math, music and Mandelbrot
Music,
the greeks thought, is frozen geometry,
and architecture - frozen poetry; the dance of musical notes is essentially mathematical. In Indian classical music, there are no fixed tones corresponding to particular notes and frequencies, it simply is a set of iterations from any reference point. Although the 'SA' (keynote, first note) broadly corresponds to the 'C' of the western scale (which begins with ~260 Hz, 'A' being at 400 hz), it can be of any frequency for the individual singer or instrument; what preserves its identity is its unique mathematical relation to the other notes, broadly x(3/2)=y, where 'y' is the next note gives the relationship.
The musical spectrum of any individual piece, then, is a unique mathematical entity representable in the 'language' of math symbols. The point is that, patterns exist, and maths is PRESENTLY the best way to describe/decipher/demonstrate them; these may be 'translated/transposed/transcribed' in any other language , for example mathematical relations can be expressed visually by co-ordinates. Thus music can be transposed to visual figures through the language of maths.
Coming to the moot point that patterns exist as fundamental structures, as unique interactions of component 'notes', take Fractals for example (figures generated by successive iterations and 'positive feedback' of a unit theme, 'discovered' just two decades ago by Mandelbrot). The living world is full of fractals, be it Broccoli, or Alveoli in lungs, structure of a neuron, or oyster shells, leaves of a tree, or human finger prints etc etc etc..
Music can be rendered into fractals (seen vis. plugins of WINAMP?);
fractals into music?, can I 'hear' the Broccoli, or my finger prints? or the maple leaf, or the orchid sitting in my vase, or colour patterns on the soap bubble?..... think........
Our problem is one of limitation of 'vocabulary', of absence of a comprehensive 'language', like trying to describe a 3D world with 2D geometry, what you get is Escher circle limit diagrams, distortions with you at the centre, see the parallels with our egocentrism, ethnocentrism, bigotry, exclusionism and misplaced confidence in our own beliefs.....
Fractals give us glimpses of the language of patterns, in music, in life, in math.... this language is known to the mind, as if 'a priori', the untrained ear also distinguishes instances of 'illegal' variations in music, in other words can distinguish between good and bad singing of the same unknown song. The pattern is known to the mind but we cannot put it in words of any sort, our apparatus is way too reductionistic to comprehend the elegance of the observed complexity, the beauty will reappear, as Penrose says, when we will be in possesion of yet another 'higher mathematics',
..............................................and the simplicity will be evident.
Comments
Unfortunately most of the patterns found in nature can only be represented on a complex plane(depicting both complex & natural numbers) or by differential equations of higher order. Most of us even with reasonably good background in maths have never learnt this in any classroom.
Therefore its not surprising that most of us are ill equipped to grasp these concepts let alone master a language which can adequately communicate them. - Fellow admirer of 'Mandelbrot' and 'The Strange Attractors'
The very idea is about a new 'languge', be it math or something else; once more we are, in the history of scientific thought at a point where to go further,new disciplines need to be invented... as Einstien did to classical physics.
In philosophy Wittgenstein has demolished almost all the earlier theories by exposing the limitations of language as a media for description of reality,science is yet to be redeemed of its own imperfections.
The language is there; the mind knows it,our reductionistic paradigm does not allow us to go beyond and look......
The 'patterns' exist and wait to be deciphered, maybe in a language of their own
..........})i({ ............ [:]-0
...........let there be light.......
looking 4ward 4 more...