Tag Archive for 'Mathematics'

The last week or so has been quite eventful at TIFR. We have had some famous/important visitors who have given public lectures and talks.

The first visitor was Prof. Kumar Patel of UCLA, the Indian origin inventor of the $CO_2$ laser. He gave two talks. The first talk was for graduate students where he shared his insights and gave us some tips. The next talk was about about using lasers to detect explosives and chemical warfare agents. Both talks were interesting but I want to share some of the tips he gave us during his freewheeling, informal conversation with graduate students:

• Be extremely ambitious and try to solve tough problems. Its no point trying to do old, solved problems a new way. Instead, go for fresh problems. Often, the greatest advances have come from scientists who solved problems that others would have considered impossible but out of inexperience the scientist never knew that! Experience can also prove to be a hindrance because it teaches you that you “can’t” do a problem in certain ways. Young people bring a certain irreverence to research that helps them make progress on so-called “impossible” problems.
• What level of research should you pick? Should you pick a system that is simplified to its core or should you study a system in all its beautiful complexity? There is no correct answer. By stripping a system to its fundamental components and modeling its essential features you can learn a lot. But you can loose understanding of the collective behavior of the components. A beautiful example is the human brain…you must understand its basic component, the neuron and their collective behavior. A complete understanding of the human brain is not possible without understanding both. You cannot understand collective behavior of the neurons (e.g. thinking, dreaming, planning etc.) without understanding the basic components and vice-versa. Therefore what should happen is an integrative approach to science: Some people work from top down and others work from bottom up. Both will have something valuable to teach each other. (My idea: We see this in physics today. Astronomy tries to understand huge aggregates of particles in the form of galaxies, stars, planets etc. Particle physics tries to understand the fundamental particles themselves. Both disciplines feed off and fertilize each other. What aspect of science you choose to study i.e. the building blocks like cells, DNA, protons, quarks etc. or complex systems like the human brain, the weather, galaxies, the immune system etc. is a matter of personal taste. All of them are important, worthy pursuits)
• I asked Prof. Patel whether science is for young people only (He invented the laser at a young age of 26). (I’m sort of an “older” student who has commenced his Ph. D. so I was personally interested in knowing whether I could still make an impact. It helped me that my question also was very applicable to him because he was in his sixties!) The answer he gave was fascinating: He said that the work he had done in the last six years was work he could never have done in the past. Its always a trade off he seemed to imply. At a young age you know a lot about a narrow area and you don’t know what is impossible. At an older age you know something about everything but are burdened by “this can’t be done” and so on. Also you just can’t keep up with the level of detail in research. (My idea: At a young age you should pursue a specific line of research to every level of detail possible. At an older age your ability to keep up with this level of detail may be lost but you can think about science which combines different areas. Here your experience helps you).

The next talk was by a French Prof. Étienne Ghys on the Butterfly Effect. The Butterfly effect is popular description of chaos: How a small event can have extremely large impacts on a system. “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” is a one of those questions that have entered the public imagination. I have my own version of the Butterfly effect (intended to be a joke of course)

[Sid Butterfly Conjecture 1] No matter how insignificant or poorly cited your research paper is, like the flap of a butterfly wing that causes a tornado in Texas, your paper will eventually have a earth shattering impact on the world of science

This has another humorous implication:

[Sid Butterfly Conjecture 2] All research papers whether by Einstein or obscure researchers have the same impact eventually.

Incidentally I shared Sid Butterfly Conjecture 1&2 with the French Prof when I bumped into him. He seemed to love it!

The third talk that I want to mention was by S.R. Varadhan a famous Indian origin mathematician from ISI Calcutta who is now at Courant Institute, NYU. S.R. Varadhan was the winner of the Abel Prize (considered the Nobel Prize for Mathematics) in 2007. I have blogged about him here.

Hoping to learn from him, I asked him about the secret to his success. The answer was “you should have passion in what you do”. True, it was boring answer but its worth mentioning here because sometimes the secrets to success are quite simple. We shouldn’t expect rocket science answers to everything. Too often, the expectation of rocket science answers or tricks means that we don’t want to concentrate on the basics (which are obvious but tough to implement) like hard work, perseverance, passion, excellence, time management and so on.

It was inspirational to hear from two Indian origin scientists who have reached the heights of success in their fields. Can I apply their suggestions in my life? Only time will tell.