[HN Gopher] 'Monumental' Math Proof Solves Triple Bubble Problem...
       ___________________________________________________________________
        
       'Monumental' Math Proof Solves Triple Bubble Problem and More
        
       Author : nsoonhui
       Score  : 46 points
       Date   : 2022-10-08 07:56 UTC (1 days ago)
        
 (HTM) web link (www.quantamagazine.org)
 (TXT) 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
        
       ___________________________________________________________________
       (page generated 2022-10-09 23:00 UTC)