Letter from a Mathematician, Concerning Fractal Forms in Indian Art

April 29, 2014 in Letters | Comments (0)


April 23

Hello Amitav:

It was a pleasure meeting you and listening to your talk.  I particularly enjoyed our brief conversation about Fractals at the end of the talk, and I am following up on your invitation to write to you.
As I mentioned I am a mathematician with a Ph.D in the very abstract area of differential topology that I earned from the University of Virginia.  I was a professor for a few years before abandoning academia for information technology where I have misspent many years.  Recently I have been obsessing over architecture, design and photography (I am pasting a link to my photoblog below).
slideshow-img2 In my self study of architecture and design I have often thought about the Indian aesthetic and how it differs so much from the Western aesthetic.  I was particularly struck by a photograph of the Meenakshi temple I saw almost a decade ago.  I noticed that from far the temple appears to have straight edges but when you pull in closer you notice the edges are made up of statues, and the first thing that popped in my mind was fractals.

Technically we say that a form has a fractal geometry, or is a fractal,  if the form repeats itself infinitely upon magnification.  Certainly nothing in the real world satisfies this classical definition but one often presents the coastline as a real life example of fractals in that a  coastline from 10,000 ft often looks like a coastline from 1000 ft.  When I say that I think the Indian aesthetic is fractal in nature I am not referring to this repeatability upon magnification but simply to the presence of details upon details that exhibit themselves as you pull in closer.  The indian psyche would not have been happy with a straight edge temple, which is very different from the Greeks or the Egyptians for example.  It was felt necessary to add details upon detail in the smallest of spaces.  Compare this with the Parthenon in Greece where the straight edge observed from afar is a true straight edge of a pillar or the roof.  Maybe it is a bit of stretch, but I see traces of this Indian need/appreciation for complexity in their music, with notes between notes, and in Indian cuisine where the interplay of many different flavors is not just the strength but also the defining characteristic of the cuisine.  To me the Western mind going all the way back to the Greeks is more interested in reducing complexity to get to the essence of a truth.  Indians on the other hand want to embrace complexity because rightly speaking the universe is a very complex dynamical system.  Its like the Indians want to grasp the universe in its totality, whereas the westerners want to do it a piece at a time.  Indians could never have built the Parthenon, or a simple pyramid, no more than the Greeks or Egyptians could ever build the Meenakshi temple.  Their tastes and world views are just so different.  It is also (thus) not surprising that India did so well in number theory where the universe is full of details upon detail (infinitely many fractions between any two fractions and so on), but did so poorly in geometry which about abstracting form to it’s simple essence.  The Greeks on the other hand fared poorly in comparison in number theory but excelled at geometry.
Of course this is just my theory based on some observations, and strictly speaking Indian art is not a fractal, but that is the geometry that comes to mind when one sees their art.
I hope we stay in touch.  My photoblog link is on this about.me page.
Harpreet Singh

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