"The important thing about 5 is that it's not 3, 4, or 6." I often find myself explaining mathematical concepts and pretty much the stuff on this channel, to my friends. I'm going to start using this quote because more then once have I been asked why 5.
+linkviii To establish or refute that assertion, one would have to perform experiments on groups of scientists. The scientists would be asked to solve novel problems for which their language was or was not compatible with the task. However, the test makers would need to have the language to describe the tasks.
Totally right. One similar example is- If we listen to a language that we don't know anything about, then we won't really "hear" it no matter how hard we try.
And of course this video refers to Schectman winning one too. Pretty cool that laureates in Physics and Chemistry, respectively, both touched on these mathematical concepts.
Im 18 and I'm a pretty well balanced kid when it comes to school, sports, and social life....but these videos just let me embrace my inner nerd and i love it
I read an interesting article in "Scientific American" back in the 80's. Titled something like, "Symmetry in Chaos." Found it quite interesting even though I have a high school education. It was specifically about Penrose tiling.
By "repeat" here, he means that any local patterns can be seen infinitely often and regularly - more precisely, for any sized patch of tiles you want, there is another radius such that that pattern can be found in the tiling to within that radius of any point in the tiling. This is an amazing property and in some way generalises the usual periodic patterns (periodic means I can pick up the tiling, move it, and it looks the same again - this isn't the case for the Penrose tilings).
Wonderful video again. Really rich in content and food for thought on many levels by using one central example and several nice anecdotes. Excellent job Brady. I have always loved the fact that humans are so linked to experience and perception and how culture, language and experience can so affect the outcome of an event.
If you were subscribed to brady's other channels, you would see why they tie their videos to a number. This channel is supposed to be a collection of videos about the numbers in our daily lives, while sneaking in advanced mathematical concepts, like sixtysymbols is a collection of symbols, but really about physics, and periodicvideos is a collection of elements, but you also learn a lot about chemistry.
I remember playing with a set tiles as a kid. There were hexagons, triangles, squares, trapezoids, and two rhombuses. It was really fun to put them together in different patterns and tilings. Maybe one day I'll pass it on to my kids, and I'll add some more pieces derived from pentagons for even more variety.
Its at a university in my city and basically the first thing you get told about the building is that there is one point, where no matter where you look it is identical on all sides.
I've been tiling for about 7 years now and I would bloody love to be asked to do a Penrose pattern! I've never even seen such tiles on sale anywhere. Victorian geometric patterns are close, but that floor at 5:13 looks amazing! I'd love to know where it is.
The question at the end is very interesting, and the conclusion that you can't see something you didn't know you could be looking for is even more interesting, particularly for those of us who intend to become professional scientists.
Brady, one thing overlooked in this one, that I can see 1st hand. I am pretty sure that quilters have been overcoming these angular difficulties with repeating, fill in shapes, farther back than the 1980s, and possibly the 1880s. Just do a simple google search of geometric quilts, and I would bet you'll find this problem has been tackled by hobbyists, my Grandmom, Wife, and a plethora of others, for quite some time....Just an interesting aside. Thanks for all your videos, they are brain candy :)
As long as your symbols don't resemble each other when written in a line of condensed text, you can use as high a base as desired. You could even encode the symbol's value into its structure. For base 32, you could have symbols consisting of vertical lines with up to five short horizontal lines jutting out from them. To avoid confusion with the middle bars, special accents can distinguish them in the digits where their neighbors are absent. One could use this method for other bases as well.
"Some support for this conjecture comes from the fact that in certain dimensions (e.g. 10) the densest known irregular packing is denser than the densest known regular packing." Check "Sphere Packing" from Wikipedia.
Of course they can do whatever they want, but my opinion is that although numbers are fascinating I'd like to hear these same people talk about mathematical ideas without having to tie it to a specific number. Math is so much more. If this series is supposed to be mostly about theoretically unimportant number games than that is fine, but I think they want to do more.
