Anand CV Mallaya

Posts Tagged ‘science’

Science and rebirth?

In math, science, spirituality on November 30, 2012 at 2:32 pm

I was little worried that I am becoming a pseudo-scientist  This feeling of guilt was burning inside my mind for sometime and wanted to do really scientific approaches in problem solving.

On the cold morning today, I had this interesting thought on rebirth. Normally I will delve in to thoughts for a few hours and then it will remain as a common religious belief. So this time I wanted to do an exercise on this to improve my scientific problem solving skills.

The problem:

Is rebirth scientifically possible?


Let us look at definition of rebirth here. Rebirth is defined here as having the same appearance of a person died before.

Now science tells us that the characteristics of body of a person is defined by mostly the genes. But this is not the only thing that shapes a body. It depends on the environment the person lives. This include the food, the climate etc. To simplify we will define a person as a set of genes. So rebirth in this context is having exactly the same sets of genes that of a previously dead person.


The number of variation or mutation in genes  are vary small. That is if we consider genes as a set of playing cards, the deck of cards are  unchanged. Each individual gets a shuffled set of cards.


This problem can be done only statistically. Let us start some number crunching

Total initial population, P0 = 10000
(Note: there is a hypothesis that entire population today are coming from a small population which survived a global catastrophe in Africa)
Reference : The Human Journey: Migration Routes (

Total genes per person, Gi = ~20600

Maximum genetic difference in the population (assuming all genes of the population are different) Gp=  Gi*P0 = 206,000,000

Total population ever lived till date Pt = 108,000,000,000

Assuming the variation in the gene pool through mutation is negligible over time, total possible unique individuals = Pt/Gp = ~524

So if there is no gene variations happening  there must have existed around 524 exact copies of every individual.
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God of small things : An approach to simulate simplest organism in a computer

In life, math, science, Technology on October 16, 2012 at 10:50 pm

Recently, scientists at the Stanford group in association with the J. Craig Venter Institute published a paper regarding the successful attempt to simulate a complete organism from its DNA in a computer cluster, for the first time in the history. They simulated a simplest bacterium named Mycoplasma Genitallium, which is capable of replicating inside the simulation. The implication of this is enormous, as this will bridge the gap between engineering and biology and in our quest for solutions to many problems. You can read about the analysis in here. The original paper here

Seven months back, on my sabbatical, I was trying to do the same.

I was trying to simulate a simple bacterium from DNA available public from here. It has only one circular chromosome. I learned about the processes involved in the cell formation from the DNA. DNA is basically the code for two fundamental things happening inside an organism – replication and transcription. Replication is the process of making a copy of the DNA itself and transcription is the process of reading the gene code blocks and generating long chain molecules called Proteins in multiple steps.

DNA transcription

DNA transcription

My work is more inspired by the theory of cellular automata and the Conway’s game of Life. I also considered the concept of fractal to model my organism.

In order to understand the DNA we have to look at it through an evolutionary perspective. If you look at a particular organism or more specifically its genotype and its phenotype, its just a small snapshot of an unbroken chain of repetitive process of replication(the output is a copy of the DNA) and transcription(the output is proteins ). The process started since the beginning of life itself and have undergone innumerable changes(evolution). This in my opinion is a fractal pattern.

Mathematicians have shown before that simple life like structures can be represented by simple set of equation iterated numerous times. A fern for eg. Barnsley fern.

Fractal Fern

Barnsley Fractal Fern

Instead of placing dots in an image as done by the  Barnsley fern equation, the DNA puts complex 3D structures with lot of different physical properties called proteins. This is similar but complex form of Conway’s Game of Life, but much complex. In Game of Life, the cells are actually square cells which can have only one of two states : “dead” or “alive”. From simple rules like ” if a cell is surrounded by at most three living cell, the cell will replicate else it will die”, we can see self sustaining life like activities emerge from the computer screen from a set of original points.

Conway's Game of Life

Bill Gosper’s Glider Gun in action—a variation of Conway’s Game of Life. This image was made by using Life32 v2.15 beta, by Johan G. Bontes. (Photo credit: Wikipedia)

The DNA is the simple set of equations that give raise to complex structures if allowed to repeat enormous time. The structure (phenotype) we see is an emerged form from this process of protein making and other associated process which are perceived as phenotype. For eg. snow flakes are beautiful complex patterns emerge from the simple physical laws.

Snow Flakes

Snow Flakes – Fractal like structures emerging from natural processes. Example of emergence.

The hypothesis is that if we can model basic blocks of  the DNA, which are the Carbon, Hydrogen, Oxygen  and Nitrogen atoms, and simulate all the dynamics between them (the fractal equation) and create conditions similar to a culture medium, the living bacteria will emerge from it! If we can put ultra-fast computers to perform probabilistic calculations and molecular level interaction.

Of-course it will be very difficult for one amateur guy like me to attempt, but I want to abstract many levels and assume certain things taken for granted.

In contrast with the simulation of whole cell by simulating all smaller sub units, which is a top-down approach, my approach is bottom up – simulate the lowest building block accurately and iterate interactions as it will naturally occur based on probability, predicting that life like features will emerge.

I am on sabbatical again and hope to make it happen this time. Visit this blog later to see if I am successful. Or tweet to me @anandcv

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Chaos theory and the evolution of sexes

In evolution, life, math, science on January 24, 2012 at 9:29 pm

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 of 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] 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]

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).

bifurcation of sex

hypothetical bifurcation of the evolution of sexes

Put your valuable comments below or discuss it in Quora 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 ideas :

Interesting Reads 

Some articles which are good read for good background of concepts in Evolutionary Biology, related to Sex:

  1. Evolutionary origins of Cooperators and Defectors
  2. Cooperation and the evolution of anisogamy
  3. A chapter from the book The Score by Faye Flam
  4. Sexes redefined @
  5. The chaos theory of evolution

Interesting videos

During further research, I got these resources which are enlightening some aspects of the truth. Reason yourself.

Evolution of Sex

Origin of Sexes

Mathematical Model of Evolution

Chaos theory

Other articles linking to this page

The future of biological evolution

In evolution, life, science on November 20, 2011 at 11:05 pm

Evolution of Man

The theory of biological evolution, the radical theory that changed the way humans looked at themselves and solved lot of our philosophical struggles, is one of the obvious facts of  life. Despite its ground-breaking revelations, the theory is still struggling to get itself accepted by the large public outside scientific communities and intellectuals. The reason is nothing but the fact that 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 what is next and thereby 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 back, though we are in a process of understanding how the earliest of them came in to existence. From single celled organisms(Prokaryote), life evolved in to multi-celled organisms(Eukaryotes) leading to our(humans) very own form. We are nothing but millions of living cells bound together by their products (like proteins) . And we along with other social animals have developed a higher dimensional synergistic 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 macro-organism 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 “by planetary seeding”. The humanity, the cells of the macro-organism, bounded by the pressures of  the shrinking resources have long started looking for them outside 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(panspermia theory). Rockets and spaceships are like pollen/sperm carrying seeds away from the parent.

Mars rover (image courtesy

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 evolving process is happening in the Internet and world wide web as well. We are probably 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 machine surpassing human intelligence. Though both are simultaneously possible.image_4[1]

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




Collective consciousness

Collective Intellignece


Gaia spore



Is the Human Species Entering an Evolutionary Inflection Point? 

Lab yeast make evolutionary leap to multicellularity

Here is an interesting talk about the human evolution :