On Tigers, diffusion and chaos

Tiger

RT @sanchan89 Always good to know that my mojo is still intact after 4 years 🙂 Take a look http://bit.ly/bGv5su

So, after quite a while, I tried sketching again. And it came out pretty neat, I suppose. But then, I want this to be a tech blog, right?

We humans, have a somewhat dull skin[1]. It is completely bereft of any fur[2] and any pattern to be had on are to be painfully tattooed. Look, on the other hand , at the pervasive presence of spacial patterns on animal coats and flora. Most commonly seen in plants are the rosette patterns, and self replicating branching systems. Mammals and fishes are so much richer – their fur coats come with stripes, spots, rosettes, bands, blocks, combination of these  and in the case of some sea shells – Serpenski triangle! Even in animal behavior, there is so much elegance – if you have not seen the movements of large schools of fish or birds in flight, you have a serious problem and you should consult a psychotherapist. Even the inanimate desert sands are beautifully patterned with near parallel curves.

Spatial patterns collage

Spacial patterns collage

It makes us think, doesn’t it? How are these patterns formed?

If every skin cell were to take on either black or white color with a uniformly random probability, then a zebra would look like white noise. Try imagining one with a coat like that. No probabilistic distribution is ever going to generate patterns as fantastic as those on every tiger. Does every cell, then, have a global spacial view of itself? Is it possible that a single cell knows that it is a part of the stripe across the head of the tiger, and therefore, it should take on a black pigmentation? That seems like something phenomenally complex for a single living cell to know.

Related problems in developmental biology are cell differentiation, and Morphogenesis. Every cell in an embryo is the same. Embryos are homogenous; and yet without a single central controller, cells in different areas of the embryo develop into different parts of the body. Some develop into the the heart and lungs and others into brain and legs.

The first explanation for this phenomenon was provided by the British Mathematician, code breaker, logician, computer scientist ( and during the later days of his life, a chemist )  Alan Turing in his paper titled ‘The Chemical basis of Morphogenesis” in 1951.  ( This paper has its own wiki page ) The paper described mechanisms; borrowing heavily from concepts of self-organisation, well known in physics; by which non-uniformity may arise from uniform homogeneous states, and outlined the reaction-diffusion theory of morphogenesis. Reaction–diffusion systems are mathematical models that describe how the concentration of one or more substances distributed in space changes under the influence of two processes: local chemical reactions in which the substances are converted into each other, and diffusion which causes the substances to spread out in space.

Independently, around the same time a Russian biophysicist Boris Belousov discovered a reaction-diffusion system, now called the Belousov-Zhabotinsky reaction. Where Turing had proposed mathematical models, here was already a demonstration of the self-organizing tendencies of the non linear systems which he had proposed. Here’s a video of a BZ cocktail evolving

From a uniformly homogeneous solution – spirals, spots and expanding rings are formed. And no two instances of the same experiment will get you the exact same results. The equations that govern these reactions are so expressive that you can actually come up with results that show stripes and hexagons! Try it out yourself in this applet.

These two works are considered by some as the founding work on chaos theory. In a nutshell, Chaos theory deals with highly nonlinear and usually self looped systems that despite being fully deterministic, are subject to abrupt and seemingly random change. It is clear in this case –  In spite of explicitly and deterministically defined rules, the reaction-diffusion yields a uniquely different result every time. The source of all this chaos is, well…, in the source itself. The non-linearity of the system greatly magnifies even immeasurably small changes in the initial state. So, the next time you round up a value from 0.506127 to 0.506, be warned! As a sidenote, the phrase “Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?“, is not a misunderstanding of chaos theory. It is in fact the title of the talk presented by Edward Lorenz at AAAS, 1972 on chaos theory. The title was the result of inferences from a run of the simulation he had built, when he changed one of the values of atmospheric conditions as stated above.

If you are interested in learning more about Chaos theory, there is a fantastic one hour program on BBC. No, it does not have equations ( well, maybe just one )

  1. Well, thats not entirely true! We have fingerprints. And they are beautiful and unique, but not colorful or macro. Guess that still qualifies as dull.
  2. This is interesting because, man is the only mammal; excluding those that are aquatic, that has no fur, check out the February 2010 edition of Scientific American

Further reading

  • Stumble this here. Follow me on twitter @sanchan89.
  • If you find my posts interesting, you can follow me via RSS here.
  • Some of my shared items are here, in case you find it interesting.
Advertisements

My faith in Humanity

Or maybe, the loss of my faith in Humanity

All these days, I have been positive, that the Human Race is simply not capable of destroying itself. Perhaps now, its about time I changed my views. I had forever hoped this day would never come. Alas, it has.