@numberphile maybe because so much in my life is associated with this number. This, of course, can be said about any number. But 5 seems to me very beautiful. It is easy to count something using 5 (well, for me personally) when you do exercise, for example. Also in Kazakhstan, where I come from, 5 is the highest mark in school, so all students want and like this number)) I just love it. Hope I'm not alone. Thank you again))
nice video. For once, I think I understood what a mathematician was saying! Some viewer confusion could have been avoided if he'd sayed "plane" means flat surface, repeat flat. And the challenge is to find the minimum set of different tiles including a regular pentagon that might be mass-produced. Did he get it down to 5? The idea of "never repeats" is worthy of a few more words. Penrose's hour long lecture is very enjoyable. I think he was 80 or 90 years old and bright as a button. And witty.
I agree that for the curious mind, Prof. Hunton's explanation is deeply unsatisfying. Do you happen to have a source of a more in-depth explanation? I admit I don't want to watch an hour long video and end up none the wiser afterwards.
Sorry, I can't help, I've only dipped a toe in the water myself. It's interesting that Escher tiled a pseudo-spherical surface with fewer shapes... birds? ... lizards? ... I forget, but you can see those on google images if you're interested.
Yes, I am subscribed to the other channels. I think we both agree that the format can be a little limiting. Form is liberating, but sometimes it feels a little artificial. If we agree on anything I think it is that. We just want different things and there's nothing wrong with that.
05:14 This is the floor of the Bayliss Building (renamed Molecular & Chemical Science Building) at University of Western Australia. Before seeing the video we spent ages training to find a line of symmetry somewhere.
Yes you do see it repeat. What he means is it doesn't repeat forever, just like the digits 314 do occur in pi after the beginning but it doesn't repeat forever.
In order to tile there is a min of 3 shapes at a junction. If they were regular polygons, the total angle size would be bigger than 360 degrees. 6 is the biggest because each angle is 120 degrees * 3 = 360.
@purplezart yes&no, that is why this is interesting. Because it is mathematically hard to describe what exactly the pattern is, but any human can look at it and see that there is. The shapes repeat, there are repetitions in sub-patterns of shapes, pick a penrose tiling and I can try to describe the pattern to it, but it won't be as simple as other classic patterns.
Just as a matter of observational curiosity...there appears to be a few striking similarities between Professor John Hunton's delivery and that of Professor Mike Merrifield (DeepSkyVideos). They have very much the same facial expressions (for example, emphasis of important facts with a raising of the eyebrows), conversational cadence, tone and gestures. :)
We can also see this in viruses with icosahedral capsids. The most obvious is the dodecahedron structure with pentagonal faces. I think it's likely that they are structured this way so that the capsid can form a closed unit since it can't tile.
6:05 wrong understanding, there was not a natural tendency towards this in crystallography. there is actually a natural aversion as three-fold, four-fold and six-fold symmetries are much simpler as stated. but recently there has been one natural quasicrystal found called icosahedrite
The artist M.C.Escher was doing experiments with these principles in the 3rd, 4th, 5th, and 6th decades of the 20th.century. The geometer Coxeter - even earlier, as also, in a rather different way - Richard Buckminster Fuller.
But if the pentagon field was all moving, how would it move naturally? Including the negative space created by the movements? what shapes could the negative space become? @2:30
@MrRuaridhDonaldson You can make a ball with just pentagons, just not a flat plane tiling. With just pentagons you can make a shape with 12 faces called a "dodecahedron". I think football designers just added hexagons to make it rounder.
I love all these videos, shame there wasn't some sort of explanation as to how some Penrose patterns are formed, I just like equations that explain things.
@mohdsfk In a soccer ball, the pentagons are connected, but among some hexagons. Besides, soccer balls have spherical surfaces and this video showed tiling of plane surfaces, it makes a lot of difference.
