Although the term 'Pythagoreanism' is inescapably vague, it surely in part names the following position: number has an absolute and generative reality, and the experience of music points the way both to legitimate apprehension of absolute reality and to a foundation for conduct and normativity.
My concept of the HAPTIC VOID is a gesture towards the commitment to access to absolute reality via the experience of music: in particular the experience of simultaneous satisfaction and dissatisfaction. I'm sure there are phenomenologies of music out there that could fill in the blanks of this idea - and I'm interested in developing it further - but I am also interested in developing a sort of revised Pythagoreanism at a more detailed level in conversation with philosophy of mathematics and philosophy of nature. The general shape of what I have in mind is this:
The Pythagoreans were especially interested in standing waves and ratios. Just as ratios like 1:2, 1:3, 1:4 produce unique harmonic tones that are correlated to these ratios and yet do not 'resemble' them in any obvious way, so, surely, ratios and vibrations underlie reality itself.
This has, of course, turned out to be quite literally true, as far as we know. The orbitals in an atom are literally standing waves, and the different elements on the periodic table are made of of the possible combinations of harmonic resonance between atoms of different atomic weight - and although the level of description at which these phenomena occur are subject to experimentation, they are imperceptible - the quantum level of reality is purely mathematical, and it is made of waves.
It was Fourier who discovered the equations that govern waves (heat waves), and his work was translated to sound waves - and is the foundation of all electronic music synthesis. The basic idea - that a wave can always be described as the sum of a number of sine waves - this is the idea the philosophical significance of which I'd like to look into more closely. One encounters this in music all the time - run Melodyne on a vocal track and it resynthesizes the track as a sum of sine waves, making it possible to alter it in the most fundamental waves. Here, where does reality end and simulation begin?