points by datsci_est_2015 3 days ago | 0 comments
> And I also think there's motivation for why scientists care so much about elegance.
It's an intuition you build pretty early on in science courses in undergrad, somewhat related to Occam's Razor. It's why the optimal packing of 11 squares[1] is so unsatisfying. It flies in the face of all the intuition we've built that simple (and symmetric) solutions are more likely to be true. Machine learning practitioners use this intuition when performing model selection as well: the simpler model (i.e. with fewer free parameters) is less likely to be overfit to the data.
[1] https://en.wikipedia.org/wiki/Square_packing#/media/File:Pac...
[–] godelski 3 days ago
[–] datsci_est_2015 2 days ago
Does your [1] link not simply prove my point that humans will search for something satisfying symmetric given a result that is less satisfying and less symmetric?
"Beauty is in the eye of the beholder" - but let me just quickly find an alternative representation of the solution that is much more symmetric and satisfying. There, "beautiful"!
[–] godelski 1 day ago
Yes, but that "satisfying symmetric" (I'd say elegant since symmetry isn't required) is meaningful and finding these elegant solutions has been shown to be important for solving further problems. Math and physics aren't as concerned with the answer as they are with understanding
[0] https://m.youtube.com/watch?v=hV41QEKiMlM
[1] https://pingyou.com/papers/eleven-squares.pdf