My days in Japan had rejuvenated my beliefs a little. Japan was clean and green and its people well aware of their duties to the environment. And then, I land at Coimbatore, a completely balded city. Dusty and in a ruin-like state. All in the name of development. I return back to Chennai, and as always there is Coovum ever ready to show off as the most violated, polluted river on the face of the Earth. My heart cringes in despair, EVERY time I take a ride on the local trains. I can’t bear the sight of the river. The sludge. That smell. And still there are those who pass over it everyday, not giving a damn as they pass by.

It is only once in a long time that I watch TV. And call it misfortune, to add to my despair, ‘An Inconvenient Truth’ was on on HBO. The hope the man has should really be commended. The ignorance of the American people, intrigues me. Why is it that everything is treated as hoax. Why? Armstrong never landed on the Moon. The 9/11 was perpetrated by the Government. And Global Warming is a lie.

Are they frigging out of their minds?

Why? Money. Isn’t that what everything is all about.

In the US, its about increasing the profits. The fuel efficiency law in force in the country is similar to the one in India, I think. And when a talk arises of putting a more stringent rule into effect, American car makers are the first to start swearing. Ford and GM are suffering heavy losses. If such laws are forced, where would they sell their cars? On the other side of the world, Toyota and Honda are flying high. And their market has the strictest fuel efficiency and emission laws. Japan. What an irony. Won’t their markets expand if GM and Ford actually embrace a strong emission rule?

In India, its about minimising expenses / trouble. Why bother to treat the sewage? Its not my problem. Why bother to properly dispose the waste? Its not my problem? Why even bother to look for a proper place to spit? Why not spit here? Why look for a dust bin to dispose the chocolate cover?

No one cares. Why should I?

There was no ice in the North Pole this Summer. I can imagine the response of anyone who I bother to tell it to. “O < like I care >”. Global warming is not a hoax damn it. Its here. And if you don’t do something about it, F*&^, you are not going to do anything anyway. And the TATAs hailed for bring the Industrial Revolution to India, yada yada etcetra etcetra yawn…, aren’t doing pretty things to the environment either. Being an e-member of Greenpeace isn’t every satisfying.

Global Warming. Thats not the only thing thats made me completely lose my faith in Humanity. Terrorism.

Unity in Diversity

What a fantastic concept, eh! The volatility pervading this Unity makes me sick. Of what use is such a unity. The only use of this is that one can swear at the other, at the other’s society and still not be called a racist. Sometimes I think we’d be better off as twenty different countries. And I pray to God I don’t start about politicians in the Country. Gandhi would be greatly ashamed.

I came home this weekend. Saturday, serial blasts in Bangaluru, and Sunday in Ahmedabad. Local news channels in each state crying out that it is their cities to be targeted next. Aaaahhh! What are they trying to be prove??? What the hell do they want? What do they gain by killing loads of innocent civilians? Frankly, I refuse to be intimidated by a bunch of demented fools. Jihad, indeed. If only someone told them what it truly means. Are they going to kill everyone who is not a fundamentalist Muslim? And a pathetic note challenging the police five minutes before the blasts. Sniggering, they must have been as they wrote the note. What a bunch of cowardly ignorants. Just look at this all from a higher plane… What an uncivilised act.

And we are humans!

So many cellular automatons, so many simulations. No simulation could possibly predict that any civilized population would eventually destroy itself. I was convinced that the analogy drawn between the human race and any virus. And perhaps then an automaton could properly predict the ultimate fate of such a race. But such a destiny!!!!

I cannot pen on anymore. I am either so full of spite or despair, or both. Please note that I have not intended to cause any harm, sentimental or otherwise, through this page. I am simply so full of despair and been this way for sometime now that I just had to pen this down. Pardon any inaccurate detail in the page, and please bring it to my notice. I’d be forever indebted.

Sanjeev

The President’s views..,

Here is a thought provoking speech given by our president Dr. A.P.J.Abdul Kalam, on the 10th of November 2003. I think it was given at IITB. Here is an excerpt from the speech.
After outlining his visions for the nation and the four greatest milestones of his career, he coutinues his speech thus:

…Why is the media here so negative? Why are we in India so embarrassed to recognize our own strengths, our achievements? We are such a great nation. We have so many amazing success stories but we refuse to acknowledge them. Why? We are the first in milk production. We are number one in Remote sensing satellites. We are the second largest producer of wheat. We are the second largest producer of rice. Look at Dr. Sudarshan, he has transferred the tribal village into a self-sustaining, self-driving unit. There are millions of such achievements but our media is only obsessed in the bad news and failures and disasters.

