Dave here is the real deal though. Kudos to him, and also the profs who took him seriously. And thanks for the great video!
It helped that he seemed humble and yet educated (himself, probably self taught )enough to know when he : 1) Might have found something others would be interested in and 2) Knew what kind of expert to contact to verify his discovery. Since they collaborated at least two more times, I'd say Dave must be easy to get along with and those three Academics must not be the snooty kind or the greedy (taking all the credit for something he first discovered )type. To me, this shows the 'best' of science and mathematics where everyone does their duty and they work together to advance knowledge.
Really ? He has produced an elegant solution to one of mathematics' more minor problems; only a very few text books will need to be updated. He will soon be forgotten, like so many other contributors to our knowledge and understanding.
There are all kinds of reasons that this tiling, even its existence, may be important to many areas of basic mathematics as well as applied mathematics. Its super that you found and decided to “cover” the aperiodic tile story. Please continue checking in on its progress! But I also want to just say what a wonderful collection of inspired and useful presentations all of your videos, both alone and taken together, create. You are very gifted at doing this important work of harnessing an often misused medium for good purposes. I am a scientist, old but still at work, and often watch your videos for amusement. But I also like to see how you explain certain things for importantly non recreational purposes - and try to understand how you might have come to the way you do it. Thanks for such good work and your channel.
Unique hierarchy could be equivalent to the 'temporal frames' of a reality that simultaneously experiences the absolute spectrum of it eternal nows but each temporal frame of 'now' is distinct from one another as it transitions from the end of its beginning to the beginning of its end.
Astonishing story! I confess it's a little over my head at present. Going to follow up and try to learn more. The material science applications are massively exciting!
Fantastic video. Great job Jade. Dave is clearly an amazing human. Massive kudos to him, and for the academic mathematicians who helped him with the formal proof.
To expand on the idea at 8:55 of two Ls being part of only one larger L... If you take two adjacent small L tiles, for them to be a translation of each other, as you move up in size, that larger L must also be adjacent *in the same way*. In other words, as you increase both e.g. up and to the right, the result would be a larger L with the same adjacency property as the smaller L. For the L tiling, this works up to point, but then you hit an L in a different orientation (e.g. down and to the right), so you cannot form a larger L at that size. -- The L you are working with has shifted from being the inner part of a larger L construction to the outer part. As such, it cannot be adjacent to a different L, it is adjacent to the inner part of a larger L. Therefore, the tiling is aperiodic.
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I'm a member of Brilliant, but I signed up through a different UA-cam channel. Am I supposed to sign up to Brilliant through multiple UA-cam channels?
There is a great book which was out of print for a while, but which seems to be available as a Dover book, It's Called "Tilings and Patterns" by Grunbaum and Shephard.
The ideas in this are so beautiful. Especially the infinite fractal nature of the tilings. Thank you
You may want to rework your headline. I thought I was going to be watching a rerun, not a sequel.
6EQUJ5!!! This is fascinating!
On 16:09 you say "he contributed to a ground breaking discovery". Actually, he didn't contribute, he made the discovery. Let's give the genius all the credit he deserves, please. The other guys just proved he was right.
With you. They proved him right.
Lots of work, for sure but he discovered it on his own with the exception of Dave's (?) contribution that pointed out every iteration of the shape was aperiodic
As Dave got his fair share of praise in the comments and the real world, I like to thank and praise the "trained" scientists for supporting Daves' finding and setting his name even first in the publication. I like it!
They are mathematicians, not scientists.
@@hb1338 whatever floats your boat mate.
@@hb1338 What do you think math is?
@@falxnecis are you just rephrasing my post or do you want to add something?
@@binbadendeno
it's amazing that Dave got credit, so many academics would have stolen/undermined his contribution. Bravo!
Team work. David submitted. The others performed confirmation, Hat. Back to David non mirroring, 2nd iteration, Turtle. Third, weekly periodic. Wiggle sides, Specter.
Don't forget the whiny moaners. I don't what's behind Dave's skills, but he spent years honing it in play. Much like mathematicians, physicists, and chemists of old. I trust that computers haven't completely robbed us of more to come. Thanks to team Up and Atom for bringing us.
Really? I can't think of any academic that would have stolen or undermined his contribution. What a strange thing for you to say.
@@Lu-db1uf Maybe that Harvard prof who falsified data in their research on dishonesty. Not everyone in academia is humble and honest, although for the most part, they probably are.
@@Lu-db1uf professors getting majority of credits for the sole of a student happens all the time
@@Lu-db1uf How naive...
