[HN Gopher] Flow Proof Helps Mathematicians Find Stability in Chaos
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Flow Proof Helps Mathematicians Find Stability in Chaos
Author : nsoonhui
Score : 33 points
Date : 2023-06-16 08:19 UTC (1 days ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| SubiculumCode wrote:
| "As with so much in mathematics, the proof started with coffee"
|
| When I knew that the article wouldn't get straight to it, and
| make me dig through for the point.
| kvark wrote:
| I wish we had a TL;DR easily. Those lengthy scientific/history
| articles are doing a good job at killing any excitement about
| the core ideas.
| dkqmduems wrote:
| Imagine there was a point to existence...
| jamann wrote:
| >> if, for instance, you don't care how fast the particle is
| moving but only which way it's facing at any moment in time --
| you could describe its motion using a three-dimensional state
| space.
|
| This is assuming we are on a curve across 2D space like the
| equator and face east or west. This sentence was puzzling me at
| first glance. In usual 3D space, direction/orientation is
| represented as a 3 dimensonal vector with length one, so on top
| of the position dimensions, that makes six dimensions, even if we
| dont care about magnitude of direction a.k.a. speed. Using angle
| coordinates changes the support domain, but still three
| dimensions are needed for direction.
| WoahNoun wrote:
| That's the point. A particle moving in 3D space can instead be
| considered as a curve on a 2D manifold (a surface) embedded in
| 3D space. So then you only need two dimensions for position and
| one for orientation.
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