I want to see more Numberphiles that focus more on some number and less about going off on some tangent. At least they tie it back to the number so they can stick with the theme. i.e. your opinion isn't any more valid, and they can do whatever they want. For example, there are so many more things you can say about the number 5 than just tiling.
How about tiling with non-equal sided pentagons? Is there a pentagon with particular proportions of side lengths/angles that you can use to tile, without using any other shapes? Or maybe you can use a shape with the same angles but different size (I see it still wouldn't work with equal-sided pentagons but what about non-equal sided?)
@@randywebb8284 It's possible to do a non-repeating square tiling. Do the first row the standard way. Then, displace the row above that row a little bit. Then, displace the next row 2 times that bit. Rinse and repeat. If this bit is not a rational number (based on the tile square lenght), you have a non-repeating square tiling.
"The important thing about 5 is that it's not 3, 4, or 6."
I often find myself explaining mathematical concepts and pretty much the stuff on this channel, to my friends. I'm going to start using this quote because more then once have I been asked why 5.
Lol
"Science can't see what it doesn't have the language to describe" What a great quote.
It is extremely surprising that the 'language' found by the Nobel Lauriet, could 'describe', infinite variety
+linkviii To establish or refute that assertion, one would have to perform experiments on groups of scientists. The scientists would be asked to solve novel problems for which their language was or was not compatible with the task. However, the test makers would need to have the language to describe the tasks.
You'll never notice something you had no idea you could look for.
It's like the old line: We don't know who discovered water but we know it wasn't a fish.
Totally right.
One similar example is- If we listen to a language that we don't know anything about, then we won't really "hear" it no matter how hard we try.
So incredible to see Professor Penrose win the Nobel Prize.
One of the greatest minds.
And of course this video refers to Schectman winning one too. Pretty cool that laureates in Physics and Chemistry, respectively, both touched on these mathematical concepts.
Too bad he now suffers from Nobel disease…
Now he has won the Nobel prize.
Yep yep great diverse guy
good to hear - more to come!
Cant wait to see the follow up on the new 13 sided shape that tiles the plane without repeating!
I love the observation about language as a limiting factor for thought. That particular idea is one of my favorite philosophical issues.
"Science can't see what it doesn't have the language to describe." Such a good quote.
This is the best explanation for penrose tiling. The ending segment blew my mind
Im 18 and I'm a pretty well balanced kid when it comes to school, sports, and social life....but these videos just let me embrace my inner nerd and i love it
This feels like a TED talk version of Vihart. That by no means is a criticism! This is really awesome.
I read an interesting article in "Scientific American" back in the 80's. Titled something like, "Symmetry in Chaos." Found it quite interesting even though I have a high school education. It was specifically about Penrose tiling.
By "repeat" here, he means that any local patterns can be seen infinitely often and regularly - more precisely, for any sized patch of tiles you want, there is another radius such that that pattern can be found in the tiling to within that radius of any point in the tiling. This is an amazing property and in some way generalises the usual periodic patterns (periodic means I can pick up the tiling, move it, and it looks the same again - this isn't the case for the Penrose tilings).
@TomatoBreadOrgasm Professor Hunton is from the University of Leicester!
And my motives are pure!
Thank you for using a sharpie instead of those other painfully squeaky markers that they normally use on this channel.
I love that last sentence! "Science can't see what it doesn't have the language to describe."
Wonderful video again. Really rich in content and food for thought on many levels by using one central example and several nice anecdotes. Excellent job Brady. I have always loved the fact that humans are so linked to experience and perception and how culture, language and experience can so affect the outcome of an event.
I agree! Massively interesting video!
This is by far one of your best videos, I loved it so much :D
If you were subscribed to brady's other channels, you would see why they tie their videos to a number. This channel is supposed to be a collection of videos about the numbers in our daily lives, while sneaking in advanced mathematical concepts, like sixtysymbols is a collection of symbols, but really about physics, and periodicvideos is a collection of elements, but you also learn a lot about chemistry.
