Roger Penrose - Forbidden crystal symmetry in mathematics and architecture

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.

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.

[M.-.D]

So incredible to see Professor Penrose win the Nobel Prize.

One of the greatest minds.

[debszta]

Roger Penrose: The man that got into science because he liked to light things on fire when he was a kid. Love this guy.

[mwilson]

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.

[petebop]

Just wow, such a brilliant display of a truly intellectual human, proving their intuition with math! The passion and humility! Thousands of years of thoughts collected and dissected to find the beautiful "chaotic" symmetry around us, bravo Sir!

[unemployicus]

I can listen to Sir Roger Penrose talk for hours, and that's why I do.

[unvergebeneid]

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!

[gwahli]

On videos like this, even the ads are more classy. I got an ad from a lab equipment company.

[jeanqnguyen]

Love his hand drawn and written overhead slides, no one does it anymore

[ddaro_ss]

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. 

[ElMauber]

Imagine seeing these patterns implemented in modern architecture. Absolutely mind blowing Mr. Penrose, bravo! 👏🏼

[jacderida]

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!

[glutinousmaximus]

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.

[markAD]

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.

[DIMentiaMinecraft]

Whatever you do, don't take the stairs to his office.

[JohnDlugosz]

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.

[shuddupeyaface]

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.

[wayneyadams]

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.

[jach]

Sir Roger never fails to amaze me. Thank you.

[mcee]

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!

[moonzestate]

The ancient Greek biographer Plutarch quoted Plato as writing, “God geometrizes continually.”