Poincare Conjecture and the weird world of topology | Jordan Ellenberg and Lex Fridman
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- Опубліковано 12 чер 2024
- Lex Fridman Podcast full episode: • Jordan Ellenberg: Math...
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Jordan Ellenberg is a mathematician and author of Shape and How Not to Be Wrong.
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I love watching these
I had an D- in Maths
This doesnt try and force a bunch of unwanted assignment.
Its learning at your own pace, your own place...their dialogue is also exciting where as a teacher can get dull in speech.
Dear Alex, will you interview Prof Velani, from France about this subject???
14:08 what is the relation between Real Projective Plane (RP3) and Special Unitary Group SU(2). As you mentioned belt trick works for both
SU(2) is homeomorphic to 3-sphere, any closed path on it is obviously able to shrink to a point: If you cut a hole on a 3-sphere that is not on the path(so it won't affect the path), it is homeomorphic to 3d real plane(R^3), and path on the plane can always shrink to a point. since the whole process on the plane does not interact with the point we cut off(which is at the boundary of the 3d plane), such process is applicable on 3-sphere.
RP^3 just identifies the opposite point on the 3-sphere, which is homeomorphic to a solid 2d ball with opposite points on its boundary identified. You can try to use the belt trick, and it will work out that a path that connects 2 opposite points on the boundary(because we identified them, so the path is closed) cannot actually be deformed into a point(you got to keep it close). But a path moving along that path twice would able to shrink to a point.
And such idea is called fundamental group(π1) of the space. In the above example, π1(3-sphere) is {0} trivial group, π1(RP^3) is Z2 group(2 elements cyclic group). Poincare conjecture claims that any 3d closed manifold(can be thought of as closed smooth 3d surface) that its π1 is the trivial group(any closed path is able to shrink into a point) is homeomorphic to 3-sphere.
15:15 sounds like the game hyperbolica
Yes
We could be living on a 3d klein bottle, like a 2d mobious strip, the line segment people are ignorant to the higher dimension
If the circumference of the Earth was slightly smaller, yet still the same Mass, and the Earth was completely flat without atmospheric dispersion, then light would bend around the earth, from the effects of curved spacetime due to earth's mass, such that you would always see the back of your head.
Define slightly smaller.
Gravity restricts its own unique space. Einstein GR surfed the idea.
The torus is the shape of the fields which hold each system energetically together. Lots of tines this creates spheres and spirals.
The field may look like a toroid, but lets say an object rotating another object, and the main object is a black hole.
A spiral will be made. Same if it orbits and increases the distance between.
The toroid is a dynamo. Magnetism, electricity and the modalities are said to all be contained here. Depending on each modalities strength, the objects will behave differently.
So what you're essentially saying is that all dynamics contained within field equations in physics can be described using the Algebraic Topology of a torus?
The Tao begot one. One begot two. Two begot three. And three begot the ten thousand things
If one begot two, then why did the two only beget three and not four?
@@adamwoodie4029 To be sure, 4 came shortly after 3 and so on subsequently.
Although, It may have multiplied Itself each iteration so integers may have been a package deal functionally speaking.
@@deadlevelled2870 word. Would you agree, though, that this whole concept is ultimately built on the foundation of a presupposition that can't be proved without coming to a point of circularity?
Cock begot balls
His speech is so infected with junk words "sort of" and so on, it is difficult to understand what he's saying. When he says "sort of" does he mean actually? When he says "like" does he mean actually? Which words am I supposed to disregard? Primary junk words infecting far too much speech -- "Sort of, "like" and "you know" along with "I mean," "so," and "right"
It's because what he is saying is not 100% precise, you need to be a bit imprecise to explain abstract mathematical concepts to a general audience in an intuitive way. So when he says "sort of", it's him telling you that what he is saying is the rough idea without the rigor. I can assure you it would sound far worse if he used the actual technical jargon.
If it offends you feel free to learn the actual math instead of watching UA-cam clips
@@mkfort You've missed the point completely. it has nothing to do with that. Why do automatically assume that? Anyway, never mind.
@@stephena.sheehan9959 he literally discusses in the podcast the difficulty of talking about math versus talking math directly. He's trying to use as precise language as he can without deceiving. I'm a native English speaker and I think he's well spoken and enjoyable to hear, I'm sorry you disagree.
Sounds like a you problem