Roger Penrose - Forbidden crystal symmetry in mathematics and architecture
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- เผยแพร่เมื่อ 6 พ.ค. 2024
- Sir Roger Penrose provides a unique insight into the "forbidden symmetry" of his famous penrose tiles and the use of non-repeating patterns in design and architecture.
It is a rigorous mathematical theorem that the only crystallographic symmetries are 2-fold, 3-fold, 4-fold, and 6-fold symmetries.
Yet, since the 1970s 5-fold, 8-fold, 10-fold and 12-fold "almost" symmetric patterns have been exhibited, showing that such crystallographically "forbidden symmetries" are mathematically possible and deviate from exact symmetry by an arbitrarily small amount. Such patterns are often beautiful to behold and designs based on these arrangements have now been used in many buildings throughout the world.
In this Ri event Sir Roger Penrose reveals the mathematical underpinnings and origins of these "forbidden symmetries" and other related patterns. His talk is illustrated with numerous examples of their use in architectural design including a novel version of "Penrose tiling" that appears in the approach to the main entrance of the new Mathematics Institute in Oxford, officially opened in late 2013 (www.maths.ox.ac.uk/new-building).
The tiling is constructed from several thousand diamond-shaped granite tiles of just two different shapes, decorated simply with circular arcs of stainless steel. The matching of the tiles forces them into an overall pattern which never repeats itself and exhibits remarkable aspects of 5-fold and 10-fold symmetry.
Similar features have been found also in the atomic structures of quasi-crystalline materials. The initial discovery of such material earned Dan Shectman the 2011 Nobel Prize for chemistry, his work having launched a completely novel area of crystallography.
Images of the completed Mathematics Institute in Oxford courtesy of Vanesa Penrose.
The filming and production of this event was supported by the Science and Technology Facilities Council: www.stfc.ac.uk. Production by Edward Prosser. Additional camera operation by Mark Billy Svensson.
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So incredible to see Professor Penrose win the Nobel Prize.
One of the greatest minds.
It's really nice to listen to him. I love his universe.
The dude is pushing 90 and still razor sharp!
you understand what "incredible" means?
apparently not
@@vhawk1951kl unbelievable as in no murmurs seemed to be hinting at his selection.
Roger Penrose: The man that got into science because he liked to light things on fire when he was a kid. Love this guy.
And his father and two brothers are scientist and another is a chess grand master.
Don't most guys🤭 He's so serious trying to show this "phenomenon"? Just look at Snowflakes, not one alike I've been told.
" If you only knew the magnificence of the 3,6,9, then you would have the Key to the Universe. " Nikola Tesla 🕊️
Yer my dad was a leading virologist and he got into science because he like blowing stuff up.
He made a hydrogen bomb and blew up the shed and caught his room on fire a few times...
I think it's quite common among scientists lol
@@jakeford9073
Reminds of my brother, Mike making lye bombs that required aluminum foil. And our Great Auntie's 1962 Comet with the paint burnt off the hood.. Big patches right down to the bare metal.. P. S. Our Great Grandmother made soap hence the lye availability 🤣
Combustion is fascinating. I enjoyed restarting the campfire in the morning from the coals just with air and kindling. Later I learned it was oxidation and latent heat.
Somehow, when something famous is named after a person, I always assume that this person is dead. It always amazes me when I find out that not only is the person still alive, I actually get to hear a talk by them!
Still going!!
Like a Duracell bunny.
What fascinates you about him? Ive heard a few lectures and hes apart of humanities problem. Pushing bs black hole theory, dark matter, and other occult symbolism as many of these "famous" do. Science is intentionally attacking empathy and we see it having effect in the world. There is no denying this. The impact that these people have on the next gen is real and kids dont know better. Apparently some adults are still indoctrinated into our upside system and cant see the problems. Its complicated but this man is no hero and no genius. Living a life dictated by memorization and numbers does things to people too.
@@prototype8137 Are you quite alright? You sound like you might have hit your head on something. You should get that looked at by a professional.
@@prototype8137 tool, that isn't how to refute his entire body of work.
)
On videos like this, even the ads are more classy. I got an ad from a lab equipment company.
Did you buy?
