3 ms·
That's not an unreasonable question, however the larger point is that this sort of thing cannot be done perfectly accurately. This was established mathematical
by DougMerritt 2y ago
That's not an unreasonable question, however the larger point is that this sort of thing cannot be done perfectly accurately.
This was established mathematically, answering an old 1966 question from famous mathematician Mark Kac: "You can't hear the shape of a drum" -- there isn't a unique answer even when allowed to use arbitrary test sounds.
Wikipedia:
https://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum https://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum
Article in American Scientist 1996 Jan-Feb:
https://www2.math.upenn.edu/~kazdan/425S11/Drum-Gordon-Webb.pdf https://www2.math.upenn.edu/~kazdan/425S11/Drum-Gordon-Webb....
- gyrovagueGeist 2y agoI love this paper, but something I think is often missed when it comes up is that you CAN hear the shape of many drums if you restrict the shape space, for example with a prior of "what a drum should look like" Zelditch proved spectral uniqueness for convex, fully connected, drums with some symmetry.
- DougMerritt 2y agoAha, I had missed that! Thanks.
- pfortuny 2y agoYou are totally right but "convex" is a very strong assumption (so strong that the shape is determined by its harmonics). Very strong.
- scarmig 2y agoIf you add multiple hearing points, you massively constrain the space of possible drums. The question then becomes something like "can you see the shape of a drum?" Proof of concept: echolocation.
- dartos 2y agoIsn’t echolocation more akin to sonar? Just hearing someone hit a drum wouldn’t give you the shape of it.