Matt Parker: An Attempt to Visualise Minimal Surfaces and Maximum Dimensions
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- čas přidán 2. 06. 2024
- Abstract:
Much of Karen Uhlenbeck's ground-breaking work involved abstract mathematical concepts which are beyond our normal human intuition. And even though there may be practical applications of the results of her work, that does not make minimal surfaces in higher dimensions any less esoteric. Matt Parker will attempt to provide visual demonstrations of both minimal surfaces and higher dimensions (although, probably not at the same time) to allow a small glimpse into the scope of Uhlenbeck's work and achievements.
If you liked this video, you can see more of Matt Parker on his own CZcams channel @standupmaths
This lecture was one of four Abel Lectures held as part of the Abel Prize Week in Oslo.
The University of Oslo, May 22, 2019
Program for the Abel Lecture 2019
1. "Some Thoughts on the Calculus of Variations" by Abel Laureate Karen K. Uhlenbeck, University of Texas at Austin, USA
2. "Solitons in Geometry" by professor Chuu-LianTerng, UC Irvine
3. "Limits, Bubbles, and Singularities: An introduction to the fundamental ideas of Karen Uhlenbeck" by professor Robert Bryant, Duke University
4. "An Attempt to Visualise Minimal Surfaces and Maximum Dimensions" by Matt Parker, @standupmaths - Věda a technologie
"I haven't done it. But it should be reasonably easy.." Parker's Last Theorum.
Or do like fermat:
"x^n + y^n = z^n. The proof is a little complicated, I will leave it as an exercise for the reader."
I have discovered a truly marvellous proof of this, in which this Q&A session is too short to contain. -- Matt Parker
I guess the algorithm just decided to no longer ignore the video
The hat with a handle can NO LONGER be ignored
My obsession with Matt Parker finally convinced the CZcams algorithm to show this to me. If that's what it takes.
I was surprised by the lack of views on this video (under 5k at the time of viewing), even though it's classic Matt shenanigans. Could as well be found on his own channel.
i honestly thought i'd seen all of the parker videos but apparently not!
@@IntendedPun 13k right now. I've been following Matt for quite some time now, but this is new for me.
@20:00 using a solution to find the solution
Same.
"He was so proud, he named himself after the loop"
I can't not give a thumbs up for jokes like that.
That has to be one of the top jokes I've heard in a while.
"Now you stand there awkwardly"
"wow.. you actually did that"
"wow.. you've done that literally"
Matt gained the respect from the remaining 20% at 21:37
Such a humble talk. The way he kinda downplays his role in math is sad, but I feel he has the most important role in mathematics: getting younger people excited about mathematics, ushering in the next generation of mathematicians
I love Matt Parker to death, but he isn't a proper mathematician. He is a clever math hobbyist, a hilarious and effective educator, but not a proper mathematician. And that's why he downplays it. He knows it, and knows that proper mathematicians would see right through him, and would call him out on it, if he pretended to be, so he prefers to set realistic expectations.
@@LeoStaley
Hi Leo,
Only a small percentage of the population are clever enough to be professional mathematicians (and I'm not one of them and suspect Matt isn't either), but that doesn't preclude their having an interest in maths any more than enjoying playing snooker means you have to be able to do it to Steve Davis, Stephen Hendry or Ronnie O'Sullivan standard.
at 11.00 i understand what the meaning of 20 percent
As he presented the square to muted audience reactions I immediately thought "Damn, you're not going to be able to do your dead inside joke when you show them the hearts now". He managed to get it in in the end though.
@@Treviscoe In short, it's ok to be bad at things as long as you enjoy doing them anyway
Thank you! The CZcams Algorithm for presenting me this 1 year and 4 months since the talk happened :D
I am a subscriber of StandupMaths and Numberphile. This video just appeared on my feed 20 min ago.
@@SaveSoilSaveSoil .
@@SaveSoilSaveSoil Same here.
This man is an absolutely brilliant communicator.
He’s funny, he has insight, he knows what matters, and he can put it all together into a coherent and fluid presentation.
That it what I want to learn from him. How to be this good at presenting on a topic.