MVP = Dave
everyone else couldnt even think of one
HE THOUGHT OF ♾
Using the word hobbyist is a very dangerous mistake. It means nothing, says nothing, clarifies nothing.
No, I'm pretty sure you're just dense. Clearly hobbyist, as opposed to mathematician, in this context means someone not formally trained in mathematics.
What is a formally trained mathematician
The way he casually proceeds to discover more versions makes it apparent this discovery was not a fluke but a stroke of genius!
So weird that a cut-up multi-hexagon didn’t prop up in an exhaustive search of some graduate’s geometric sim or something.
It might have been interesting to hear more about Dave's process of discovering this
Ok. Your willingness to apply the word genius to somebody who is male is proof of where you are coming from
@@edwardk3 unsure where *you* are coming from... OP isn't comparing men to women, he didn't claim women can't be geniuses. Emmy Noeter, for instance, is an undisputed legend in Mathematics.
@@edwardk3 You jumping right into a feminist rant without regard for what was actually said shows where you are coming from. It isn't a good place either.
@@edwardk3 he's right, a woman would never have figured this out as they very rarely ever do tiling
Genuine props to Dave for discovering a full hat trick of advancements in aperiodic tilings.
This is the story of your enslavement 👉The Connections (2021) [short documentary]💖
I see what you did there ;)
@CLipka2373 I'm gonna be real with you the pun was unintended.
He is incredible! No matter how much people complained, he just busted out an even better solution until it was perfect. Even with all eyes on it, he still found improvements before anyone else! Incredible
@@VeganSemihCyprus33 A large collection of uncorroborated assertions, made worse by the use of music where none should be present. Good luck finding subscriber #582.
Dave's achievements make me think of Escher, another person who approached quite mathematical geometric concepts from an artistic standpoint.
Escher inspired Penrose who found the solution for two tiles.
This is the story of your enslavement 👉The Connections (2021) [short documentary]💖
@@VeganSemihCyprus33bot
Escher is love.... Such a great artist!
Hopefully Dave's achievements are lost through time. And he gets future credit for this discovery
People point out that the first tile cannot be the One because it uses its mirror, and their reaction is "haters"? Doesn't seem very scientific
Dave is how old math dudes should look, IMHO.
When it comes to 'formal' Dave lacks more than just training. Don't change Dave, you rock. Jade, you too rock, thanks for brightening my day with Dave, ha.
Dave is a case of someone reaching an abstract solution after a life of empirical work, actually pretty common for craftsmen, but he knew to contact the people who could distill it into formal knowledge
A great example of reaching out to people with similar goals but different methods
Just to know. That's good enough for me. I don't need the flashing lights and neon signs. Fame is vanity, and so is fortune. To know... It doesn't matter if I get there first. Just simply to know. From there I can construct wisdom. And from wisdom I can shape those who come after me, so they can find it too.
Life isn't a race. It's not a competition.
This is the best comment here.
I love your point here. Sometimes there are people who learn & understand something - in spite of not having “appropriate” training. Their thoughtfulness can overcome their lack of experience, making them useful collaborators. We would do well to nurture such people.
@@BKNeifertKnowing is all well and good. But sharing opens windows of opportunity to people who will or can know more within different context.
What might be mundane in your knowledge could very well be groundbreaking in others.
Knowledge without sharing is always a waste of potential. It's not about fame. Other people put that on the knowledge and the person. Even if sought after or not. It's about outreach potential.
@@Lloocii When the LORD opens that door for me.
One of my favorite stories, is Washington sitting in the Continental Congress. He's the only Founding Father with any experience as an officer, and he sits there, quietly, every day in his colors. He waits, waits, waits, and then is appointed his position by the congress unanimously.
There's something shameful about pushing yourself and advancing your own goals. Rather, to humbly sit and wait for your peers to accept you, that's honorable.
One thing I love is that Dave is credited as lead author on the paper, even though the way the story played out he discovers the shape versus created the mathematical proof (eg inspiration was the lead over perspiration)
I noticed that as well. Goes to show that not everyone who publishes a scientific paper is a raging egomaniac. I'm talking to YOU, Sheldon Cooper!
Dave made the discovery and the others confirmed it and ran with it. Others will always expand upon, generalize, and study the implications of a discovery. That takes using standard math theory, so anyone with that background can fill that role.
@@davidanderson_surrey_bc Dave contacted the others with his discovery which they confirmed with their mathematical proof, so they are not the lead authors by definition. Otherwise, the others had nothing.