@@mokopa No. We're just a software company and have no need for that kind of equipment.
why you not using ad blocker?
@@gordonrussell9110 For ethical reasons.
I got an ad for the Reno 9-1-1 reboot. So much for that theory.
I'm almost 15 minutes in and I'm totally engrossed into the lecture. This is tremendously fascinating and informative. This fully explains the observations I've made under the microscope of my synthetic corundum (ruby and sapphire) as well as the formations observed in natural corundum. I'll probably watch this several more times to take it all in. We're lucky as a society to have resources like this available for free.
I studied crystal symmetries and point groups as they relate to electron diffraction spectroscopy and still found this lecture incredibly difficult to follow. I think the problem is that he moves along so quickly without explanation of so many of the things he says are "obvious." They are not "obvious" to the average people watching this video who have never had an advanced Chemistry (or maybe Physics) class. PhD does not necessarily mean good teacher.
The case about "obvious" seems to be a maths thing. I remember a math professor who used the word "trivial" a lot, when most of the students didn't find the topic/proof at hand trivial at all.
I learned: there are us mere mortals and there are some mathematical minds, capable of highly abstract thinking.
Love his hand drawn and written overhead slides, no one does it anymore
Some years ago, I wanted to have a small bathroom floor tiled with Penrose rombic style tiles, but every contractor ran away screaming.
It's interesting to see that people have actually done that now.
John Długosz kept you from running scared at the price
What prevents you from doing your own tiles?
@@brianmackey7682 Usually the pitch of the bedding.
I am a flooring contractor as a side job--you would have made my day asking me to do that.
Easy job, unless you have to hand cut the tiles. If you can buy them as a working kit no problem, it lays itself out.
I initially wanted to stop the video at around 8 mins in but - contrary to some comments complaining about how boring the talk was - i just got so engrossed that I finished the whole thing. The slides may have limited the talk in some ways (IMO mainly just time-wise) but without the slides we wouldn't have the awesomeness that was 26:00 to 28:00. A powerpoint simply wouldn't have the same oomph factor.
In any case, it's always inspiring to see someone so passionate about their work.
Greg Queen of Everything schizophrenia is believed to be a defect in the brain in regards to timing. unlike your comment which is just ugly.
Sir Roger never fails to amaze me. Thank you.
Imagine seeing these patterns implemented in modern architecture. Absolutely mind blowing Mr. Penrose, bravo! 👏🏼
Roger is perhaps one of the unsung heroes of the 20th Century. His work is brilliant and his book "The emperor's new brain" is a triumph. I corresponded with him a few years ago, and he is a very down-to-earth guy. Good stuff.
Whatever you do, don't take the stairs to his office.
I laughed really hard. Thank you.
I always had trouble understanding math teachers with the exception of a few. Mr. Penrose would definitely fall in the latter category. Wonderful almost magical quality of his connection to mathematics. Universal or infinite patterns of symmetries or near perfect are indeed fascinating and probably very relevant to future discoveries of great import.
You have to be able in your minds eye to paint a Rembrandt before you put your sights on modern art. He is genius in that he relates it to math.
To be is to encompass a space. To encompass a space, you have to equally displace. The two realities are fundamentally intertwined. Thank you Mr Newton.
What a wonderful and enlightening presentation. One feels that there are more applications as yet unknown, for this.
I particularly like the Rhomboid pattern with it's suggestions of 3D that jump out as one focuses on different loci.
I've watched this twice now. It's inspired me to take on a wee project to do some programming to generate some of these tiling patterns. Fascinating lecture!
Brilliant to hear! Did you ever end up with any code? Is any of it available on github or anywhere else? :)
I'm so grateful for this. Thank you so much. 😊👏
This is so simple yet fascinating!
Just love the Royal Institute! Penrose, Dawkins, going to sleep with geniuses!
From Faraday and keeping the standard high. Makes you proud. For everyone, even dummies like me can enjoy it. Love it, keep it up!
Haha, yeah, same for me!
