[HN Gopher] Can you hear the shape of a graph?
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       Can you hear the shape of a graph?
        
       Author : pizza
       Score  : 20 points
       Date   : 2022-07-16 07:20 UTC (1 days ago)
        
 (HTM) web link (mathweb.ucsd.edu)
 (TXT) w3m dump (mathweb.ucsd.edu)
        
       | amelius wrote:
       | Conversely, can you make a graph that sounds like the song "happy
       | birthday", and would the graph suffer from copyright claims?
        
         | treeman79 wrote:
         | Happy Birthday is now public domain. "Owner" had to pay back
         | royalties.
         | 
         | https://arstechnica.com/tech-policy/2016/02/happy-birthday-i...
        
       | travisjungroth wrote:
       | Now I want to hear charts. Market crashes would be fun.
        
         | danielvaughn wrote:
         | I'm imagining Rachmaninoff's Prelude in C# Minor.
        
         | whatshisface wrote:
         | The stock market would sound like this most of the time:
         | https://en.m.wikipedia.org/wiki/Brownian_noise
        
       | mgdlbp wrote:
       | You sure can hear the shape an orbit:
       | https://www.youtube.com/watch?v=GiAj9WW1OfQ&t=384s
        
       | _the_inflator wrote:
       | Makes a great sound reference for any nerdy science fiction
       | movie.
        
       | SeanLuke wrote:
       | 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://www.math.ucdavis.edu/~hunter/m207b/kac.pdf
        
       | waqf wrote:
       | Slightly better explanation:
       | 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 wrote:
         | that sounds like a modification of the graph laplacian;
         | https://en.wikipedia.org/wiki/Laplacian_matrix#Laplacian_mat...
        
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       (page generated 2022-07-17 23:01 UTC)