@@donaldkasper8346I agree, even though the others might have invested more time building the proof, that assumption is actually irrelevant. And this might not even be true, perhaps Dave was only able to discover this, because he has been experimenting with shapes all his life. :-)
@@joostdriesens3984 Many people deal with shapes. He has a pattern recognition ability once he applied it to the geometry problem.
That is not the guy I was expecting to see singlehandedly solve a 50 year-old math problem. What a legend
And then he found another tile
when you write this comment he found another tile 😂😂
Like, totally far out man✌️
@@YevhenSavchukand don’t forget the penultimate ein stein tile, the tile that is aperiodic without using its reflection.
Given who solved the Poincaré conjecture, Dave seems to me like exactly the sort of person who would solve this kind of problem. Sometimes you need a somewhat eccentric person with a lot of time, passion and little to no connection to academia to come up with something novel.
This is the best video I’ve seen explaining this concept to non mathematicians. Thank you a lot. Beautiful work.
No one talks about Joseph Myers who is probably an AI
15:01 "a lot of you wouldn't be happy unless I talked about possible *practical applications* "
Amazing! She knows us very well !!!
As a math enthusiasts in the middle of a home remodel, I think my tile guy is going to be extremely upset that I learned about this
Can you imagine those mathmaticians while working on the first proof?
“Alright guys, this is big. We’ve possibly got an Ein Stein tile, we need to spend all our time with this. This is a mathematic breakthrou-“
*phone rings*
“Dave? What is it? We’re working on proving your tile!”
“I’ve found another one.”
…
…
…
“What?”
“I’ve found another one.”
Dave is a goddamn legend!
I haven't read the paper yet, but I'm honestly a bit confused why the spectre tile was not found by the people working on the paper.
@@607 Something that academia is often loathe to talk about is falling into rigid thinking. They can often have the answers right in front of them, but because of built in biases due to education/training, they fail to see them until something or someone brings them to their attention. They get trapped in a "This is the way!" thinking process until jarred out of it.
Another way to think about it that they tend to spend most of their time working on more practical shapes and applications. Ask them to design new wing shapes for a heavy hauler plane, a hyper fast supersonic plane, and a high efficiency wing for a solar powered plane for a world record attempt, and they can probably get you proto-type designs in a few hours. When you ask them for a non-standard shape that is not in any currently applicable endeavor, they have to first break out of the methods of thinking that make creating the wing designs easy before they can see those new shapes.
Is this true of EVERY mathematician/academic? Absolutely not. However, the ones that can think in both manners easily are the minority. Additionally, sometimes they can be attacked for advancing an idea that is outside the norm because it can change how other areas have to be contextualized. This can make some academics mad, especially those that have built careers bolstering the current paradigm.
@@tmac2744, it's sad how scientists can be that without an actual scientific mindset 😔
"Oh, hey, i found out the new tile he just made is related to it, and that there's actualy an infinite family of tiles!"
@@tmac2744 Your anti-academia bias is showing. The simplest answer is that the first tile was emailed to the academics on November 20, 2022. The second tile was emailed on December 6, 2022. The academics spent that time analyzing the first tile, to confirm mathematically that it was aperiodic. They were looking at the 'how', not the 'what'. That's quite reasonable, as that is their expertise, not Dave's. Dave's lack of formal training precluded him from working on the 'how', so he simply continued looking at the 'what'.
And as a result, he found another shape quickly, before the academics had finished analyzing the first. He was running down the road while they were checking the road for its structural soundness. Both are laudable pursuits. Now as to the spectre, the third shape(the proto-spectre), Dave only noticed it based off of Joseph's model that morphed between the hat and the turtle. It was the academic expression of the relationship between the two discovered shapes that allowed Dave to discover the third shape. However, it still wasn't perfectly aperoidic either. But the academics now could apply their training to adjust the sides with the 'wiggles', which is a lot more complicated than was laid out here.
While you're pointing out the 'oh the academics are too rigid, they don't have vision', you miss that the non-academic Dave used his unique ability to 'see' shapes to give clues to the academics to then discover more, and their ability to represent the new discoveries both mathematically and to morph those shapes with computer rendering then allowed Dave to think up a new shape, which they then modified, to create a final, perfect aperiodic shape. There were two halves to this equation: The intuitive driving the curiosity and discovery, and the logical driving the proof of what is there, and demonstration of the limitations of it as well.
I cant believe someone would name their kid "one stone" only for that kid to grow up to be one of the most renowned genius.
That's one of the best hat-tricks I've ever seen.