I really want to use this pattern in some construction project. One of the cool things about it is that you do not *have* to do a layout first, or think too deeply about how you are meeting the edges of your field. You can't exactly buy penrose tiles from the flooring section at Home Depot.. so it would mean cutting and wasting a lot of tile.. and then you have to figure a way to score the alignment patterns on them in an attractive way. Almost easier to buy a kiln and make the tile from scratch yourself. But then I had another thought! To put this in concrete.. all you need is two stamps! Much faster way to create a penrose floor.
I love his quaint hand drawn diagrams !
Amazing. Transcript or reference of the articles mentionned would be great!
It's really impressive if you move the the top pattern and come up with stripes.
And i kinda got the impression, that there is more to it than that. If you rotate the top shape, it almost looks like it is zooming in on the pattern.
that is the exact feeling i got. and when you are zoomed in at maximum the strips appear.
he did say you can make it as big as you want it, i guess you missed that
incredible stuff, very interesting thanks for posting this
Interesting intersection of disciplines. Mathematics as art and vice-versa.
That's the essence of art. Showing the mathematical harmony of world, thats the utility of art.
Random shapes without meaning or natural pattern is not art. The thing that pleases eye in art is the harmony, the proportions, even in the human forms, facial shapes.
Art is reproduction of natural order, laws, patterns. Other part of it is visualization of ideas but still meeting the overall laws. And this is the essence of civilization - building on natural foundation - not destroying things, doing opaque, rebelling against the essence of world or to prove loss of own basic roots or human reflexes (and most of modern "art" is exactly that, meaningless ugliness, betrayal of world creation laws to prove own childish ungreatfullness to the world which brought us to be, to build on ruins of the old/real world, neverending progress for sake of progress, everlooking for a different, new, extreme in selfhate, sadomasohism, insane objective of disproving basic intuition that art for art is not art; formlesness, antiform is the modern cult of soulless aberrant nihilism).
The best crossovers between math and nature brought us the best human inventions. The looking for unreal, utopias, desacralisation of nature brought us communism, cultural destruction & unnatural magic-pill-based, not treating causes of diseases caricature of medicine.
Good day to you :-) Take your daily dose of sun or fishoil/vitamin D please. Take care.
Love geometry, and especially love Sir Roger, precious man.
Crystal condensing symmetry breaking during lava condensation produces differential crystal veins as a function of temperature as applied in metal retrieved at different temperatures.
No rulers used in the construction of images? Knowledge and intuition always present in his modus operandi. Nice stuff to show to young people involved with science. Not everything has to be computable...Why pen and paper still have their power? Hands on experience adds something...
i found myself short of breath a number of times. This is absolutely something of great importance.
wonderful time passed on this Oxford courtesy
This many is simply amazing.
If you want to share the incredible moiré pattern demonstration, we've posted it here: Incredible Moiré Patterns!
+MrAaronvee "The Royal Institution" is short for "The Royal Institution of Great Britain". It's a proper name. The RI has different aims from the Royal Society. Plenty of FRSs also belong to the RI. Eric Lathwaite was never director of the RI, he just gave a few children's lectures there.
+MrAaronvee childrens lectures!! my oh my! the pseudo effort just as such effort. interesting wáy to worthy it attention. not wronging none nor is it credible ya ...consern..? ... aaaw!
The thing I love about Penrose is that he loves mathematics and he has no clue that most of the people that he is explaining it to have no idea what he's talking about. It reminds me of myself explaining anything to anyone.
The ancient Greek biographer Plutarch quoted Plato as writing, “God geometrizes continually.”
Awesome! I love this.
superb content !
Thank You Sir Roger Pentagon Rose
What I like the most about this is that its consequences has lead to thoughts on consciousness and then on to physics and so 'everything'
Very enjoyable... Would love to understand this more..
What you are seeing here is TRUE GENIUS -- someone to whom problems that stop others in their tracks are merely somewhat tedious, not barriers to solutions. "The improbable we do at once, the impossible takes a little longer" in a person...
stunning!
Does Mr. Penrose or anyone else have a book that describes all this in detail? This is great stuff, and I'd love to slowly read and savor it.
Thanks.
20:54 Tiling the plane without repetiton: «I knew you can do it with five tiles, then I started fiddling around for a bit and realized you can do it with two»
Some people are paid to fiddle around and make creative progress.
