Aphex Twin's Equation: Meaning and Significance

[LAHLH]

Hi,

If you're unfamiliar with this check out http://www.bastwood.com/?page_id=10. Basically this is a hidden face in one of Aphex Twin's tracks viewable when the sound is played through a spectrogram.

The track is called by the catchy name of :[tex] \Delta M^{-1}_{i}=-\alpha \sum^{N}_{n=1}D_i[n]\left[\sum_{j\in C} F_{ji}[n-1]+Fext_{i}[n^{-1}] \right] [/tex]

I'm guessing this is something to do with fast/discrete Fourier transforms, something I'm not vastly familiar with having only really used continuous FT's much, but this form doesn't look like an FFT I see on the web after a quick google, so just wondering if someone could shed more light on the exact meaning of this equation.

 

[torquil]

This is a really cool mystery!

I don't know the answer, but I'll venture a wild guess that is has to do with many-particle physics/chemistry, and that the expression represents a correction to the value of a property M of a particle i.

The F-terms remind me of sums over contributions from pairs of particles (i,j), and Fext might be the influence in particle i of an external field. The C might be a list of particles that influence particle i.

Should it also be n-1 in Fext_i[...] ?

Could alpha be the fine-structure constant?

 

[LAHLH]

I was thinking more along the lines of Fast Fourier transforms, or inverse fast Fourier transforms, since that is in effect what he is actually doing by converting the image of his face into sound on the track. So the equation name of the track could be a clue to what was hiding for those who were mathematically inclined. Perhaps however it's just a random string of maths symbols he thought would look good, and doesn't actually mean much. It certainly doesn't look like the fast Fourier transform algorithms that google presents me with...hmm..

 

[torquil]

It didn't look like a Fourier transform to me either. I don't know much signal analysis, however. Let's hope someone else on here has seen this or something similar before. I want this cleared up, even if I don't listen to Aphex Twin!

 

[Phyisab****]

I don't know, but it doesn't look like it has anything to do with Fourier transforms. No exponential or sines or cosines. torquil's suggestion seems more likely to me. I would guess deltaM is the magnetization of particle i.

 

[LAHLH]

Looking some more at his background, he was an engineering student, which makes me suspect more it really is a genuine equation...

I'm coming around more to these ideas of it describing many particle systems, seems quite odd he would use that however. But yeah...doesn't like like it's Fourier related.

 

[Phyisab****]

To elaborate, it looks like it is a sum of the interaction forces plus external forces over all components of the system, which is then summed over something else. But if you take that to be the case then what is n and why are the interaction terms and external forces multiplied by n-1 and 1/n?

 

[fashizzle]

necroing with what i believe is the correct answerIf you extrapolate and think of:

∆ as Aphex Twin (the arrow symbol used in some of the albums); Mi as "Am I"; -1 as "Minus One"; = as "Equals", you get:

"Aphex Twin Am I Minus One Equals"...

... A flawed result.

−α∑Di[η]∑Fji[η−1]+Fexti[η−1]

Where you read Fji, should be Fiji.

There's an "i" missing. could it be that part of him (his twin?) is missing from the equation? Richard did mention losing his twin. In fact, that is why he named the project "Aphex Twin".