The amazing thing is that David Smith was not the first amateur mathematician to make a series of breakthroughs in tiling theory. In the 1970s, amateur mathematician Marjorie Rice discovered four different, previously unknown pentagonal tilings on the plane (among many other findings involving tilings). In 1999, one of those pentagonal tilings was made into actual floor tiles and used to tile the foyer of the headquarters of the Mathematics Association of America, in Washington DC.
i think math is mind numbingly simple in a way so you need to be less immersed to see something new
After seeing this video, I do believe that foyer is due for a re-tiling.
I disagree altogether. @@jamescheddar4896
"Moneyball" doesn't tell the story of Bill James, the man you are thinking of. The movie tells the story of how the Oakland A's achieved great success with his ideas though. @@beaviselpastafarian5039
@@davidanderson_surrey_bc No, because that would diminish her work and her accomplishments.
Dave clearly always dressed like a legend, but now he literally is one. Very cool stuff.
or some sort of rockstar..
.. or hobo, jk :D
This is the story of your enslavement 👉The Connections (2021) [short documentary]💖
The truth is, Dave is actually a genius, even though he has not the same mathematical training as his co-authors.
This is the story of your enslavement 👉The Connections (2021) [short documentary]💖
He’s a computer science professor I think?
For sure!
He can imagine things - its very important - the One-Stein thought experiment :) - btw he also looks as if he was skateboarding, driving hoover and smoking his lungs for the last 40 years :)
@@xxxkueckxxx"a retired printing technician" - She told us that in the video.
So many times we see complex mathematics being used to make a finding that doesn't look very useful in real world...until it does and then it changes the world. Hats off to scientists and mathematicians!
People saying that they want to tile their bathroom with it and Dave just saying "why? you're wasting your money" cracked me up
couldn't an infinite amount of these shapes be created by just shifting the lines a little bit here and over there?? Or is that the concept itself...?? This shape is an infinite number of shapes... ??
10:49 OHHH ITS EXPLAINED RIGHT HERE LETS GOO
@@a--------------- gg
Damn, i swear that Dave has a nice mathematician mind! Even if he only considers himself as an artist. Well done Dave, you just got immortal in maths ❤
Did Dave invent/construct all these shapes? The video seems to suggest so. Is that true
@@nielskorpel8860 no its not true
@@nielskorpel8860 Half true. I didn't invent them but I discovered the hat and turtle after constructing them. I also recognised that the polygon in the middle of Joseph's evolutionary timeline could possibly tile without mirroring.
@@JellyMonster1You're the man!
@@nielskorpel8860 This ties into (or tiles into) the age-old philosophical question about whether mathematics is discovered or invented.
It's entirely plausible that such shapes have been used at some point for some purpose in our vast history, but the aperiodic tiling property was apparently overlooked until now. 😉
I love how Dave didn't just strike gold once, but three times and counting. It points to a way of thinking that isn't available to most mathematicians - and it seems to come relatively easily to Dave.
No its called having too much time on his hands, mathematicians dont spend their free time (and definitely not the job time they get paid for) to look for solutions to useless meme shit like this....
@@SeaShrimp You're a bitter soul. Here's a guy helping mathematicians to further their understanding of complex geometry, and all you've got is resentment and insults. You're a sad case - but I suspect you already know that.
everything is useless until its not@@SeaShrimp
@@SeaShrimp the video itself points to practical applications in Materials Science.
@@SeaShrimp Literally just watch the video. It talks about mathematicians spending their free time looking for solutions to this problem This is not very sigma of you Shrimpy Simpy.
i could’ve drawn this a million times as a kid and never even thought of it being ground breaking. So could have anyone. This definitely isn’t the first time it’s ever been drawn, it’s first time it’s been drawn in this context. Which kind of begs the question, what other things have been “discovered”, but in the wrong context and was just discarded?
Funny that this was hiding in plain sight for so long. Just a subset of the boring old hexagon.... Love how these things happen.
This is so fascinating. I would never have thought that new mathematical discoveries could be made by mere mortals at this point. I was certain that would be a “a computer calculated the aperiodic monotile” video. Go Dave!
The way I understand it, a computer was involved, but I have no reason to doubt that Dave wrote the code, so Dave deserves the credit. Dave's program
1) tried to prove that the tile couldn't tile, by trying all ways to put tiles together with no gaps or overlaps, the point being to prove that every way fails. But with this hat tile, the program managed to keep going successfully, surrounding the first tile with 16 rings of tiles. No non-tilable shape previously discovered can be surrounded by any more than 6 rings of other tiles.
2) tried to find a way to tile it regularly, by putting some tiles together to make a bigger block that can tile by just shifting. But with this hat tile, the program tried all ways to put up to 64 tiles together, with no success. The previous record for a tilable shape is I think one that needs a 20-tile block.