I tend to use opacity to represent the fourth dimension when i try to manipulate 4D objects in my mind. I just keep in mind that if two pieces have different opacities then they don't touch. I like to define 0 in the opacity dimension as 50% opacity so i have room to go in both directions
Then for rotations it helps to realize what a rotation is. So for 2D you pick a point (a 0 dimensional shape) and everything keeps the same shape and every other point stays the same distance from that point. In 3D you take an infinite line (a 1D shape) and everything keeps the same shape and distance from the line. So in 4D you take a plane (a 2D shape) and do the same thing. I recommend limiting what planes you can use just to keep things simple. So the 3D equivalent is just rotating around the point at (0,0). In 3D it's the lines corresponding to (X, 0, 0), (0, Y, 0), and (0, 0, Z). In 4D each plane is defined by two coordinates. If one of those coordinates is opacity then it just looks like one of the lines you use in 3D and the rotations look the same, that accounts for 3 of the planes ([o, x, 0, 0], [o, 0, y, 0], and [o, 0, 0, z]). The other three are the planes where you've picked 2 of the normal 3 dimensions (x, y, or z). You've got four dimensions and you're picking 2 of them, that's why there are 6 rotations in 4D, it's 4 choose 2 (look up the choose function to learn more or to easily calculate it for higher dimensions).
To rotate around the latter 3 options the points either stay in the same spot (if they're already touching the plane, like how the earth's pole's don't move when the earth rotates), they move farther away in 3D while their opacity matches the plane more or move closer to the plane while their opacity starts to match it less. Things on one side of the plane should become more opaque if they move closer and things on the other side should become more transparent as they move closer, that way opposite sides of the object maintain the same 4D distance apart even if they are in the same spot in the 3 normal dimensions
I recommend starting by rotating 3D objects in 4D. Like try a 3D sphere that starts centered on (0, 0, 0, 0). All possible to be done just in your mind
mind = blown 🤯
Matt would like you to think the soapy mixture found the minimal surface with a small cube bubble in the large one. I think he was using a square straw.
From 39:00 in, the number of possible rotations in d dimensional Euclidean space over the reals *R* where d > 1: (d choose (d - 2)) = (d choose 2) = d(d - 1)/2. In other words the triangular numbers 1, 3, 6, 10, 15 and so on. So Matt was right when he said 10 for d = 5.
Holllllly shiiiit. The upmost respect for dealing with a heckler live on stage at the very beginning - that was awesome
I was just going to relax for a few minutes and Matt’s videos are always great fun. 50 minutes later I experience the true relativity of time. Matt is so cool. And what a wonderful way to round off the Abel Lecture.
“A lot of the time mathematicians have the solution of not caring. A lot of problems in math are fixed by, ‘Have you tried not worrying about it?’”
I have never related to a statement so strongly.
came to the comments for this quote
I love that he starts his Abel lecture with Numberphile's video on a non-standard summation method. Very fitting.
For the 3D/4D cube, try reading a short story by Robert Heinlein. The story is called "And He Built A Crooked House". Essentially, he built a house which was an unfolded tesseract, i.e. it was four cubes stacked vertically, with extra cubes glued on each of the four sides on the first floor. This is EXACTLY like the picture at 35:45 or thereabouts.
In the story, he built the house in California, and California has earthquakes, so... one of these earthquakes caused the house to fold itself into a real tesseract. Mayhem ensued.
I mean, gotta love the talks by Matt. It‘s always a pleasure to see a subject, which I understood half-way so far and having it explained with that amount of humorous elements.
A few years on now but I love seeing all these maths profs loving Matt’s show 😁
Always need more Matt Parker
okay with the bit about rotating a cube then a hypercube, i squinted a bit and i suddenly was *seeing* rotation rather than self intersection.
my brain is in the process of evaporating as we speak
This video deserves more views and likes. I am going to do the 2 Möbius strips to interlocked hearts with my daughter and her friend that is coming to stay over tonight. I also loved the cube bubble inside the cube.
Thanks!
Watched it with my six year old, she loved the bubbles (obviously the bubble isn't going to be a cube with a square bubble blower!) then was delighted by the actual cube bubble payoff later on.
@MattParker, some extension to 1-twist Möbius strip cutting:
* Cut strip in half as you did. Then cut it *again* in half.
* Cut strip in 1/3 of its width, not 1/2.