@Thegeeksquadofone thank you... we're really enjoying it too.
I remember playing with a set tiles as a kid. There were hexagons, triangles, squares, trapezoids, and two rhombuses. It was really fun to put them together in different patterns and tilings. Maybe one day I'll pass it on to my kids, and I'll add some more pieces derived from pentagons for even more variety.
I'm trying to draw up my own patterns to make templates for a quilt I want to make..
@mimicici13 glad you liked it!
AAAH, SO THIS IS THE WAY I SHOULD TO PLACE THESE SQUARE TILES, THANK YOU
"We didn't see it because we didn't look for it"
Happy searching, people
Its at a university in my city and basically the first thing you get told about the building is that there is one point, where no matter where you look it is identical on all sides.
I've been tiling for about 7 years now and I would bloody love to be asked to do a Penrose pattern! I've never even seen such tiles on sale anywhere. Victorian geometric patterns are close, but that floor at 5:13 looks amazing! I'd love to know where it is.
Google: The University of Western Australia - Bayliss Building
he has an appealing accent... he can talk for hours and I won't get bored!
The best videos of the world. thanks Brad.
The question at the end is very interesting, and the conclusion that you can't see something you didn't know you could be looking for is even more interesting, particularly for those of us who intend to become professional scientists.
Brady, one thing overlooked in this one, that I can see 1st hand. I am pretty sure that quilters have been overcoming these angular difficulties with repeating, fill in shapes, farther back than the 1980s, and possibly the 1880s. Just do a simple google search of geometric quilts, and I would bet you'll find this problem has been tackled by hobbyists, my Grandmom, Wife, and a plethora of others, for quite some time....Just an interesting aside. Thanks for all your videos, they are brain candy :)
As long as your symbols don't resemble each other when written in a line of condensed text, you can use as high a base as desired. You could even encode the symbol's value into its structure. For base 32, you could have symbols consisting of vertical lines with up to five short horizontal lines jutting out from them. To avoid confusion with the middle bars, special accents can distinguish them in the digits where their neighbors are absent. One could use this method for other bases as well.
Thank you!
"Some support for this conjecture comes from the fact that in certain dimensions (e.g. 10) the densest known irregular packing is denser than the densest known regular packing."
Check "Sphere Packing" from Wikipedia.
This is like the shapes that make up a football. I've always wondered why they don't just use pentagons all over, NOW I KNOW!!
I get a big smile when i see my sub box and you guys uploaded a video
Of course they can do whatever they want, but my opinion is that although numbers are fascinating I'd like to hear these same people talk about mathematical ideas without having to tie it to a specific number. Math is so much more. If this series is supposed to be mostly about theoretically unimportant number games than that is fine, but I think they want to do more.
Ever since I read about penrose tiling, I've hoped I got the chance to use it in practice. Thanks for the video!
2:22 WHAT WAS THAT STRANGE NOISE!!! IT SOUNDS WEIRDER THAN A MINECRAFT VILLAGER!
IT SOUNDS LIKE A PEACOCK WITH A NASAL INFECTION!
murr
oh yeah mb
i thought about it like 6 hexagons together but it does not make a 36gon i went to fast >
It is a sheep making the noise.
It was Brady's dramatic realisation that everything he thought he knew was a lie.
Wow, I've never head of this before. That's pretty awesome!
@Bugside That pattern will not tile well in a flat plane though.