So all credit to Dave for finding that this shape is interesting.
Actually, Dave was using my software to explore his ideas. My Polyform Puzzle Solver is for designing and solving packing puzzles. It is a pretty good program, but not at all suitable for the things he wanted to do, which is why he got Craig involved whose software was. I got thanked in the paper, which was a big surprise as I was not aware of their research until the paper was made public.
Dave is not a mere mortal; he is a supremely gifted mortal. Yay Dave.
@@jaapsch2 That is very cool! A collaboration between talented programmers and insightful individuals, then. I can only ever hope to be the former, but I fear I’m neither 😅
He could be a savant for all we know, he's not just a mere mortal thats for sure
that is so wild. go from none to Dave saying "hey maybe this hat?" to "oh by the way, found this turtle?" the moment she said there was a connection between the two figured it was going to prove more but didn't expect a continuum afterward. i would've been impressed with that until the mention of the reflection was different (thinking of the z and s and the L and J in Tetris). this wiggly thing (OMG!) totally impressed!
I love stories of people with weird abilities. Without any formal training, this guy seems to have brain that’s somehow wired to find aperiodic tiles. It just goes to show how amazing the human race is!
I mean. Ironically the more formal education you have the more unlikely you are to find NEW solutions or ideas
I disagree. He just took the time to look into it, because he enjoyed it. If I understand correctly, he's been working with tilings for fun for many years, so it makes sense that he got a feeling for them. :)
I could not agree more. There are many problems in math where most mathematicians (most probably rightly) think that only highly trained professional mathematicians will be able to make any significant contribution (e.g. Collatz). Here, this was/is different and this is makes the whole story very sympathetic. There was a lot of training and, as you call it, weird abilities but not from somewhere mathematicians would have expected.
Dude has some great intuitions for shapes - so cool that people have some weird abilities that they're maxed out in lol
Ramanujan-esque
3:15 only some cool hippie dude could do this!
Interesting how David named the Undisputable Einstein Tile "Spectre" and amazing that a non-mathematician came up with all of them just by working with geometrical shapes. How picky and petty that mirror images were balked at, but Dave did it anyway, giving them what they demanded. I don't think I'd want to tile any floors or walls with it, except for maybe a framed display commemoration for its creation and creator, but Dave solved a 50-year mathematical question which provides possibilities for science, engineering and technology. One possibility could be Run Flat Tires for vehicles. They exist, but this could make them better. Maybe a Graphene organization for cell phone touch screens. I enjoyed your video and the story of development. Thanks
15:24 This is fascinating! But now wouldn't a 3-dimensional aperiodic monotile be needed?
This story proves how modern 'academia', while amazing, can also act as a cage and box where confined and incomplete thinking exists. Dave was not in that cage. What a guy!
This is easily the best exposition of the hierarchy argument. I've seen several videos on the aperiodic monotile but you're the first one to really help me grasp that part. Thank you!
Kudos to Myers, Kaplan and Strauss for being humble and down to earth enough to work with David Smith and not dismissing him as a "crank". Academia is full of professors that would, or worse, just steal the idea and claim it as their own discovery.
Dave, probably: "Why spend your time aperiodic tiling your bathroom when you could spend it planting these lovely aliums and then chilling amongst them?"
I love how you can tell that tile guy's brain is wired in a *completely* different way from everyone else's. Like he is not "doing math" as anyone would understand the term but he's still running laps around people who made careers of "doing math" about this problem.
No. He took a geometrical but non-mathematical approach to the problem. When he found a solution he asked mathematicians for help with the maths. Dave did the visualisation, the mathematicians did the maths. All are worthy of credit for their contributions.
I’m starting my computer science bachelor tomorrow, it’s good to know that I can always watch this channel if I don’t understand a lecture😁
Good luck with CS!
That puts a whole new slant on the primordial struggle for all Puzzle enthusiasts
Russel Brand explaining math is just as astonighinh as the discovery itself
"i'm just a bloke off the street, just playing with shapes." 3:24
Let’s not overlook the phenomenal job Jade has done here distilling the essence of the proof for a broad audience - awesome video, as usual!!
thank you so much! :)
@@upandatom amazing interview with the einstein guy with no formal training however defined wow wow wow wild stuff who knows how people get inspired by other people considered living or dead even wow wow wow wow yeah the true einstein tile however defined now found indeed wow wow wow🧩♾♾♾♾♾☮️💟😍😘🥰🌈🗽🤯🤯🤯🤩🤩🤩🎬🎬🎬🤖🤖🤖🥳🥳🥳…
@@upandatomis L tile periodic?
