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Can One Hear the Shape of a Drum? [pdf] (maa.org)
41 points by luu 7 months ago | hide | past | favorite | 16 comments



This is one of my favorite problems :) It's so easy to state to people and surprisingly wasn't solved in the 2 dimensional case until 1992!

I also like how unrealistic the "drumheads" proposed in the proof were: https://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum


Interestingly, to me at least, I knew a local music store that made their own instruments for years, and had a kick drum shaped almost exactly like the one on page 1 of the pdf linked to (like a kidney bean). Of course, the head was ancient, as the creator had (IIRC) REMO put their heads on the hoops that he custom bent and sent to them.

Sounded different than a normal drum. Was pink sparkle coated, so perhaps that had something to do with it :)

The drum kit is still in the shop to this day (crazy old guy wants far too much for anything in the shop, as it has been there for an eternity, and well, all old is expensive, right?) I think about that set every now and then, as I myself was interested at one time.


You could look for an old Trixon drumset if you want an oddly-shaped bass drum:

https://www.trixondrums.de/trixon/trix249.htm


Regarding realism, I wonder if it's possible to hear the difference between drums if you assume dampened vibration.


I thought it would be a link to https://www.jstor.org/stable/29775597?seq=1.

I heard about this problem from David Webb (one of the people who found that the answer was no) back when I was a grad student at Dartmouth College.


Relatedly: Can one hear the fate of a coin? https://cs.stanford.edu/~kach/can-one-hear-the-fate-of-a-coi...


Reminds me of my time in music school. The ear training department had a special resident visiting that week and their skill was such that someone joked you could jingle the change in your pockets that person could tell you how much you had and in which denominations.


Related: can you hear the temperature of water? https://m.youtube.com/watch?v=Ri_4dDvcZeM


Still unsolved for 2-manifolds embedded in 3D I believe.

You can’t hear the shape of a drum. But can you hear the shape of a cowbell?


You have to really explore the space.


Obligatory: https://youtu.be/bkJZbyrfx-Q

It’s really too bad that PBS canceled infinite series.


More recently Kelsey Houston-Edwards has been writing for Quanta: https://www.quantamagazine.org/authors/kelsey-houston-edward...


Cool, didn’t know that.


I might click if you say what the link is.


They do tell you it's from the PBS Infinite Series, if only in an indirect way. The exact video is "Can We Hear Shapes?"


Ah ok thanks. (Well, their sentence told me nothing...maybe because I'm not in USA.)




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