As much as I love the content of this video, what I really need to know is what bubble mixture did Matt use?
Nice.. @35:30 "actually that's 2d, now lets show you the 3d.." changes angle of 2d projection to a classic three point perspective.. this is 3d.. hahaha. And nobody stands up and leaves the room. That's the genius of Matt Parker..
I cannot believe I missed this one.. I know exactly what hes going to talk and show but is so nice to hear it again XD
Forget Möbius, _this_ guy is so vain, he named square after himself. Well, _a_ square.
Well, he actually said that he wouldn't name it the Parker Square, and then Brady Haran was like "let's use that name for this video" and started selling T-shirts of it etc, so it was actually Brady who made that name a thing. =P
adding a small amount of glycerin to your soapy water will help with the bubbles, makes them stronger
6:50 sadly this is not the recycling logo. I don't know why, but one of the 3 arrows flips the other way which makes the recycling logo a vanilla mobius strip.
If you google "recycling logo" you see some that do 2 one way and 1 the other, but also some that do all 3 the same direction. And the wiki page for "recycling" has a logo with the flips the same way.
@@SirRebrl If you check the wikipedia page for "recycling symbol" you'll find the 2/1 variant featured with a short history about the twists. The original version was 2/1, but there seems to be a modern trend to have them all be the same way. I'm not sure if that's an intentional change people are making or if they are just trying to replicate the original and don't notice that one is different and made a mistake. It's funny that the two wikipedia pages on the topic "disagree."
Emoji implementations are a toss up as well, but favoring the 3 twists. Check emojipedia for a full view of the versions.
That four towns problem just used hexagons. Since hexagons come from circles it makes me think the problem could be solved with circles.
Minimal surface of cube doesn't work out as obviously cleanly though. It's did make me want to see the minimal three dimensional surface of a tesseract though.
I love when CZcams algorithm .. recommend something useful...
I tried the two conjoined Moebius strips with the same handedness, and I got two loops: one sorta boring one that looked like a boat hull, but one more interesting one that looked like two half-heart shapes with a full twist in them.
I took Calculus from Tony Tromba at UC Santa Cruz (1981 ... AD). His research is on minimal surfaces, soap bubbles, etc.
I love Matt Parker, he's awesome
the optimal ratio of the side of the small inner square to the edge of the outer cube is roughly 0.0729:1
Godddd dayyyum, you did it. I am impressed. [DiowE]
For some reason my brain combined Trey Parker and Matt Stone and I genuinely thought one of the South Park guys was about to give this lecture...
I am the kind of person to point out “hey that is a three twist möbius loop” to my friends and family. Thank you for telling me this.
So many amazing jokes just ignored because “I’m far to academically brilliant” to laugh at that.
Well, it took you a while, algorithm.
개념을 단순히 문자로 이해하고 있는 것과 입체적인 감각을 가지고 있는 것은 천지차이라고 생각합니다. 최소면적과 최대 차원에 대해서 시각적으로 표현해주신 이 영상을 통해서 제 머릿속의 개념을 입체화 할 수 있었던 것 같습니다.
okay, what happens if you dip a mobius loop into bubble mixture?
Warp bubbles.
6 comments and 163 likes? What? This was quite entertaining and insightful... What happened?
Too highbrow for the average CZcams user.
@@user-ge8yn4ql4i Or at least, that is what the algorithm thinks the advertisers think.
The CZcams algorithm didn't show this to most people until recently...
@@user-ge8yn4ql4i more likely just has to do with the fact this isn't on Matt's actual channel.
Wonderful talk - deserved a better audience.
Cool, this video has inspired me to come to the conclusion that as dimensions increase anything and everything becomes reality.
Time is either much higher or a much lower dimension...
Really great. Fun
Oh my god! He had a tough crowd. Nobody laughed at: "...torus and doughnut, torus is the outside surface, doughnut is the solid object...and is more delicious". Unbelievable.
The optimal ratio of square length to cube length, if I did this right, is (3+sqrt(985+64sqrt(241)))/6, or approximately 8.
hahaha - you're brilliant and hilarious Matt! Thank you very much.
11:23 "Instead of getting two [connected] hearts, you end up with disappointment." Oh, so THAT'S what I've been doing wrong. ;-)
If real math classes were as well taught as this one, I could be a mathematician.