I didn't get that part
@@vipulpoddar8045 1:31
@@vipulpoddar8045L is both if I understood correctly as is one of the partial einstein tiles BEFORE it is squiggled to get highly technical!🤯
Damn the production work of this video was insane. I really enjoyed the visualisations a lot. Thank you for all that effort.
69 likes. Nice.
Dave is an example of why curiosity is a do thing. And active mind pondering a variety of ideas is a happy mind.
I can tie my shoelaces with just one hand!
I use my left-hand.
Of course, my right-hand is just a reflection of my left-hand, so it would be wrong to say that I use two hands to tie my shoelaces. I just use my left-hand and its reflection.
2:00 AHA! So, this ISN'T the first shape that doesn't repeat.
Massive credit to that Dave guy. I'm really glad this video touched on the fact that the scientific community will grab hold of this, because that was my very first thought. This is only the beginning.
Thank you for reporting on this. Kudos to David Smith on never giving up! When people had complaints about one tile, he came up with more shapes until he shut them up for good. Way to go!
This is the story of your enslavement 👉The Connections (2021) [short documentary]💖
@@VeganSemihCyprus33 Trolling will not improve your chances of success.
He certainly mogged his attempted moggers with his intense mewing shape inducing edging streak
For those who wonder why the L tile does not qualify as an aperiodic shape: it is because you can tile it in a periodic way too. For example, you can put two rotated L shapes on top of each other to form a rectangle and tile it. The shape they propose cannot be tiled in any periodic way.
Thank you! I spent the whole video wondering why we were shown an aperiodic pattern with a single tile but it didn't qualify as a monotile, and didn't have the mathematical literacy to look up the answer myself.
That’s literally explained in the video. Pay more attention next time maybe.
@@abcdefghilihgfedcbatimestamp?
i know it's easy to put people down, but
try not being cruel..."they explain that in the video, you missed it"@@abcdefghilihgfedcba
Same here @NiteSaiya
And thanks @leoisikdogan!
Anyone have a timestamp for where this was explained in the video?
The shadow of a non repeating 4d object
Good luck getting a clean edge to terminate at your bathroom floor/walls!🤣 Very cool!
Dave has an amazing visual way of thinking. It is a gift and it is a gift that is very useful in many fields not just in mathematics and bathroom floor tiling.
He definitely is a certified Skibidi sigma of shape-ohio
This is inspiring stuff. I have a long background in Computer Science and Applied Mathematics, which sees my recreational focus gravitate towards patterns, symmetry, etc in Art, Logic, Music and Science.
I’ve just recently (at age 62) gotten into drawing. I love transcribing renditions of geometric objects, whether they be simple, have rotational, reflectional or translational symmetry, and then to try creating tilings. This includes 2d drawings of “impossible 3d shapes” and sacred / Islamic geometry (shapes which are constructed using only a compass and a straight edge) and many other sources of inspiration.
Watching the animations in this video gave me chills running up and down my spine in waves, exacerbated by the current ambient room temperature of 9°C at 1:30 am. [I should have something something warmer to wear!]
So THANK YOU Up and Atom for your continuing high quality and interesting content. My salutations to Dave and his collaborators for original, imaginative and spontaneous creativity at the pinnacle of excellence. And an incredible effort by all of you in combining talents to produce this masterpiece. I really am impressed!!! Also I am really cold and should get under my blankets in bed!
There is a lot to learn from you, sir!
Suffering for your art is no longer considered to be essential !
There are some areas of STEM where you can contribute even without a formal background; where curiosity, lots of experimentation, an encyclopedic knowledge of the subject and a keen eye can carry you pretty far. My warm congratulations to Dave for spotting not one, not two, but three solutions to a half-century-old problem.
Not that the three other collaborators don't also deserve credit for the rigourous proof, an essential part of the full solution. But this is the type of problem where coming up with a good conjecture is the most difficult part, not proving it. It was mainly Dave's insight and observation (and hard work, presumably) that cracked this one.
So yeah... congrats to all, but Dave's the man! :P
It’s creativity through and through. Lots of people consider it the antithesis to formal science/math. He posited the solution before solving the problem.
It would be better if it was a woman though. For equality
@@edwardk3 look up Marjorie Rice for a female example.