YOOO WTF IS THIS GRANDAYY
@@xxfazenoscoper360doesnosco7 yo
Wtf lol
pleased to be of service
@numberphile maybe because so much in my life is associated with this number. This, of course, can be said about any number. But 5 seems to me very beautiful. It is easy to count something using 5 (well, for me personally) when you do exercise, for example. Also in Kazakhstan, where I come from, 5 is the highest mark in school, so all students want and like this number)) I just love it. Hope I'm not alone. Thank you again))
The very first sentence was the one that got me. Although I found the last intriguing as well.
nice video. For once, I think I understood what a mathematician was saying! Some viewer confusion could have been avoided if he'd sayed "plane" means flat surface, repeat flat. And the challenge is to find the minimum set of different tiles including a regular pentagon that might be mass-produced. Did he get it down to 5? The idea of "never repeats" is worthy of a few more words. Penrose's hour long lecture is very enjoyable. I think he was 80 or 90 years old and bright as a button. And witty.
I agree that for the curious mind, Prof. Hunton's explanation is deeply unsatisfying. Do you happen to have a source of a more in-depth explanation? I admit I don't want to watch an hour long video and end up none the wiser afterwards.
Sorry, I can't help, I've only dipped a toe in the water myself. It's interesting that Escher tiled a pseudo-spherical surface with fewer shapes... birds? ... lizards? ... I forget, but you can see those on google images if you're interested.
Ray Kent
alright, no worries, thanks anyway!
Ray Kent m
Yes, I am subscribed to the other channels. I think we both agree that the format can be a little limiting. Form is liberating, but sometimes it feels a little artificial. If we agree on anything I think it is that. We just want different things and there's nothing wrong with that.
05:14 This is the floor of the Bayliss Building (renamed Molecular & Chemical Science Building) at University of Western Australia. Before seeing the video we spent ages training to find a line of symmetry somewhere.
Yes you do see it repeat. What he means is it doesn't repeat forever, just like the digits 314 do occur in pi after the beginning but it doesn't repeat forever.
Epic quote. This is what stood out most to me, as well.
"Science can't see what it doesn't have the language to describe."
wow the part at the end was pretty profound!
This was a really great episode.
Indeed. That's probably why they have proved so crucial in the development of so many fundamental sciences! :)
I tend to become mesmerized by tile patterns. This was really interesting!
Brady (the editor) saying with enlightment: "Aaaaah... ah!
The building featured at 5:20 - is it the Bayliss Building at the University of Western Australia, or a different one?
One of my favourite numberphile videos so far. You guys should do a video on infinity :)
In order to tile there is a min of 3 shapes at a junction. If they were regular polygons, the total angle size would be bigger than 360 degrees. 6 is the biggest because each angle is 120 degrees * 3 = 360.
@purplezart yes&no, that is why this is interesting. Because it is mathematically hard to describe what exactly the pattern is, but any human can look at it and see that there is. The shapes repeat, there are repetitions in sub-patterns of shapes, pick a penrose tiling and I can try to describe the pattern to it, but it won't be as simple as other classic patterns.
Ah Brady you do such a great job.
Just as a matter of observational curiosity...there appears to be a few striking similarities between Professor John Hunton's delivery and that of Professor Mike Merrifield (DeepSkyVideos). They have very much the same facial expressions (for example, emphasis of important facts with a raising of the eyebrows), conversational cadence, tone and gestures. :)
Who first discovered Penrose tiling in nature? It must have been the most thrilling moment of his life.
@EquitoErgoSum I've posted the periodicvideos film about quaiscrystals and Nobel Prize as a video response
Today I learned that Prof. John Hunton is really bad at drawing pentagons. XD
nah kusai nori mori
lol cairo tile
3:58 - Wow! These patterns remind me a lot of the game CirKis! Especially the ones with several colours!
That's because CirKis was explicitly based on Penrose tiling.
We just talked about this in geometry. Thanks for the pre-lesson so I sound smart compared to others :)
We can also see this in viruses with icosahedral capsids. The most obvious is the dodecahedron structure with pentagonal faces. I think it's likely that they are structured this way so that the capsid can form a closed unit since it can't tile.
We will!