Hahaha
yes specially when they have a knighthood
not us mere mortals
ah yes, those people are called fiddlers or maybe more often violinists
Great sharing
Amazing!
This really makes me wonder about the difference between dimension and perspective. Is a cube really a cube? How many more sides might be out of sight, or merely an illusion caused by relative movement?
At certain points during the rotation, it looks a lot like the prime number spiral.
Neat stuff!
A cube could be a hexagon or
26:30 blew my mind.
Truly a WTF moment
Fall in love with structure & shapes, make u doing things like that
beautiful!
"Something doesn't look quite right. That tile on the end doesn't work with the one on the other end." I'm not convinced that Penrose is human.
Fascinating.
I was inspired to use this on the job - Penrose Tiling on a concrete floor
I love scrolling down and seeing intelligent comments. I guess I can go on living another day.
Sometimes it's depressing how far you have to scroll.... :)
Compared to comments 6 years ago, one person asked for transcripts and articles.
Nowadays we got "Hugo Guthrie 1 day ago
Mathematics can be processed and learn by images. Mathematics?"
This guy doesn't even know that in medieval times we thought all shapes shown all life, and describes math. We found that Maths describes everything. Thats why most were hellbent on learning shapes and triangles. A squared plus B squared equals C squared. And if you put two right angle triangles together, you get a box with 4 corners, a rectangle or a square. This is literally elementary school.
@Boco Corwin 😂
whoa. this is amazing
The Moiré effect is particularly interesting.
Roger really wanted to show that the wobbling crystal symmetry is broken to have differential boundary of crystals for example as opal black crystal or rubies as differential veins of crystal condensing boundaries of lava as a function of temperature condensing differential.
He deserves the Nobel prize simply for tileing the plain asymmetrically.
Wait what....
Is there any way you can put where is Roger actually pointing at while he is showing his slides? I just seem to see a picture and I get confused where on the picture should I look when he is talking about it.
"this point" "that point" doesn't really work without a pointer for the camera =[
i wanted to ask,... for the square, triangle, parallelogram and hexagon tiling, i can find many points as my axis of rotation so as the whole tiling can overlap itself, but how about penrose tiling? does it have only a single point as its rotational axis or are there an infinite number of points for me to choose as the axis of rotation for the penrose tiling to have 5 fold symmetry...
I noticed that at time frame 27:59 when intersecting lines began to form that a fractal "cardioid" pattern may have been forming which implies that the "Phi" value may be at the "heart" of the crystalline structure.
Good Catch. It indeed is.
He is on to the something
That leads to everything.
Jolly good show . What what.
Yep yep
Reminds me of the multiple universe theory, which I think of in this way where one really fits inside of another, perhaps more complex one, ad infinitum.
Does somebody have any information on the type of granite used that made the pattern look different in dry and wet surfaces? 53:29
Those granite and stainless steel tiles at the end are beautiful
When you subdivide the pattern is it a halving or another ratio of sizing?
brilliant
5.and 12 are the combination for the dodecahedron which is the only polyhedron which allows vertex to same vertex uninterrupted surface path. Geodesic.
If I could spend five years of my life on this kind of math, I would love it. For all those questioning where this math takes you...it can form the basis for some pretty sweet future tech.
five years later! how do you view this subject now? I'm intrigued and glad that i stumbled upon this at the right time in space!
6:00 Roger: "Straightforward..."
Me: < rewinds to 4:00 >
Steve Smith I get it....! Duh! Back to the beginning 8
Please look carefully at the surface patterns of the Maclura Pomifera, called osage orange, spherical seed pod. Hypothesize that the five-fold Penrose pattern may form the basis of its seemingly confusing design. Requires careful analysis. What do you think?
Reminds me of fractals or the Turing pattern
Came here just for this guy. He is sooo cooool!! 😍
I love his tie.
When he draws the green circles over the green pattern I see the seed of life. and in the end the fruit of life. Nice TY
When growing crystals in sounds the shape is very difficult to get x the most common form of surface that with no vibrational effect has become the same as the magnetic styles...
