Shiva and Chaos

Shiva and Chaos

One of the notions in Chaos theory (and I’m still reading up on it so take what follows with a pinch of salt) is that simple patterns can be repeated over and over again to create complex systems. My reference is James Gleick’s

Chaos-The Amazing Science of the Unpredictable.

In it he talks about the reason that our DNA, or DNA in general can store so much information is that information for creating the parts of our body is encoded in patterns that can be used over and over again at different scales.

This “scaling effect” is apparently apparent in organs like our liver and in the structure of our veins and arteries.

In plant life, one researcher showed how smaller pictures of a fern could be layed in to produce a picture of a bigger fern.

(I may need some proper references or at least web links here.)

Anyway, reading all of this I became quite excited because it occured to me that Dance of Shiva can display this scaling effect. It offers an infinite amount of possibility just from a few simple moves.

Warp 1

Allow me to use the Warp 1 sequence to illustrate. In this sequence, there are four movements, (where the movement to the left of the dash is that of the left arm and the movement to the right that of the right arm):

  • Change Forwards-Transquarter
  • Change Forwards-Change Forwards
  • Change Forwards-Backwards
  • Forwards-Change Backwards

We repeat this sequence of movements 4 times to return the arms to the position from which they started.

In the table, each column represents one repetion of this sequence. The movements are highlighted in blue in the column on the left. We start at position 1-1 (top left red square,) and move to b-3, 3-d, d-c and finish at a-4. The next column or repetition starts at a-4 (the second red square from the left.)

The red squares represent the position the we finish at after each repetition. If we look closely we may notice a pattern, a relationship between one stopping point or check sum and the next.

From 1-1 to a-4 the left arm does the equivalent of a change, from 1 to a. From a-4 to 1-3, it does a Change again. Then from 1-3 to a-2 it Changes back to a. Then from a-4 the arms return to 1-1. The right hand undergoes a similar repeated transition. It moves from 1 to 4 to 3 to 2 and back to 1 again (1-1, a-4, 1-3, a-2, 1-1.) It does the equivalent of a Backwards move.

We can thus think of this sequence of movements as equivalent to a C-B move.

(I actually selected each Warp so that their equivalents where all different.)

If we were so inclined we could create any number of warps using any of the pairs of movements to create C-B equivalents. We could also use sequences of other than 4 moves.

Now, suppose we did any four movements at random. What could happen? We could figure out the equivalent single move for those four random movements. More to the point, for any number of moves we could figure out the equivalent single move and it would always be one of 64 possible movements (They are all shown in the table above.)

Why 64? Because there are 64 possible positions and so to join any position to any other position including itself we need 64 possible movements. The movement that connects a position to itself is a zero move.

So what does this mean? If we have the freedom to do any number of moves, then we can always find different ways to do the equivalent of any of the 64 movements. There is infinite potential, all based on a few simple moves.