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I am sorry I know the resolution won't please all traders! As an engineer when I hear about a method that can hear the shape of most drums but not this one special case, I think that means the proposition is true. But this is posted in the mathematics group. So proof by contradiction should be the only burden the negative side should have to uphold. I thought about restricting it to real drums (convex, with an analytical boundary), but one person brought up a concave drum. You can hear the area and perimeter of a drum but not necessarily the shape!

@tftftftftftftftftftftftf In the future I will try be much more rigorous in constructing the resolution criteria of the markets and anyone who feels unfairly treated by this resolution can request mana from me.

@tftftftftftftftftftftftf Sg. As penitence, please graph the convolutional field your thinking had to undergo to arrive at this conclusion. There seem to be highly unique, non-intuitive parameters to that space that could prove useful to further mathematics research.

The question is can one hear the shape of A drum, not ALL drums.

@Duncn But the description has “the”drum. Which one?

@Duncn In the context of this paper “a” means “an arbitrary”

@derikk This is the mathematics group so

Uh oh: "So, the answer to Kac's question is: for many shapes, one cannot hear the shape of the drum completely. However, some information can be inferred.

On the other hand, Steve Zelditch proved that the answer to Kac's question is positive if one imposes restrictions to certain convex planar regions with analytic boundary."

Conceivably not all drums are convex, so I think this has to resolve in the negative. At least, that’s the answer to the question as it is typically formulated. If “infer any information” were the criterion this would be trivially true.

@derikk can you give us one example of a nonconvex drum? I am just not convinced those are even constructible

@derikk wow fair. good point.

@tftftftftftftftftftftftf as shown by @derikk , this has to resolve NO. It's a well-known paper, too https://www.ams.org/journals/bull/1992-27-01/S0273-0979-1992-00289-6/S0273-0979-1992-00289-6.pdf

OK I think resolving this market is more complex than I imagined it seems like you can hear the shape of some drums but not every drum. So now I need to determine what 'a' means.

@tftftftftftftftftftftftf https://www.merriam-webster.com/dictionary/indefinite%20article

used in English to refer to a person or thing that is not identified or specified

and also: https://www.merriam-webster.com/dictionary/a

used as a function word before singular nouns when the referent is unspecified

“a man overboard”

So, in short: resolve and pay me, plz 😄

@MattCWilson Ok how about this. 'Can you hear the shape of "most" drums.' That way if any individual drum is sampled, more likely than not you can hear its shape

@tftftftftftftftftftftftf There’s a reason after skimming the paper I still didn’t bet. Seemed too subjective

@tftftftftftftftftftftftf I mean, do as you please, but you put “the” drum and and “it” makes, so you’re really stretching “a” here.

“the problem in two dimensions remained open until 1992, when Carolyn Gordon, David Webb, and Scott Wolpert constructed, based on the Sunada method, a pair of regions in the plane that have different shapes but identical eigenvalues.”

https://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum

https://www.math.ucdavis.edu/~hunter/m207b/kac.pdf

“As our study of the polygonal drum shows, the structure of the constant term is quite complex since it combines metric and topological features. Whether

these can be properly disentangled remains to be seen.”

Yes, with training; but you could also develop confounding examples.