Topology, Geometry and Life in Three Dimensions - with Caroline Series
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- čas přidán 10. 02. 2015
- If you imagine a three dimensional maze from which there is no escape, how can you map it? Is there a way to describe what all possible mazes look like, and how do mathematicians set about investigating them?
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Caroline Series describes how hyperbolic geometry is playing a crucial role in answering such questions, illustrating her talk with pictures that have inspired some striking examples of digital art.
Caroline Series is Professor of Mathematics at the Warwick Mathematics Institute, University of Warwick
Her academic interests are in hyperbolic geometry, Kleinian groups and dynamical systems. Her research has been on the theory of dynamical systems and geometric patterns in three-dimensional hyperbolic spaces.
Her work has been recognised through awards and prizes, most recently with the Senior Anne Bennett Prize from the London Mathematical Society. She is also a founding member of the European Women in Mathematics (EWM), which aims to support and encourage female mathematicians across Europe.
This was filmed at a Friday Evening Discourse at the Royal Institution on 28 November 2014.
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Brilliant lecture! 👌 For those who're interested, this woman is also one of the co-authors of the great book, Indra's Pearls.
I checked it out on Amazon. Have you read it? What do you think?
Thank You gotta get my hands 🙌🏽 on that!!
@@SaveSoilSaveSoil2222222
I have a baccalaureate in Mathematics in 1965. I am very excited by the great progress that we see in Mathematics
This puts me back to school. My 9/10th grade math teacher was kind of like her. I barely got a passing grade.
She just made me go back to chrochet kniting, I´m looking at it from a very diferent angle now XD
One of the rather satisfying uses of 3-D printers these days, is to be able to print off 3-D structures like these. Nice.
Excellent lecture
Do viruses have hyperbolic structure?
47:47 Poincare Conjecture :
The diagrams show a sphere with a rubber band circling around it in a circle. You could slip the rubber band off the spherical surface till it reduced to a minimum ie circle reducing to a point.
Compare this to a torus/doughnut shape.
A rubber band around the external rim could be slipped off BUT a rubber band looping over the doughnuts internal and external rim CANNOT be slipped to a point. It can only rotate around the doughnut.
The point being that a fly living on a doughnut could prove that it was citizen of a doughnut and not a sphere with this test.
Which was the immediate thought coming to mind concerning a hyperbolic surface: sides of length 1, would create a different structure than sides of length 2, which means a probability of length 1 being a distance or space so minimal we would define it as a Planck h. such a minimal distance would be infinitesimal in the first two geometries, but might be any defined length on a specific torus, related to some other dimension .
This is difficult to explain in words, but expresses a fundamental difference from the other two geometries.
What constitutes zero dimensions in hyperbolic geometry?
Alas! I'm merely taking a momentary break from contemplating normality, and the extremely bounded descriptions of it common to most, which do not even extend to the reality we experience. Most human individuals create a very limited heuristic set, outside of which they ascribe both events and behaviors to phantasmagorical delusionary constructs.
She’s really good 👍 Soo glad I found her!!
poincare taught the french to some extent what a circle is:
“qu’est ce, un cercle?” , the french yoof asked, after many expositions on poincarre’s circles..
and the answer they got from erudite french wisemen was :”Ce n’est point carré!”
😂😂
Bien dit !
Its funny that people like to learn. But not from everyone only from those that "have funny presentations". You need to go past the presentation skills. Remember there is someone really smart telling you something. If you find it boring then you are not really seeing the potential of the information that you are receiving or not understanding the subject. With topology specially I fit on the 1st. I think topology subjects are really weird and is a relative new area in mathematics so there is not much application to compare or to introduce the subject. It sucks I know, but nonetheless its what we have for now in this area.
Ricci flow can be used for data analysis (community detection in social networks)
Thank You madam.
just when you think she'll explain something, she says, "I won't explain it."
I was using works by Caroline in my own many times because her writings are always clear, clever and of lasting significance.
Thank you
i'm not british, could someone tell me what a cro-chay is?
+Madhur Agrawal Crochet is sort of like a variation of knitting using a single hooked needle.
Travis B thank you!
"Point (Carry)" in the subtitles translation in a strange english is, of course, "Poincarré, Henri, mathématicien et physicien quantique français" (see Wikipedia). I understood her english without a problem so why make a problématic translation by a non scientist?
The subtitles are machine generated (hence the weird mistakes) and are for the benefit of hearing impaired viewers.
What does this mean "space looks the same in all direction?"
the air molecules are all little balls ;)
i agree it’s confusing: you’d have to put some stuff in watever space, to make any judgments at all..
It’s like a cylinder, which is infinite in one direction and loops around in the other direction. If you look in one direction you see the whole length of the cylinder, and if you look in the other, you see only the short and finite width of the cylinder.
