4 ms·

Can you hear the shape of a graph?

41 points by pizza 4y ago

amelius 4y ago
Conversely, can you make a graph that sounds like the song "happy birthday", and would the graph suffer from copyright claims?
- treeman79 4y ago
  Happy Birthday is now public domain. “Owner” had to pay back royalties. https://arstechnica.com/tech-policy/2016/02/happy-birthday-is-public-domain-former-owner-warnerchapell-to-pay-14m/?amp=1 https://arstechnica.com/tech-policy/2016/02/happy-birthday-i...
SeanLuke 4y ago
I'm guessing this is in reference to a famous math problem, open for quite a long time, posed in the paper "Can One Hear the Shape of a Drum?" by Mark Kac. https://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum https://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum https://www.math.ucdavis.edu/~hunter/m207b/kac.pdf https://www.math.ucdavis.edu/~hunter/m207b/kac.pdf
waqf 4y ago
Slightly better explanation: https://web.archive.org/web/20141114091039/http://math.iit.edu/~rellis/comb/graph.html https://web.archive.org/web/20141114091039/http://math.iit.e... You still have to figure out their convention for the matrices they're taking eigenvalues of though. Looking at the eigenvalues for K8, it seems to me that their adjacency matrices have 1 on the diagonal, and -1/n wherever there is an edge (n being the degree of the vertex), so that each row sums to 0.
- dekhn 4y ago
  that sounds like a modification of the graph laplacian; https://en.wikipedia.org/wiki/Laplacian_matrix#Laplacian_matrix_normalization_2 https://en.wikipedia.org/wiki/Laplacian_matrix#Laplacian_mat...
travisjungroth 4y ago
Now I want to hear charts. Market crashes would be fun.
- danielvaughn 4y ago
  I'm imagining Rachmaninoff's Prelude in C# Minor.
- whatshisface 4y ago
  The stock market would sound like this most of the time: https://en.m.wikipedia.org/wiki/Brownian_noise https://en.m.wikipedia.org/wiki/Brownian_noise
_the_inflator 4y ago
Makes a great sound reference for any nerdy science fiction movie.
mgdlbp 4y ago
You sure can hear the shape an orbit: https://www.youtube.com/watch?v=GiAj9WW1OfQ&t=384s https://www.youtube.com/watch?v=GiAj9WW1OfQ&t=384s
kretaceous 4y ago
Slightly OT: I'm on FF. Is it suppose to download a .wav file or play it?
akamoonknight 4y ago
Makes me think of potentially using sound as a way for humans to conceptualize higher dimensional spaces. I feel very bound to 3 dimensional visualizations frequently and often wish that conceptualizing that next step to even 4 dimensional spaces would be more 'obvious'. E.g. space time diagrams (even though I can't say that I'm good at evaluating movement in even one dimension of space and one dimension of time on a 2-d plot, I can't even comprehend trying to 'visualize' movement through three dimensions of space and one of time.) For some reason feels more possible in audio space.

41 points by pizza 4y ago

Conversely, can you make a graph that sounds like the song "happy birthday", and would the graph suffer from copyright claims?

treeman79 4y ago
Happy Birthday is now public domain. “Owner” had to pay back royalties. https://arstechnica.com/tech-policy/2016/02/happy-birthday-is-public-domain-former-owner-warnerchapell-to-pay-14m/?amp=1 https://arstechnica.com/tech-policy/2016/02/happy-birthday-i...

SeanLuke 4y ago

I'm guessing this is in reference to a famous math problem, open for quite a long time, posed in the paper "Can One Hear the Shape of a Drum?" by Mark Kac. https://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum https://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum https://www.math.ucdavis.edu/~hunter/m207b/kac.pdf https://www.math.ucdavis.edu/~hunter/m207b/kac.pdf

waqf 4y ago

Slightly better explanation: https://web.archive.org/web/20141114091039/http://math.iit.edu/~rellis/comb/graph.html https://web.archive.org/web/20141114091039/http://math.iit.e... You still have to figure out their convention for the matrices they're taking eigenvalues of though. Looking at the eigenvalues for K8, it seems to me that their adjacency matrices have 1 on the diagonal, and -1/n wherever there is an edge (n being the degree of the vertex), so that each row sums to 0.

dekhn 4y ago
that sounds like a modification of the graph laplacian; https://en.wikipedia.org/wiki/Laplacian_matrix#Laplacian_matrix_normalization_2 https://en.wikipedia.org/wiki/Laplacian_matrix#Laplacian_mat...

travisjungroth 4y ago

Now I want to hear charts. Market crashes would be fun.

danielvaughn 4y ago
I'm imagining Rachmaninoff's Prelude in C# Minor.
whatshisface 4y ago
The stock market would sound like this most of the time: https://en.m.wikipedia.org/wiki/Brownian_noise https://en.m.wikipedia.org/wiki/Brownian_noise

_the_inflator 4y ago

Makes a great sound reference for any nerdy science fiction movie.

mgdlbp 4y ago

You sure can hear the shape an orbit: https://www.youtube.com/watch?v=GiAj9WW1OfQ&t=384s https://www.youtube.com/watch?v=GiAj9WW1OfQ&t=384s

kretaceous 4y ago

Slightly OT: I'm on FF. Is it suppose to download a .wav file or play it?

akamoonknight 4y ago

Makes me think of potentially using sound as a way for humans to conceptualize higher dimensional spaces. I feel very bound to 3 dimensional visualizations frequently and often wish that conceptualizing that next step to even 4 dimensional spaces would be more 'obvious'. E.g. space time diagrams (even though I can't say that I'm good at evaluating movement in even one dimension of space and one dimension of time on a 2-d plot, I can't even comprehend trying to 'visualize' movement through three dimensions of space and one of time.) For some reason feels more possible in audio space.