And I think it would be better if it was a child because younger people need recognition too
@@breni1518 yeah but woman are oppressed by men who solve before they get a chance
I wonder how many people also messed around with these tiles but never got to emailing an academic or never even knew it was in fact a mathematical goldmine
"a ginormous translation" - what a word! Kudos to you for just casually slipping it in
He sure has an exceptional visual thinking ability
Great video! As a high school maths teacher, this is so inspiring to me. I will definitely be showing my students... Dave reminds me of all the brilliant, self sufficient hippies I know aren't willing to be cogs in the system. What an absolute legend
I'm dyscalculian. I'm unable to comprehend any form of maths that goes beyond simple counting and at the same time there is a high chance I will make lots of mistakes at addition or substraction already. So it's pretty safe to say maths has been the bane of my life. BUT I think it's really awesome how so many people spent so much time and effort into discovering a unique shape and share it with everyone.
I love all the Dave's of the world... Reminds me of the proverb, "Man who says it can't be done.... should get out of the way of man doing it."
the round edges are a real clever solution for the problem
Major props to Dave for scoring a trove of examples of this geometric phenomenon, i wonder if this is related to the theory of six-fold symmetry in planar geometry
Dave is one of those guys who proves anyone can do something remarkable! And anyone can play with maths.
This is the story of your enslavement 👉The Connections (2021) [short documentary]💖
I'm pretty sure Dave is quite remarkable and his achievement proves nothing about "normal" people.
The fact that he doesn't present himself in a certain expected manner doesn't mean he's less of a genius.
He is one of those guys that has an exceptional natural pattern-matching ability. I wouldn't be surprised if he were on the high-functioning part of the spectrum. AKA not really a "normal" person.
Recognizing what he had is the exceptional part. There are precious few people who can recognize a potentially great discovery that they stumble onto, trained or not.
I bet more than one kindergartner has cut out that shape randomly.
As a 3D artist, this is a great move because texturing 3D models would be more non repetitive, but it still depends on its practicality
Yeah Imagine if a game developer uses this shape to tile the oceans in the game. We'll no longer have the repeating waves in the game oceans lol
The games ussually code the space into square tiles for simplicity. Computing the perfect allignment of pixels and shapes on the edges of tiles would make the game more laggy.
@@LonelyRacoon perfect. Although since the tile rotates it’ll need to applied in sheer so that the rotation remains within a horizontal influence.
Not practical.
Shit I didn't think about that you are right!
A mini gallery of the shapes tiling an area, from penrose tiles, the hat, the extremes, and the spectre sounds good to me.
Dude found the shape almost too easily from using kites. It's like he said, it was in plain sight.
Most of the time such things are beyond my understanding, logic and intelligence. But here the subject is so well conveyed that I not only got an idea or feeling for the problem and the solution, but also thought that there must consequently exist many more tiles before it was mentioned here. Great job, thank you!
Love this story and nice follow up on the story. I gave a workshop about this at a mathematics camp for young students (12-14 years). Very inspiring topic to present.
I let them play with penrose tiles, then the L shape and finally with the newly discovered tile. The last one I made two colors, so they would discover the need to put some upsidedown. Was great fun!
A heart ❤️ I'm honored! ☺️
I really think dave deserves all if not most of the credit for these shapes. Dont get me wrong I know the other people helped prove and publish the findings but he really seems like the one who discovered the einstein shape to begin with. And the second one, and the third, and so on. And the "true" einstein tile that beat the moaners. "co discoverer of the einstein tile" next to the others names... I mean yeah they helped prove that it was and publish findings but.... Dave really did actually discover the shapes from what I can tell
He's listed as the first author. In academic community authors get listed in the order of their contribution. Being the 1st name on the list is huge honour. And when cited, in some cases it would go something like: D. Smith et al (2023)
With no discernable repeating patterns. It is probably the world's most efficient camouflage tile shape.
After like the third "Well Dave found another" I just became convinced he sees the world in a way no one else can.
I really loved this video! Not only did Jade given us a very simple explanation to what appears to be a complex proof, the storytelling was also great and made us all love Dave.
One of your best video ever and that's something! The in-person interviews, the storytelling, the explanations, the animated diagrams! Everything drips passion and effort.
Thank you!
This is the story of your enslavement 👉The Connections (2021) [short documentary]💖
Dave is not just a bloke off the street, he's an absolute legend. Great video Jade!
This is the story of your enslavement 👉The Connections (2021) [short documentary]💖
The *proof* was even more mind-blowing than the discovery of the SHAPE to me. 😳
100% intrigued. I am a retired math teacher and a quilter. ❤🎉❤
Isn’t it beautiful how art can go hand in hand with science? Imagine how much more potential there is when combining those two ways of seeing the world. ❤
Math is not science - it's art
@@TheloniousCube it is!!
