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Comment by aqme28 | Hacker News Reader

You're correct, but I'm also curious how you could measure accuracy here. There isn't any easy way that I can think of.

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

Article in American Scientist 1996 Jan-Feb: https://www2.math.upenn.edu/~kazdan/425S11/Drum-Gordon-Webb....

I 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.

Aha, I had missed that! Thanks.

You are totally right but "convex" is a very strong assumption (so strong that the shape is determined by its harmonics). Very strong.

If 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.

Isn’t echolocation more akin to sonar?

Just hearing someone hit a drum wouldn’t give you the shape of it.

If you can't measure the results then the entire thing needs a rethink.

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