Not sure who the audience this is for. I thought this was a layman's lecture but she pulls out all these terminology without explaining it. As a science major I know what matrices are as well as non-euclidean geometry, and even to an extent what a lorentz transformation is but there are other terms I wish she had explained more in depth. It is odd to me that she started with what a torus is and 30 minutes in she's talking about all these other stuff without elaboration.
etatauri welcome to Topology. A beginner to the class is expected to know these terms. This video isn't for the majority of people. But yeah. Very fun course and very fun for those mathematically inclined. You should check it out.
"Moscow theorem" might be Mosta theorem...
Wish the graphics and animations were displayed better. A picture is worth a thousand words but an animation is worth a thousand pictures. Both Literally and effect wise.
The speaker looks like a Vulcan.
Looks like a drinker. *burp*
i am redonkeylusly confuzzled right now
Jesuschrist you leave a nanosecond for each slide. Leave at least 15 seconds for each.
CZcams "... and for our slower students, we have the pause button".
π = 3D
It is worth remembering that lines and surfaces are intellectual constructs, not things in the world of our lives' experience.
Nothing is flat in reality. A thing that has no extension isn't there. Nor anywhere else except in our minds. Some of the time. And "three" "dimensions," the bulk world we live in, has an infinite number of directions notionally and a very great number in fact. The two directions front and back are no more important than off at an angle to the left. Down may very well be toward the centre of the Earth, but if so this would mean up is different for everybody.
The excellent E.O. Wilson, in his very good book "Consilience" suggests that any advance from the Standard Model is going to come from epistemological, not experimental, change. It seems to me that clearing up the very sloppy misuses of the word "dimension" is a prerequisite for this project.
I'm really enjoying this lecture, but it is rather difficult to get past the exceptionally poor presentation. Sadly, while the content IS fascinating, in this medium presentation and communication accessible to a wide public audience is far more important as not everyone who enjoys what the RI offer will have the background to feel comfortable with this content. It's more likely to turn some of these people away from this type of material.
silentgamingRO If you have not studied pure mathematics, this video probably isn't the best place to start.
Great talk. BTW she reminds me of a female version of Roger Penrose.
Love & Division I also enjoyed the talk but she doesn’t remind me of Penrose. He is like an other dimensional being!
You can put your boots in the oven but that won't make them biscuits.
Uuuuuummmmmmmmmmmm.....
"If you imagine a three dimensional maze from which there is no escape, how can you map it?" Look at my work.
The tone of her voice and the resonance of the hall makes for a very difficult to understand talk. :-(
I know some of this stuff and can't comprehend anything she's talking about.
I don't get why people don't understand this stuff. She's not saying anything all that complicated, just putting shapes together.
What a bunch of hyperbolic hyperbole!!
***** ER... rather what I *meant* to say - or rather what I *would* have written had I the ability to go back and edit what i wrote in the first place - would have been 'seems like a bunch of hyperbolic hyperboLE to ME!!' Get it? heheharharhohohahaha!
Interesting subject but terrible use of Keynote (Power Point like presentation software). Text was too small and crowded in the corner, too many things on each slide, wrote like it was a textbook rather than showing the point to be made and used laser pointer rather than highlighting and graphic techniques. She talks to the slides rather than the audience and doesn't realize that she can have speaker's notes to guide her.
I have always loved mathematics and geometry but this talk will make almost everyone hate these wonderful subjects. She really needs to develop the skills of public presentation before she ever speaks again. I pity any student she has ever 'taught'.
The term Powerpointlessness seems apt
It's sad that so many academics inflict substandard presentation skills on an otherwise interested audience
I dont feel I'm going out on a limb here, but I would argue that a person's listening and reasoning skills should be more of a priority than their performing and speaking abilities. This is especially true in today's society. There are a plethora of information to sift through in many forms of media. Everyone has a completely different background and perspective of any given subject. Instead of worrying about which word is emphasized, keeping eye contact, and other public speaking skills, they should instead focus on the subject.
Yeah, I'm out after 7 minutes. And I'm that person who watched hours of Stanford's recorded biology lessons!! I'm walking away knowing next to nothing from those seven minutes... I've had those kinds of teachers in the past... every. minute. a. torture... I'm sorry, but this how you teach robots, not how you share knowledge with humans. 🙇
maybe you shouldn't have spent so much time on the biology then
(but in all seriousness, I couldn't stop thinking about how bizarrely she was targeting the lecture the whole way thru. I think there's enough stuff here that if you have even a small background it could really pique your interests but the intent of the talk is to get you curious, not learned. I think it would only be relevant to a very specific group of people who are at a particular stage in their learning of topology.)
I survived 14 minutes. Probably first lecture I haven't watched till end on this channel, maybe second.
It would be a bit easier to follow if she stopped walking backwards and forwards all the time!
It's like stereographic projection. Nothing more than that.
Useless