Saturday, April 7, 2012

Spontaneous Symmetry breaking and Alan Turing

An embryo in its spherical blastula stage has spherical symmetry, or if there are any deviations from perfect symmetry they cannot be regarded as of any particular importance ... But a system which has spherical symmetry, and whose state is changing because of chemical reactions and diffusion, will remain spherically symmetrical for ever ... it certainly cannot result in an organism such as a horse, which is not spherically symmetrical.
- The Chemical basis for Morphogenesis, Alan Turing.
Resin deposit and butterflies
Spontaneous symmetry breaking is also quite common in Physics. The origins of a lof of forces and particles can be accounted for by asymmetric systems being more stable as whole than a completely symmetric system.

This has a very simple statistical explanation, a perfectly symmetrical state is a very rare occurence compared to the total possibility space of random occurences. Hence the system rapidly deviates from this state. Symmetry is not impossible, but highly improbable. This however does not prevent the consituent elements in the larger system from being highly symmetric, in fact the symmetry is desirable to allow mobility of the constituent to a lower energy more stable state if one becomes available.
Asymmetry is also the basis of the modern economic system globally. There is distinct patchiness in the the distribution of resources on the earth's surface and the reaction-diffusion mechanisms operate by transport of currency or materials (raw or processed) from one part of the earth to another. As the speed of the transport increases the patterning of wealth distribution oscillates. Online transactions have made currency transport nearly instantenous, materials transport still depends on cargo ships and aircraft, but is much much faster today compared to what it was 100 years ago. The wealth spots on the surface of earth are changing faster than the trade winds are blowing, yet they can set up stationary waves where in-spite of the movements the distribution does not shift.

We are all eating off the plate the earth has handed us. In a system with constant energy input, such as the earth receiving energy from the sun and its core via mass-energy conversion, thermodynamic truths such as the total entropy of the system not decreasing do not hold. As we become more proficient with the laws of the universe, we will build more and more symmetric systems/organisms without making a dent on the net asymmetry.
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