## Archive for the ‘Math/Physics’ Category

Saturday, August 15th, 2015
I had heard from Connie Jones (Secretary of the High Energy Physics group) that Prof. Okubo had written a paper with a Japanese colleague. I helped her put it on the arxiv. She wanted me to help him with publishing it.

Okubo left a copy of it in my mailbox. I read it and left a message with Connie that I would like to talk to him. He came by. We discussed the paper, on certain non-associative algebras. Then he said somewhat uncharacteristically that he was very sick. And in pain.

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Posted in FP, General, Math/Physics, Personal, Philosophy, Religion, Science | Comments Closed

Monday, August 18th, 2014
God is kind to physicists. They get an interview after death where questions which stumped them in life are answered. Most ask about Quantum Gravity.

Wolfgang Pauli too, got his chance.

God: “You have any questions for me? ”

Pauli: “Of course not. May be your staff didn’t tell you who I am ?”

God. “Oh yes, they told me some Pauli stories. And I see what you did there with the matrices.”

Pauli: ” So.. do you have any questions for me?”

God:”Yes. Explain turbulence.”

Posted in General, Humor, Math/Physics, Philosophy, Religion, Science | Comments Closed

Friday, November 8th, 2013
I spoke to Anand, an astronomer at the new ISRO institute in Trivandrum, when I was there in June. He also moonlights as a science journalist and wrote this article about our conversations on mathematics in medieval Kerala.

Posted in Astronomy, FP, General, History, Math/Physics | Comments Closed

Friday, August 7th, 2009
Finally I post something about physics. Here are notes from lectures on mechanics to freshmen at the IISER-TVM. I didn’t have time to edit it. Any corrections ( spelling mistakes, algebraic errors etc.) are welcome. It usually takes me a few iterations to get everything right.

Posted in General, Math/Physics, Mechanics | Comments Closed

Saturday, March 21st, 2009
So that is the payoff. A few months ago India launched a spy satellite for Israel, using its PSLV rocket. So why take the risk of doing a favor for Israel, when the political situation in South Asia is so inflammatory?

Now we know. Indian satellites lack the Synthetic Aperture Radar that can see through clouds and at night. The Mumbai terrorist attack highlights the importance of being able to track small vessels in the Indian ocean and to watch terrorist training camps within Pakistan. The two countries can fill the gaps in each other’s capabilities. And then there is the whole enemy of my enemy thing happening also.

It is not something either side wants to talk about much: (more…)

Posted in Desi, General, Math/Physics, News | Comments Closed

Sunday, October 21st, 2007
Perhaps the most spectacular early prediction of quantum mechanics was tunneling: that particles can do things that are forbidden in Newton’s mechanics, although with a small probability. (more…)

Posted in FP, Math/Physics | 1 Comment »

Monday, October 8th, 2007

Thermodynamics is the study of heat. Originally developed to understand steam engines and such, it led to a revolution in physics. It showed that time has a preferred direction. Also, that physics is not fully deterministic: the best we can do for large systems is to predict averages of physical quantities and probabilities of events. But with the even greater revolutions of quantum mechanics and relativity that happened soon after , thermodynamics lost some of its original wonder. Nowadays it is thought of a staid old field, barely taught in physics departments anymore ( except as a preparation for a Stat Mech course). This is a pity, because thermodynamics is perhaps the most remarkable of all physical theories. We have none other than Albert Einstein vouching for this^{1}: (more…)

Posted in FP, Math/Physics | 1 Comment »

Wednesday, September 5th, 2007
Earnest Rutherford used to say that all science is either physics or stamp collecting. This could have been a dig at the biologists of his time, who were still collecting samples and classifying species. He probably would have thought more highly of modern molecular biology, which is a lot like his physics in outlook: everything is determined by the DNA. It is said that Rutherford’s worst insult for a student who had done something stupid was–*Chemist*. The chemists had the last laugh though: Rutherford was awarded the Nobel Prize not in Physics but in Chemistry for having achieved the transmutation of elements.

Should we understand the world bottom up or top down? Which is the proper scientific view? (more…)

Posted in FP, General, Math/Physics | 1 Comment »

Saturday, September 1st, 2007
It is hard to think of a problem more ubiquitous than the diagonalization of a matrix.I will discuss today a statistical approximation method for finding the eigenvalues of a symmetric matrix. (more…)

Posted in Math/Physics | 1 Comment »

Tuesday, May 29th, 2007
Part 1

To understand the origin of this non-commutativity, let us again consider the example of a hurricane. It is an extended object, whose radius is of the order of 100 km. It wouldn’t make sense to have two such objects within a 100 km of each other: the two hurricanes will interact strongly with each other and combine into a single one. (This phenomenon of a `reverse cascade’ can been seen clearly in some simulations.) Thus there is a limit to the resolution of the co-ordinates of a hurricane, given by the area of a hurricane. This is reminiscent of the uncertainty principle of quantum mechanics, except that there it is the co-ordinates of phase space that is fuzzy: the analogue of the area is Plank’s constant.

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Posted in Math/Physics | 2 Comments »

Tuesday, May 29th, 2007
Introduction to Talk at SIAM DS07 Conference Snowbird Utah May 28th-June 1

The equations of motion of a fluid are obtained by averaging over the equations of motion of the large number of molecules that occupy even a small volume: we are not for the most part interested in the details of the motion of individual molecules. The equations of a fluid so obtained ( Euler or Navier-Stokes) are quite different from those of particle mechanics, being partial differential equations. Nevertheless the fundamental symmetries (translation and rotation invariance) of particle mechanics are preserved in this reformulation.

The conservation laws (energy, momentum,angular momentum) are preserved for ideal flow (Euler). In the next approximation, the effect of the transport of these conserved quantities to molecular scales are incorporated (viscosity). Even higher order corrections from molecular scales can be incorporated ( Chapman and Enskog) but are rarely needed.

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Posted in Math/Physics | 3 Comments »

Sunday, May 13th, 2007
Terrence Tao has made some deep observations on why the regularity of three dimensional Navier-Stokes is such a hard problem. Although he has gone on to many other equally interesting topics, I remain fascinated by his main point there: that Navier-Stokes is **supercritical**. The nonlinearities become stronger at small distance scales, making it impossible to know (using present techniques) whether solutions remain smooth for all time. Thus, it is crucial to understand the scale dependence of non-linearities in fluid mechanics.

(more…)

Posted in Math/Physics | 11 Comments »