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2d
comment Distributing points evenly on a sphere
What's most surprising to me is that there is a link between a global property extrinsic to the surface (energy) and a local, intrinsic property (curvature).
2d
awarded  Pundit
2d
comment Distributing points evenly on a sphere
There is a problem similar to the Thompson problem, which is to find the minimum potential energy of a continuous charge distribution on a nonspherical conductor. There is a surprising set of exact solutions for some special shapes, in which the charge density is proportional to the fourth root of the absolute value of the Gaussian curvature. I W McAllister 1990 J. Phys. D: Appl. Phys. 23 359 doi:10.1088/0022-3727/23/3/016
Jul
26
awarded  Civic Duty
Jul
12
awarded  Notable Question
Jul
1
comment Ordinals separate from set theory
Conway's surreal numbers include the ordinals. They can be developed separately from set theory, and that's what Conway did in "On Numbers and Games." Some discussion here: personal.psu.edu/t20/fom/postings/9905/msg00074.html
Jun
22
comment Flat Riemannian manifold
This doesn't seem like a research-level question. It might have been more appropriate for math.SE.
Jun
22
comment Finding Riemannian metric for this geodesic
I don't understand the motivation for the question. Since no coordinate system has been specified, isn't it vacuous? For example, I could just associate the $tb^i$ with the Cartesian coordinates in a flat space, and take the given equation to be a change of coordinates. And what is the motivation for the constraint on the sum of the $\gamma$'s? This would simply seem to restrict our attention to a $(d-1)$-dimensional submanifold.
Jun
21
comment What notions are used but not clearly defined in modern mathematics?
This seems to me to be a poor answer, for the same reasons I gave in a comment on the answer by Buschi Sergio.
Jun
21
comment What notions are used but not clearly defined in modern mathematics?
This is very unclearly written and doesn't make much sense to me. For example, "Concept and existence of points, and spaces as sets of points." This sounds like a description of an axiomatic style of mathematics, in which we have certain primitive notions that we make no attempt to define explicitly. This is part of the normal process of mathematics and does not indicate that something is "not clearly defined" in the nontrivial sense of the OP's question, as I understand it.
May
19
comment Kinematics of rolling knots
The relevant material seems to be at the end of the talk, around 9:00? One thing to think about would be whether you want to ask these questions about knots with ideal shapes, or knots that are arbitrary fattened embeddings of the topological knot in 3-space. Ideal shapes are poorly characterized: arxiv.org/abs/1402.5760 . It's not obvious to me whether the dynamics are Hamiltonian. See, e.g., en.wikipedia.org/wiki/Chaplygin_sleigh .
May
19
comment Kinematics of rolling knots
possibly related: mathoverflow.net/questions/180194/…
May
19
comment Flat Riemannian manifold
An example that the OP might wish to think about would be a cylinder with a flat metric. That might help to clarify why the answer is framed in local terms.
May
18
awarded  Necromancer
May
18
comment Diffusion on a semi-Riemannian manifold?
if we lived in a space which was only semi-Riemannian Huh? We do live in such a space. There is no a priori guarantee that such a space is time-orientable, has Cauchy surfaces, or lacks closed, timelike curves. You may be interested in notions from general relativity such as global hyperbolicity. See, e.g., Hawking and Ellis, The Large Scale Structure of Space-Time, p. 206.
May
14
comment How to learn QFT from mathematical perspective?
We have a body of math that was created for the sole purpose of understanding topic X, and which is still practiced for almost the sole reason of applying it to X. It seems odd to me to be so insistent on refusing to learn about the application to X. This is not an example like group theory, where the original motivation was much more specific (permutation groups) but now constitutes only an insignificant portion of the whole landscape. If you learn an entire field of math without understanding a single application, I would question whether you understand the field.
May
12
comment Physics that needs “new” math
Physicist to string theorist: You've had this research program going on for 35 years, and it's not yet looking like a healthy physical theory. Why should anyone keep giving you funding? Standard answer from a string theorist: String theory is a piece of 21st-century mathematics that's fallen out of the sky into the 20th century, and it's going to require 22nd-century mathematics to solve it. Even if it's never going to be a correct Theory of Everything, keep funding us, because it's wonderful mathematics.
Feb
12
awarded  Yearling
Feb
12
revised space at the Planck scale
added 4 characters in body
Feb
12
answered space at the Planck scale