6:05 wrong understanding, there was not a natural tendency towards this in crystallography. there is actually a natural aversion as three-fold, four-fold and six-fold symmetries are much simpler as stated. but recently there has been one natural quasicrystal found called icosahedrite
The artist M.C.Escher was doing experiments with these principles in the 3rd, 4th, 5th, and 6th decades of the 20th.century. The geometer Coxeter - even earlier, as also, in a rather different way - Richard Buckminster Fuller.
Penrose loved Escher and I think met up with him to discuss his work and think Escher made a drawing for him.
Great video. It seems like this knowledge will be of use to me.
@Ypthor Yes. Consider the outline of a house (square box with triangular roof)
5 is my lucky number!!! It's crazy that it is this special.
But if the pentagon field was all moving, how would it move naturally? Including the negative space created by the movements? what shapes could the negative space become? @2:30
Time to program parameters for computer for simulations xD
oooooohhhhh holy shewt, i didnt finish the vid. already did it. i wanna see it in a dynamic setting
@Romik2508 cool... why 5 I wonder?
@numberphile AH, I missed that. Thanks!
I've just discovered your channel. It's great.
loved this video :) don't forget you told me you were going to talk about the Graham number :)
@MrRuaridhDonaldson You can make a ball with just pentagons, just not a flat plane tiling. With just pentagons you can make a shape with 12 faces called a "dodecahedron". I think football designers just added hexagons to make it rounder.
i run into this whenever i try to draw a tortoise shell
their shell scutes are inexorably pentagonal, but they don't tesselate properly
I love all these videos, shame there wasn't some sort of explanation as to how some Penrose patterns are formed, I just like equations that explain things.
@mohdsfk In a soccer ball, the pentagons are connected, but among some hexagons. Besides, soccer balls have spherical surfaces and this video showed tiling of plane surfaces, it makes a lot of difference.
I want to see more Numberphiles that focus more on some number and less about going off on some tangent. At least they tie it back to the number so they can stick with the theme.
i.e. your opinion isn't any more valid, and they can do whatever they want.
For example, there are so many more things you can say about the number 5 than just tiling.
how do you make these patterns from 3:00 to 5:00?
Thank you! I enjoyed this video very much..... keep up the good work!
Amazing vid!! Thinking of painting it in my bedroom wall :))
If I ever have to retile a bathroom... it must be a Penrose pattern! this is awesome.
How about tiling with non-equal sided pentagons? Is there a pentagon with particular proportions of side lengths/angles that you can use to tile, without using any other shapes? Or maybe you can use a shape with the same angles but different size (I see it still wouldn't work with equal-sided pentagons but what about non-equal sided?)
Keep doing 2:21 over and over again and it sounds like a goat XD
I really like your work. Thank you!!!
Minor correction: The name of the Nobel laureate is Dan Shechtman. Very nice chap with whom I had the pleasure of sharing a meal some 10 years ago.
Wasn't there an example of aperiodic tiling similar to Penrose in some ancient architectural feature? Islamic?
+Michael Bauers Yeah, something about "Girih tiles"
But were the tiles in the Islamic example equilateral?
Thank you Brady! You're awesome!
Glad to help!
you can mix 8-sided with squares, it looks quite nice :)
Yes but this is more fun
you probably are!
Instructions to renovation company: Pentagon tiles, no gaps
Squares.... "non-repeating, tiled".
@@randywebb8284 It's possible to do a non-repeating square tiling.
Do the first row the standard way. Then, displace the row above that row a little bit. Then, displace the next row 2 times that bit. Rinse and repeat. If this bit is not a rational number (based on the tile square lenght), you have a non-repeating square tiling.
"Here are squares, the sort of squares we all put on our walls." No, my tiles are actually square.
4:00 - The tiling equivalent of the Rorschach test.
Can you still buy those colouring books with these types of patterns in? I used to love those as a child.
interesting! It's almost as if no matter how complicated something might seem, theres always a pattern somewhere within
brady stop disliking your videos
@DaithiDublin Professor Hunton did his kitchen... I'll ask how?