@doubleOR1 Imagine all natural numbers from 1 to infinity, on a line. Now imagine playing a click for each number in a certain frequency. You would hear a regular beat of clicks. If you increase the frequency, you would hear a smooth buzz. The sound of this buzz would depend on the spectrum and width of the click. Now, calculate n/log(n) for each number and play that instead. You would hear an increasing density. Next, remove all numbers except the primes.
Now you would hear a locally non-smooth yet globally smooth sequence of clicks, in other words the weird buzz you hear. The global smoothness is due to the prime number theorem. The local roughness shows the semi-randomness of the primes.
@skatty14 There should not be any difference according to the base used. To explain further, the time dimension is the number dimension. For every prime a click is played.
@AkiraBergman Ah, ok. I know that multiplication is the same (and I suppose all math is the same) regardless of base. Prime numbers just don't seem the same in say base 2 or something. We are just all so accustomed to base 10 that others almost seem wrong? :)
uh. What is this? I'm lost.
doubleOR1 7 months ago
@doubleOR1 Please read the comments and if you have specific questions I am happy to help.
AkiraBergman 7 months ago
@AkiraBergman well, how are the prime numbers turned or represented by sound?
doubleOR1 7 months ago
@doubleOR1 Imagine all natural numbers from 1 to infinity, on a line. Now imagine playing a click for each number in a certain frequency. You would hear a regular beat of clicks. If you increase the frequency, you would hear a smooth buzz. The sound of this buzz would depend on the spectrum and width of the click. Now, calculate n/log(n) for each number and play that instead. You would hear an increasing density. Next, remove all numbers except the primes.
AkiraBergman 7 months ago
@AkiraBergman (continued)
Now you would hear a locally non-smooth yet globally smooth sequence of clicks, in other words the weird buzz you hear. The global smoothness is due to the prime number theorem. The local roughness shows the semi-randomness of the primes.
AkiraBergman 7 months ago
@AkiraBergman ***correction***
You would hear an increasing density ---> You would hear a decreasing density.
AkiraBergman 7 months ago
@AkiraBergman ah ok I get it now.. lol thanks. Cool video
doubleOR1 7 months ago
Haha, this is awesome! This is for numbers in base 10, right? Is there much difference in the noise between this and other bases?
skatty14 9 months ago
@skatty14 There should not be any difference according to the base used. To explain further, the time dimension is the number dimension. For every prime a click is played.
AkiraBergman 9 months ago
@AkiraBergman Ah, ok. I know that multiplication is the same (and I suppose all math is the same) regardless of base. Prime numbers just don't seem the same in say base 2 or something. We are just all so accustomed to base 10 that others almost seem wrong? :)
skatty14 9 months ago
@skatty14 In some cases the base may be important to consider. Perhaps not here, since in the end all calculations are done in binary anyway.
AkiraBergman 9 months ago
fascinating
atree3 11 months ago
@atree3 Exactly.
yannbane 7 months ago
I'm going to play this over and over loudly next to my baby's crib so he'll have an intuitive understanding of prime numbers.
LogicalPhallusy 1 year ago 2
@LogicalPhallusy
It maybe better for the child if the sound is passed through a low-pass filter, and then maybe increase the bandwidth as he/she get used to it ;)
AkiraBergman 1 year ago
do these prime have anything to do with pi? there seems to be a curvature in the pattern that keeps forming
nickharvey7 1 year ago
Interesting observation. Riemann Zeta function adds up to many pi related values. This may be what you see.
AkiraBergman 1 year ago