Chaos theory and the evolution of sexes

Chaos theory is considered by many modern mathematicians and scientists as one of the  four pillars of modern science. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the butterfly effect. Chaos theory has  applications in multiple scientific disciplines including:  geology, mathematics, microbiology, biology, computer science, economics, engineering, finance, meteorology, philosophy, physics, politics, population dynamics,psychology, and robotics.

This article is an examination on the significance of chaos theory  in the evolution of sexes in sexually reproducing species including humans.

Chaos Theory

Chaos theory in simple terms states 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. In real world this has big consequences because many systems in nature are extremely sensitive to initial condition (such as weather,stock markets,chemical reactions etc.) and which makes it very difficult to predict and control.

Bifurcation and strange attractors

One interesting property came from the study of chaotic systems is that there is a phenomenon called strange attractors. Some systems tends to be chaotic with most of input space(called phase space) except certain region of the phase space. The diagram below shows the two attractors of the system represented by the logistic equation x = 4 x (1 – x)

[image courtesy wikimedia.org]

In many of the systems this process tends to be centered around two attractors. And this is called bifurcation process. This phenomenon is of interest and significance in this article.

[image courtesy wikimedia.org]

Evolution of sexes

Evolution of sexual reproduction and sexes are of great interest among modern biologists and is one of the mysterious area in biological evolution. There are many competing theories trying to explain this process. Here the attempt is to give a mathematical dimension to the search.

As we now, through evolution, living organisms takes all possible forms and tactics to survive and propagate. In most of the species, it is striking that the number of sexes are limited to two(male and female). This is either by chance or limited by certain constraints exerted by nature(like mitochondrial efficiency in the nucleus). But the number two gives rise to the question of its relationship with mathematics.

Here are some patterns that connect the chaos theory with evolution

1.  The biological system(morphology) of any organism is dynamical system.
2.  Evolution process is mostly in the change in DNA.
3.  Sensitivity of the morphogenesis of organisms to initial conditions(the DNA).
4.  Sensitivity of the sexual dimorphism of organisms to initial conditions(X,Y chromosome region of the DNA)
5.  Large number of iterations over time to support bifurcation(the evolutionary timeline is of the order of billions of years).
6.  The evolutionary process tries to takes all forms(phase space of the life form) based on the change in DNA(initial condition)
7.  The number of sexes tends to attract to two(strange attractors,bifurcation?).

The figure below show the hypothetical bifurcation of the evolution of x and y chromosomes. Start from a common ancestor of chromosome pair x’x’ the ancestors of x and y sex chromosomes. Assuming there were no sexual dimorphism at this phase and the evolutionary change can be in any direction. But the number of sexes converges to 2 rather than n types able to reproduce with each other leading to xx(female) and xy(male).

hypothetical bifurcation of the evolution of sexes

Put your valuable comments below or discuss it in Quora

http://www.quora.com/Is-there-a-connection-between-evolution-of-two-sexes-and-the-bifurcation-of-the-chaos-theory

The chaos theory of evolution:  An interesting article published in in New Scientist discusses similarity of evolution of life and non-linear systems, fractal nature of life and chaos.

My own conversation in TED.com ideas :

https://www.ted.com/conversations/11233/evolution_of_sexes_are_the_res.html

The future of biological evolution

The theory of biological evolution, the radical theory that changed the way humans looked at them selves and solved lot of our philosophical struggles, is one of the obvious facts of  life. Despite its ground braking revelations, the theory is still struggling to get itself accepted by the large public outside scientific communities and intellectuals. The reason is nothing but it challenges the basic belief systems, that are millennia old, of what we are and how we came to existence. As we, the currently alive organisms, are the latest of those ever lived on earth in its history, this is an effort to identify whats next and their by designing the future and our role in building it.

