[HN Gopher] 'Monumental' Math Proof Solves Triple Bubble Problem...
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'Monumental' Math Proof Solves Triple Bubble Problem and More
 
Author : nsoonhui
Score  : 46 points
Date   : 2022-10-08 07:56 UTC (1 days ago)
 
web link (www.quantamagazine.org)
w3m dump (www.quantamagazine.org)
 
| keepquestioning wrote:
 
  | sidlls wrote:
  | Tons of physics problems are problems related to minimizing
  | some quantity or set of quantities given other constraints. A
  | solution for something like this could very well provide
  | insight into whole classes of unsolved physics problems, and
  | thus to practical applications.
 
  | eggsmediumrare wrote:
  | Better this than quantitative finance or ads.
 
    | black_puppydog wrote:
    | Aiming for a "chaotic neutral" would frankly be an
    | improvement for many people in the industry. Not even
    | joking...
 
| graycat wrote:
| Yes, I saw that article.
| 
| But I was surprised it didn't mention Plateau's problem, that is,
| with the minimization in soap bubbles, as at
| 
| https://encyclopediaofmath.org/wiki/Plateau_problem
| 
| or F. Almgren as in
| 
| Frederick J. Almgren, _Plateau 's Problem: An Invitation to
| Varifold Geometry_, W. A. Benjamin, 1966.
 
| MauranKilom wrote:
| The article does not point it out (and I can't find good search
| terms for a source), but "real life" bubble clusters are not
| guaranteed to be optimal. There is definitely energy minimization
| going on, but it can easily get stuck in local minima.
 
| fuzzythinker wrote:
| Anyone know real world usage other than animation/games?
| Tangentially, what drives the authors into solving them?
 
  | sidlls wrote:
  | Curiosity; a desire to know the answer is usually enough for
  | me, for the problems I enjoy working on anyway.
 
  | graycat wrote:
  | Motivation? Minimization is a large and old problem. In
  | physics, some problems can be solved by noting that energy,
  | momentum are conserved and maybe also minimized or _action_ is
  | minimized.
  | 
  | In operations research, minimization is a central theme --
  | linear programming, Kuhn-Tucker conditions in nonlinear
  | programming, dynamic programming, integer linear programming
  | (early source of NP completness theory), etc.
  | 
  | But more generally, it is nagging that something as simple as a
  | soap bubble a child with some wire can create is so difficult
  | to analyze with math. So, a guess would be that math needs some
  | new techniques.
  | 
  | However, none of that would motivate me to get involved with
  | soap bubbles. I heard Almgren lecture, and then and to now I
  | still am not interested in investing time in soap bubbles.
  | Instead, I want a more visible and greater need.
 
  | aaaaaaaaaaab wrote:
  | Predicting the minimum-energy configuration of any physical
  | system that can be modeled with a cluster of bubbles.
 
  | bdamm wrote:
  | Wouldn't one good usage be enough?
 
    | dvh wrote:
    | Wouldn't the existence of the puzzle be enough?
 
      | tux3 wrote:
      | If we wanted to argue against, we can appeal to priorities.
      | 
      | Despite the popular adage, human ingenuity is limited. We
      | can distribute more hard puzzles than puzzle solver can
      | solve.
      | 
      | All else equal, if more puzzles exist than we can solve, we
      | should solve puzzles that help advance our goals.
      | 
      | If we can show more important problems exist, it could be
      | possible to make a good faith attempt at trying to see from
      | the point of view of someone who thinks some puzzles should
      | be ordered after other puzzles.
      | 
      | In that frame, the mere existence of all puzzles might be
      | enough to justify many problems (even some "suboptimal"
      | problems lower down the list), but there would also exist
      | problems so uninteresting that their mere existence is not
      | enough.
      | 
      | (All that being said, I'm not entirely sure why I bothered
      | typing all of that in response to a rethorical question...
      | but I suppose you could see arguing as a puzzle, and isn't
      | the existence of _that_ puzzle enough? :P)
 
        | WanderPanda wrote:
        | "more important problems", very slippery slope Edit: I
        | also have the feeling that quite often "the shoulders of
        | giants" things stand on looked like less important
        | problems
 
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