Chaotic Structure

Since Henri Poincare stated more than one hundred years ago, that the only surface in three dimensions that could contract to a point is the sphere, an effort has been made to decode the meaning of this statement.

Now Terry Tao, has taken an important step for this quest. In the arXiv you can read his proof that the classical Navier-Stokes equation does not have a regular solution in three-dimensions. One has to look into non-traditional approaches to understand turbulence. One possibility, which he considers, is to have a liquid universal computer, i.e., to have a fluid which can act like a universal computer, such that the eddies calculate how much energy flows to smaller scales, if we want a mathematical model that does not blow up, unlike real turbulent fluids, which may look unruly, but definitely do not explode in our faces.

In a similar vein Stephen Hawking, has recently stated that there is no information paradox, on the black hole event horizon, because deterministic chaos comes to the rescue. Non-linear mathematics can easily produce this behavior, without invocation to Quantum Theory. No need for a new theory, when classical mathematics can deal with loss of human predictability. Of course, one may need an Einstein-Rosen bridge, but that was constructed by the old man, when he was neglected at the Institute of Advanced Studies, maybe because he did not support the likes of Edward Teller, who wanted to blow up civilized people, with weapons of mass destruction.

Grisha Perelman finally found the way to avoid singularities, and proved the Poincare Conjecture, interestingly, with a series of constructs, similar to those used by Terry , who does not give credit to Grisha.

Now I get to the most interesting part of this note. Leonard Susskind, proposes a universal computer to calculate the complexity involved in the Hawking Information Paradox, very similar to Tao's liquid computer.

To my mind all these elements answer a very old question I asked myself.

How does the electron know where to go?

The answer is: There are universal computers all over the universe, not just in our cell-phones!

Stephen Wolfram at Urbana, and Harold V. McIntosh at Puebla, have done the heavy lifting computer work on which I base my conjectures here.

A New Era is Coming.