I was in Tel Aviv once and I was reading the Israeli newspaper. It was the day after a lot of attacks and bombardments and deaths had taken place. The Hamas had struck. But the front page of the newspaper had the picture of a Jewish gentleman who in five years had transformed his desert land into an orchid and a granary. It was this inspiring picture that everyone woke up to. The gory details of killings, bombardments, deaths, were inside in the newspaper, buried among other news. In India we only read about death, sickness, terrorism, crime. Why are we so NEGATIVE? Another question: Why are we, as a nation so obsessed with foreign things? We want foreign TVs, we want foreign shirts. We want foreign technology. Why this obsession with everything imported. Do we not realize that self-respect comes with self-reliance?

I was in Hyderabad giving this lecture, when a 14 year old girl asked me for my autograph. I asked her what her goal in life is: She replied: I want to live in a developed India. For her, you and I will have to build this developed India. You must proclaim. India is not an under-developed nation; it is a highly developed nation.

Allow me to come back with vengeance. Got 10 minutes for your country?

YOU say that our government is inefficient. YOU say that our laws are too old. YOU say that the municipality does not pick up the garbage. YOU say that the phones don’t work, the railways are a joke, the airline is the worst in the world, mails never reach their destination. YOU say that our country has been fed to the dogs and is the absolute pits. YOU say, say and say. What do YOU do about it? Take a person on his way to Singapore. Give him a name – YOURS. Give him a face – YOURS. YOU walk out of the airport and you are at your International best. In Singapore you don’t throw cigarette butts on the roads or eat in the stores. YOU are as proud of their Underground Links as they are. You pay $5 (approx. Rs. 60) to drive through Orchard Road (equivalent of Mahim Causeway or Pedder Road) between 5 PM and 8 PM.

YOU comeback to the parking lot to punch your parking ticket if you have over stayed in a restaurant or a shopping mall irrespective of your status identity. In Singapore you don’t say anything, DO YOU? YOU wouldn’t dare to eat in public during Ramadan, in Dubai. YOU would not dare to go out without your head covered in Jeddah. YOU would not dare to buy an employee of the telephone exchange in London at 10 pounds (Rs. 650) a month to, “see to it that my STD and ISD calls are billed to someone else.” YOU would not dare to speed beyond 55 mph (88 kph) in Washington and then tell the traffic cop, “Jaanta hai sala main kaun hoon (Do you know who I am?). I am so and so’s son. Take your two bucks and get lost.” YOU wouldn’t chuck an empty coconut shell anywhere other than the garbage pail on the beaches in Australia and New Zealand. Why don’t YOU spit Paan on the streets of Tokyo?

Why don’t YOU use examination jockeys or buy fake certificates in Boston? We are still talking of the same YOU. YOU who can respect and conform to a foreign system in other countries but cannot in your own. You will throw papers and cigarettes on the road the moment you touch Indian ground. If you can be an involved and appreciative citizen in an alien country why cannot you be the same here in India.

Once in an interview, the famous Ex-municipal commissioner of Bombay Mr.Tinaikar had a point to make. “Rich people’s dogs are walked on the streets to leave their affluent droppings all over the place,” he said. “And then the same people turn around to criticize and blame the authorities for inefficiency and dirty pavements. What do they expect the officers to do? Go down with a broom every time their dog feels the pressure in his bowels? In America every dog owner has to clean up after his pet has done the job. Same in Japan. Will the Indian citizen do that here?”

He’s right. We go to the polls to choose a government and after that forfeit all responsibility. We sit back wanting to be pampered and expect the government to do everything for us whilst our contribution is totally negative. We expect the government to clean up but we are not going to stop chucking garbage all over the place nor are we going to stop to pick a up a stray piece of paper and throw it in the bin. We expect the railways to provide clean bathrooms but we are not going to learn the proper use of bathrooms. We want Indian Airlines and Air India to provide the best of food and toiletries but we are not going to stop pilfering at the least opportunity. This applies even to the staff who are known not to pass on the service to the public.

When it comes to burning social issues like those related to women, dowry, girl child and others, we make loud drawing room protestations and continue to do the reverse at home. Our excuse:

It’s the whole system which has to change, how will it matter if I alone forego my sons’ rights to a dowry.”

So who’s going to change the system? What does a system consist of? Very conveniently for us it consists of our neighbors, other households, other cities, other communities and the government. But definitely not me and YOU. When it comes to us actually making a positive contribution to the system we lock ourselves along with our families into a safe cocoon and look into the distance at countries far away and wait for a Mr. Clean to come along & work miracles for us with a majestic sweep of his hand.