"No matter how big the region is, you can always find it in the other one." This threw me in relation to "there's more than one pattern possible" until I realized that identifying a region necessarily means reduction to a FINITE section (no matter how large) outside of which you could always create variation. Only if infinite patterns perfectly overlapped could you say that there is only one pattern. But you could have the same pattern for light years and light years of space, and then--bam!--variation.
Sir Roger Penrose is awesome as a brilient thinker
I wish he was more Escher in thinking & less an inelegant Chompsky simulacrum. Fractals exist as representations of sound as a commutable entity. More Parallax & Tycho Brahe. Then du Sautoy & black hole firewalls. Have a lovely day, Dr Cliff x
Seeing these as atomic arrangements and not just tiles, it begs the question, is this a possible solution for the neutron packing problem? The cubic solution bothers me immensely, but this has me wondering now...
What about the dodecahedral Iron pyrite crystals?
Are there currently any applications of this tiling pattern in cryptografie? Looking at how these patterns are arranged and what interesting properties they pertain i imagine very smart algorithms could be constructed using this knowledge
This video shows how brilliant Professor Penrose really is.
@The Royal Institution
Am i right in thinking that that bench is actually the same one that has always been there? I mean, are we looking at the same bench from which Michael Faraday enunciated his field theory of electromagnetism?
It's actually the fourth Faraday desk. When the first one broke from all the wear and tear, we commissioned another one built to the same specifications, with a few added improvements. And the same happens whenever it breaks down. The current one can be unlocked, elevated and moved on castors, and also has inbuilt charging and display cables. Considering the desk is used almost daily for demonstrations and lectures, we feel that a roughly 70 year lifespan is pretty decent for a desk.
I wonder how long it would take Faraday to understand the concepts behind an HDMI cable. Quite a lot has happened in 200 years. Faraday could sit in the audience and lead the way by asking questions of a panel of experts in the relevant fields. That would be a fascinating journey to watch.
You can't get Faraday, but you could get a celebrity in a room full of boffins and record the process of them asking questions until they felt able to present a lecture live on TV from the RI. That would broaden the public understanding of science.
A reality TV show covering the celebrity exploration, followed by a real lecture at the RI. That could be a horrible load of fake nonsense, or it could be something wonderful and inspiring.
Jodie Whittaker (Dr Who) explores and lectures on...
So intelligently humble
oh my , the man is a true genius
PLEASE make a post on the relation between DIV GRAD at finite density charge sources and the relation of this to gravitational curvature for finite density mass distributions. For zero charge density DIV GRAD X=0, while for mass the mass on a rubber sheet model suggests negative (Gaussian) curvature in the surrounding vacuum, suggesting DIV g
Are Penrose tiles scale independent ?
For those who do not see a practical use, i say there is one major and that is infills of a stucture that may be 3d printed. All his first patterns are the typical infills nowdays and each has pros and cons. A good algorithm would make strong partsmat fast speed. So whats it gonna do for you? If we can get fdm printers as fast as resin, without the flaws resin printers have then the world would change a lot in terms of how we buy things. Ten years ago only enthusiasts printed, now consumer models exists and it has still a bit to go before we find real practical use as it takes time, but eventually we can print shoes when we want new etc. You can already do that but at a time or high cost. A proper infill algorithm would help the future.
that was so cool,
Is this the stacking of 8d and 24d oranges?
what does this have in common with angle graphene layer
Meta Magical Themas, by Douglas R Hoffstadtler, an abstract description of why it is forbidden is a bose einstien condensate process moment. In ,geometry in contrast to relativity, a radius in a process that generates two virtual radius, is the maximum value. three radius rebounds in growth back towards one radius. It never reaches four radius which stops the pattern needed to be crystalline. the equivalence of too much information needed to define system.
can not wait for the 'forbidden' part
25:15 you can see a blurry pattern getting zoomed
So platonic solids describe translational symmetries?
amazing. rivaling the math in ancient structures or is it more complex just not as massive
Concidering atomic structure exhibits co similarities
We can also see this exhibited within language
As all structure is a form of language projection and overlap
This man's comb over makes him a 'legend' indeed. Wow. Just WOW. And it is MC Escher who made him famous (not the other way around).
Roger is an absolutely wonderful human being top quality that one haha