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Anand CV

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Evolution of sexes are the result of bifurcation of chaotic system called life.

Chaos theory is concept which implies that dynamical system which are deterministic (having finite numeber of states and depends only on the initial condition of the system) are unpredictable by nature.
The characterstics of a dynamical system to be considered as chaotic are
1. it must be sensitive to initial conditions;
2. it must be topologically mixing; and
3. its periodic orbits must be dense.
Refer Wikipedia: http://en.wikipedia.org/wiki/Chaos_theory

Here are some patterns that connect the chaos theory with evolution
An interesting characeristic associated with chaotic systems are patterns called strange attractors , bifurcation and period doubling.
In these charecterstic, the chaotic systems becomes less chaotic in certain region of the phase space( set of all possible states of a system)
Another pattern associated with chaos is the fractal nature.The bifurcation often has a fractal pattern.
The ideas connecting chaos theory and evolution are
1. The phenomenon of life is deterministic
2. It is sensitive to initial condition
3. Evolution of life is fractal
4. The path taken by evolution never overlap.

In the lights of these, we can also see there is a pattern of bifurication happeing in the life process. Organisms evolve over time in to two sexes(genetically close, but morphologically different forms).
The observations supporting this are
1. Evolution process is mostly in the change in DNA.
2. Sensitivity of the morphogenesis of organisms to initial conditions(the DNA).
3. Sensitivity of the sexual dimorphism of organisms to initial conditions(X,Y chromosome region of the DNA)
4. Large number of iterations over time to support bifurcation(the evolutionary timeline is of the order of billions of years).
5. The evolutionary process tries to takes all forms(phase space of the life process) based on the change in DNA(initial condition)
6. The number of sexes tends to attract to two(strange attractors and bifurcation?).


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    May 5 2012: So, what I gather from you explanation is that even 'chaos theory' has a plan. It's results are limited to its initial state and it has built in 'tendencies'. That's why we have only two sexes. Very interesting. Is it possible, in your opinion, that that as a result of these 'tendencies' and the fractal nature of growth, that life and it's components seek relationship to each other?
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      May 5 2012: The chaos theory is a hot research topic. Observations are that chaotic systems are predictable. But there are too complex systems which are difficult to predict. Here we are exploring parallels between observed chaotic systems with biological life.
      Fractal nature is observed in many areas of life. The evolutionary tree of life is fractal like structure. Our body is a fractal pattern formed from cells. Fractal in the sense simple repetitive processes. Even the entire development of life is simple repetitive process. Birth-reproduction-death. We just don't have a good mathematical model of an organism.
      The parallel between chaotic systems and life is that, something as complex as human body evolved from repetitive process of DNA/RNA like molecule replication. We are dealing with very abstract concept. But the similarities are striking.

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