A great video Jade. Nicely reduced the complexity of the proof so that everyone understands easily. And a nice chronology of explanation from aperiodic tiles 1964 to Penrose tiles to current hat turtle Daves's eye and the spectre. Keep doing more ..Thanks!
Jade is back! Woo hoo! ❤🎉😊
Ready to fight in the next mortal kombat
Tan tan Tan tan tuta Tan tan Tan tan tatu Tan tan Tan tan tura Tan tantara tura rarara
The flaw with “the math world” is the arrogance of mathematicians. Whenever there’s a problem that hasn’t been solved for some time, the old heads discourage the newbies from pursuing it because they just assumed that if it hasn’t been solved, that it’s unsolvable. I believe the reason it took 50 years was because people were told NOT to try to find the answer as there isn’t one, and you’d only be wasting your time.
The fact that he called this shape a Spectre calls for attention of certain special agent.
Fascinating story of discovery! A problem that some of the greatest minds in math and physics could not solve but a bloke just playing around with shapes figured it out. Absolutely inspiring!!!!! Way to go Dave👍. Thanks for posting Jade your a Rock Star ⭐.
Amazing video! I remember hearing the buzz and excitement about this with the first discovery, and super nice to hear the mathematical proof behind it laid out and explained so clearly. Which is a testament to your teaching ability, since proofs seem to always be the hardest thing for people to wrap their heads around. And the animations in this video are wonderful too. Great work!
It is such a great success story. Pros sometimes lump all weird hobbyists into the crackpot category because there are so many of them (crackpots). Dave here is the real deal though. Kudos to him, and also the profs who took him seriously. And thanks for the great video!
It helped that he seemed humble and yet educated (himself, probably self taught )enough to know when he : 1) Might have found something others would be interested in and 2) Knew what kind of expert to contact to verify his discovery. Since they collaborated at least two more times, I'd say Dave must be easy to get along with and those three Academics must not be the snooty kind or the greedy (taking all the credit for something he first discovered )type. To me, this shows the 'best' of science and mathematics where everyone does their duty and they work together to advance knowledge.
I don't like how they call it "moaning" about it. It was a legit point.
This ol' geeza is like a proper old school squatter or bicycle courier. He's a legend
He'll be remembered in the math world for generations for this, yet he's so humble, amazing.
Really ? He has produced an elegant solution to one of mathematics' more minor problems; only a very few text books will need to be updated. He will soon be forgotten, like so many other contributors to our knowledge and understanding.
@@hb1338 Hell yeah, forget the bitch this ain't that interesting !
@@hb1338 His contributions will be remembered, and he'll live on through that.
@@Axodus whos?
@@ft.nufonia David Smith's.
Fascinating story! Dave is probably a genius. I hope he also gets into other fields. Maybe he'll solve some long standing problem!
There are all kinds of reasons that this tiling, even its existence, may be important to many areas of basic mathematics as well as applied mathematics. Its super that you found and decided to “cover” the aperiodic tile story. Please continue checking in on its progress! But I also want to just say what a wonderful collection of inspired and useful presentations all of your videos, both alone and taken together, create. You are very gifted at doing this important work of harnessing an often misused medium for good purposes. I am a scientist, old but still at work, and often watch your videos for amusement. But I also like to see how you explain certain things for importantly non recreational purposes - and try to understand how you might have come to the way you do it. Thanks for such good work and your channel.
Unique hierarchy could be equivalent to the 'temporal frames' of a reality that simultaneously experiences the absolute spectrum of it eternal nows but each temporal frame of 'now' is distinct from one another as it transitions from the end of its beginning to the beginning of its end.
Penrose tiles are such a beautiful and sophisticated solution though.
Astonishing story! I confess it's a little over my head at present. Going to follow up and try to learn more. The material science applications are massively exciting!
Fantastic video. Great job Jade.
Dave is clearly an amazing human. Massive kudos to him, and for the academic mathematicians who helped him with the formal proof.
Yeah the co-discoverers kinda latched on for the credit.
To expand on the idea at 8:55 of two Ls being part of only one larger L... If you take two adjacent small L tiles, for them to be a translation of each other, as you move up in size, that larger L must also be adjacent *in the same way*. In other words, as you increase both e.g. up and to the right, the result would be a larger L with the same adjacency property as the smaller L. For the L tiling, this works up to point, but then you hit an L in a different orientation (e.g. down and to the right), so you cannot form a larger L at that size. -- The L you are working with has shifted from being the inner part of a larger L construction to the outer part. As such, it cannot be adjacent to a different L, it is adjacent to the inner part of a larger L. Therefore, the tiling is aperiodic.
This is the most bizarre type of bed. Never seen anything like it.