We leave the country and run away. Like lazy cowards hounded by our fears we run to America to bask in their glory and praise their system. When New York becomes insecure we run to England. When England experiences unemployment, we take the next flight out to the Gulf. When the Gulf is war struck, we demand to be rescued and brought home by the Indian government. Everybody is out to abuse and rape the country. Nobody thinks of feeding the system. Our conscience is mortgaged to money.

Dear Indians, The article is highly thought inductive, calls for a great deal of introspection and pricks one’s conscience too….I am echoing J.F. Kennedy’s words to his fellow Americans to relate to Indians…..

“Ask what we can do for India and do what has to be done to make India what America and other Western countries are today.”

Let’s do what India needs from us.

Clearly, It has all to begin with us, the individuals. Ignorance of our social responsibilities and lethargy will take us nowhere.

India needs a spiritual regeneration

Sri Sri Ravi Shankar (H H) had recently visited Chennai. Having taken The Art of Living classes in school, I decided to attend his classes (three evenings) which were going to be held in the University grounds in spite of End Semester exams.

For a man who could recite parts of the Bhagavad Gita at the age of four, Sri Sri Ravi Shankar, was very different from what I had expected. He has the voice of a small child and yet, when one listened to him it was as though it was as if he was speaking to each one of us in particular. Being born in Tamil Nadu and brought up in Karnataka, he was familiar with Tamil. However his Tamil did prove to be quite a cause for smiles. He was in loss for a few words. Also there was this one time when he said “All of you shout like a lion. Ellarum puli (tiger) mathiri kathunga”.

Yet the image of the man with long hair and intermittently muttering “good good” into the mike is what I’ll never forget in my life. Those three days were really nice (apart from the fact that this was the only real life celebrity I had met after coming to Chennai). A few hundred people had come and the sports ground was filled with people for as far as the eye could see in the dark. This is not much, I hear, when compared to the last time he visited Chennai. Last time there had been no entry fee. The whole of Chennai had turned up to see the Guru who had brought along with him five terrorists. I don’t know what happened then, but I hear that they gave up their arms. Hey, this time he had brought along village women. Well, that was to demonstrate, how come village woman don’t grow obese unlike their counterparts in the cities. But let me move on to the more thought provoking things he said.

When the Art of Living volunteers were helping with the relief operations following the Gujarat earthquake, an old lady came up to one of the volunteers and unfolding a notch in her sari, gave him the only money left with her. Ten rupees. The volunteer politely rejected the money saying that he was not there for money, and that serving those in need itself contented him. The lady in turn replied, “The Earth has taken away all I have. Please don’t take away my Dharma as well.”

Tears well in my eyes as I write these lines. He continued:

“There are such people in the country. There always has been. Do any of you know of Lord McCauley’s address to the British parliament? Good. McCauley had visited India during the early 1800s and when he went back to his country he told the parliament that he had toured the entire country and had seen not one beggar. The people are brimming with spiritual energy. He told them that colonising the country would be impossible without breaking her backbone, her spiritual strength…….. Before they came, Chennai had over a 1000 colleges of Medicine. The first thing they did when they came here was to shut down all of them………”

I have at your service the excerpt from his speech which Guruji was referring to:

“I have travelled across the length and breadth of India and I have not seen one person who is a beggar, who is a thief. Such wealth I have seen in this country, such high moral values, people of such calibre, that I do not think we would ever conquer this country, unless we break the very backbone of this nation, which is her spiritual and cultural heritage, and, therefore, I propose that we replace her old and ancient education system, her culture, for if the Indians think that all that is foreign and English is good and greater than their own, they will lose their self-esteem, their native self-culture and they will become what we want them to be, a truly dominated nation“.-Lord McCauley in his speech of Feb 2, 1835, British Parliament.

And that is what the British have done. They have stripped us of our pride, our heritage, our ancient education system, and our culture. And we remain today, with our compasses steadily pointing west. In two hundred years, we have forgotten ourselves. Swami Vivekananda alerted us “O ye modern Hindus, de-hypnotize yourselves!”

What remains to be done now, Guruji hinted “India needs a spiritual regeneration. We need to remember our culture ”. Yes, I realise, we need to remember who we are. If the auto driver, who throws cigarette butts out of the window and onto the pavement where people are standing, is spiritually in touch with himself, or at least with the moral values our people adhered to two hundred years ago, would he do it? Would a person knowing the glory of this great nation dare to spit on the road? The knowledge of the life that our forefathers lived alone would make us think twice before urinating on the streets. And this will result in a nation infinitely more stronger and integrated than we already are.

Most text books note that of all the ancient civilizations, India’s culture is one that has not been broken through history. Today, on looking at the ancient way of life that is rarely followed nowadays I realise the blissful ignorance we all have been immersed in.