True fact.
"You're all dead inside!" Well, it is a math video.
You do _NOT_ get "-1/12" if you sum all integers to infinity.
The correct answer to that kind of series is that it _diverges_ - it approaches infinity.
I am assuming that the "-1/12" thing must haver something to do with Ramanujan Series - it is certainly not an _ordinary_ series.
Any one have noticed the semilarity between the cube surfaces and the teserract?
43:44 "You can't just shove this through this! There's gonna be a hole there!"
I didn't even click this video, CZcams played it for me 👍
Truth in all is literally an oxymoron, thank you for that, almost as much as the quote in it's use "Whatever you're imagining, it's bigger."
I can barely into the presentation not help but drift away in my childs mind wondering about all life's possibilities in math.
Even my digital typewriter is showing me my words are wrong, yet they are exactly what | want them to be.
zero dislikes.
gold
Your surface tension was too low in the 4D bubble box demo. Your bubble mix probably had too much soap or not enough water. The soap to water ratio in other words. Any instability in the system will show as a square. Higher surface tension would give the singularity more stability.
A parker square, as it were
A Parker mix of soap and water :D
The best part of this is him laughing at his own jokes
I thought the audience was asleep until 21:28
Thanks for this and the guy should do standup just for fun :x
You may be joking (in which case r/whoosh right over me) but he does.
Look up standupmaths
@@LegendaryFartMaster thanx! Will check it out. He s good!
Matt Stone and Trey Parker created the ultimate character Matt Parker.
he skimped on the bubble bath :D
huge South Park fan and I never knew those guys were so smart, just goes to show you can write comedy AND be a genius too
I thought that too at first
There's also the Simpsons writers doing the same thing whenever they need an equation for a chalkboard. Most comedians are extremely smart, you often have to be a level above something to know how to twist it enough to make it funny.
31:41
Can’t believe this is the guy who made South Park wow 😮
wow that's a difficult audience
I’m straight up about ya use that heart trick to pick up girls in college (I go to a tech school)
I had to search for this myself.. :(
Parker cube? 👀
10:30
Is he the love child of the Southpark guys?
Recycling Logo 😆
Except it isn't. That logo has one net twist (the other two are in opposite directions and cancel). Typical Parker error.
silly me, i thought this was the love child of trey parker and matt stone... good day.
Oh, it's a long video, I will stop watching the moment I got bored. 50 minutes later....
the Mobius loop or whatever is just like those weird colorful things at the playground with holes that you climb on lol
Sorry as an architect interested in geometry I so not see the Klein bottle or the Mobius strip as real 3d objects. The look real but theoretically are not real 3d objects as described. Call me old fashioned. They have no actual depth. I see them as pseudo objects, attempting to describe an ideal, not real things. Am I wrong?
0:32 What's a blog post grandpa?
Tough crowd...
I may have dyslexia. I read the title as “Meat Packer”
Doctor: "Don't worry, you are a perfectly healthy idiot"
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Σαιδ ρποιητ ις ΣΔαιδ το β Α
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20:30 that's a Hexagon, a Bestagon!!! @CGPGrey
2021-7-10
.
15:57, where I actually clapped physically and left the video🙄
The able clover preliminarily bow because ravioli relatedly pinch unlike a lavish swimming. past, silent june
What? I need to stop looking for meaning in the comments section.
@@onering20 Didn't something like this happen on DS9?
The panoramic dredger sporadically bury because kendo spectacularly carry between a grandiose ash. feeble feigned, weary screw
The video was really helpful and AWESOME, BUT..... as Thor says; YOU TALK TOO MUCH!!
_"He was so proud he named himself after the loop."_
Seems like he slipped there with the pronouns. In late 2019 he was still an apprentice in calling everybody "they", and the correct pronouns were still slipping here and there. Nowadays he has trained himself a lot better in being obnoxious about it.
You english speaker cry for little. You would only have to change a couple of pronouns. I speak portuguese and, like in other languagues, some words (most) have gender declination. Eg. "boy and girl" is the same word with gender declination: "garoto e garota". They want to introduce a third neutral declination for every word that have a binary one.
On the other hand, it would be such a pain that will be even less likely to happen.
Half of these comments are recent lol