The macro-organism, the man-machine hybrid society

We now know that all organisms evolved from simple cell like organisms millions or billions of years though we are in a process of understanding how the earliest of them came in to existence. From simple celled organisms(eukaryotes), life evolved in to multi-celled organisms(Prokaryote) leading to our(humans) very own form. We are nothing but millions of living cells bound together by synergy. And we along with other social animals have developed a higher dimensional synergetic entities called societies. Social entities include ant colonies, animal herds, flocks of birds, human families, cities…

In the same line if we can extend, we can see a bigger organism forming. A macroorganism of global scale. Many call it gaia, biosphere, noosphere etc. As most organisms matures( growth process is peaked or stabilized) , it reproduces. So how is this gaia/noosphere/biosphere is reproducing? Answer may be planetary seeding. The humanity, the cells of the macro-organism,bounded by the pressures of  the shrinking resources have long started looking for them out side our planet. The ever increasing interest in space missions and research is clear evidence for this. So noosphere/gaia/biosphere , although complex with in itself, will act like a eukaryote splitting in to two as we will find a habitable environment in other planets or stellar systems. Latest researches hints life could have been reached from outside our planet through meteorites or comets. Rockets and spaceships are like pollen/sperm carrying seeds away from the parent.

Silicon based life forms?

As evolution is through changes in all directions, another notable phenomenon is the development of brain and the ability to use tools. These features are not limited to humans. In fact numerous animals show some levels of intelligence and tool using abilities- crows, dolphins, chimpanzees, octopuses and other cephalopods etc. One of the remarkable tool invented by human collective intelligence is the computers and the Internet. This is amazingly analogous to the neural networks of animal brains. And the fractal expansion of the simpler to complex evolution process is happening in the Internet and world wide web aw well. We are in a process of creating a complex man-machine hybrid society that complements each others functions. The spawn of artificial intelligence is most likely will be in this hybrid society as a collective intelligence rather than the conventional notion of a single organism surpassing human intelligence. Though both are simultaneously possible.

The basic element powering the computers and other electronics is the element Silicon. As we know that Carbon is the basic element of the foundation of all living organisms on earth, the rise of Silicon and an artificial intelligence like the one humans are creating on earth in the form of Internet and world wide web is a striking shift in the evolutionary process of a Carbon based life form learning about the evolutionary process and uses the lessons and spawning a silicon based life form further in the chain. This is not exactly like the concept of Silicon Biochemisty

Reading

Evolution

Self-organisation 

Collective consciousness

Collective Intellignece

Gaia

Gaia spore

Noosphere

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Peter Brook’s Mahabharata

Mahabharata is one of the earliest literature of mankind. It is the story describing an epic battle between cousin brothers. It has been adopted in to big screen as well as silver screen, both partially as well as completely many times. Peter Brook’s Mahabharata is big screen adaptation which is interesting mainly due to the intentional use of a international selection of cast and the presentation style. The movie is adopted from the 9 hour stage play by Peter Brook. This was also remade as a TV mini series of 6 hour length.

The Cast

Vyasa - Robert Langton-Lloyd

Lloyd appears as a bearded veteran man, Vyasa, the author of the epic itself. He appears as the narrator of the story as he recollects its and narrates it to his grand son as well as Lord Ganesha,who writes it down as a poem. The appearance is different than the conventional appearance of a sage like Vyasa in mainstream media.

Krishna - Bruce Myers

Krishna’s appearance is, again,different from the conventional bohemian image attributed to him throughout the Indian subcontinent. Bruce Myers appears more like a diplomat and a psychologist. Neither he is blue or dark skinned.

Sotigui Kouyaté as Bhishma

Bhishma is picturised as an african. Perfect for the role. Sotigui Kouyaté immortalized the grandfather of Mahabharata.

Jeffrey Kissoon as Karna

Georges Corraface as Duryodhana

The prince of Dark Triads is depicted as a playboy looking Georges Corraface.

Vittorio Mezzogiorno as Arjuna

Arjuna, the most popular hero of the Epic, is made perfect by Vittorio Mezzogiorno. His eyes speaks focus and his face enlightened.

Andrzej Seweryn as Yudhishthira

Yudhishtira was perfected by Andrzej Seweryn.

Mamadou Dioumé as Bhima

An african Bhima was perfect for the strong man.

Urs Bihler as Dushasana

The Norse warrior looking Dushasana was realised by the Swiss Urs Bihler

Miriam Goldschmidt as Kunti

Ryszard Cieslak as Dhritarashtra

Mallika Sarabhai as Draupadi

Only Indian among the cast, the beautiful Draupadi, was immortalized by Mallika Sarabhai.

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Tapasudana as Lord Shiva/Pandu

The Balinese Tapasudana played Shiva and Pandu.

Overall the epic is narrated in a different style and with out loosing the tempo of the exciting story. Must watch kind of classic drama.