[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)