Saturday, June 18, 2011

The world's most beautiful sea-beach

This last weekend I took a break from my Hensel's lemma and statistical physics of molecular dissociation and cobordism of framed manifolds to travel to some of the far flung places of West Bengal. Places which can be as distant from my familiar world as anything can be. For one thing these are places in unthinkable poverty. One is going to be horrified looking at the life-styles of the localities there. Its way deep into the perforated lower edge of Bengal. The travel to these places is pretty primitive in its ways - travel in a local train, then a boat, then a motorized "bullock" cart and then luckily a car. None of the steps are as comfortable as one would want it to be. While at that place I tried traveling to another nearby island but the plan had to be canceled since the Bay of Bengal turned out to be a bit too rough for the small boat that I had hired. There was always this constant fear of the boat capsizing. I guess one wouldn't be so scared if drowning was a painless death.

Do we fear the fact that we will die or the possibility of the pain during the process of death?

But the first destination where I landed held such a mesmerizing spectacle before me that, I almost instantaneously forgot the agony of the journey till there. It is the world's most beautiful sea-beach. I have been to some of India's major beaches and I know what a mess they are and have seen photographs of many more beaches on the internet. I can't see how any beach in this world can be better than this one. Its just empty! I was the only one on the beach when I reached there. As far as I could see, I could spot neither any other human being or any other human creation. It was nature left alone on its own. It was just beautiful.

Being alone on a vast sea-beach with sand plains all around as far as one could see, one is tempted to feel like Robinson Crusoe :D

Nature looks most beautiful when left alone with me :)

Far away one could see the edge of the mangrove forest and the erosion edges of it. At that end at various spots one could see the dying pneumatophores sticking out through the sand as if gasping for the last breath. Inspite of a lot of locals warning me against it, I did travel to these edges. Here one is mostly scared of various wild animals. Though the only thing I had the fortune of seeing were footprints of possibly some wild boars.

The water was clean as one can imagine it to be. And it brought along to the beach various curious organisms which one gets to read of only in the books. I did see a few starfishes, sea-pens and sea-anemones. It was just bizarrely wonderful to be gazing at this apparently infinite sea in front with vast sand plains behind and no other trace of human civilization anywhere else!

A queer sense of excitement to imagine how the world might have been when humans hadn't yet arrived to destroy it.

I walked and walked along the sea as far as I could go. It was like almost trying to gulp down this immense beauty. Nature when on its own without being bifurcated by human's "narrow domestic walls", feels just a bit too large to take in at once. I sat down to gaze at the serene barrenness. I screamed with joy and shed all inhibitions knowing that no other human is ever going to hear this sound.

But this is in sharp contrast to the horrifying images of human poverty that one has to pass by while in the train. Even the train that one needs to use to reach this place can be nightmarish to someone not used to traveling in such muck and filth almost like cattle packed for slaughter. Its a 3 hour long train journey and what one gets for this long is barely a 1 feet wide edge of a wooden bench to sit on. And not alone! While sitting in this precariously uncomfortable situation, one would be gasping for breath as one gets crushed in by the hordes of people pressing into the train from all sides. To add to the troubles there is the regular flow of the vendors carrying huge baskets of enormous amount of cheap stuff or unhygienic food or even pirated foods. "Pirated" in the sense that one would be selling locally made drinks in re-sealed bottles of the standard soft drinks and even standard biscuits at dirt cheap prices. On asking, these vendors would invariably remain mum about how they managed to do this. Looking at the packets one realizes that they do have manufacturing and expiry dates and batch numbers printed on them. Nothing to rule out that most of these are just stolen stuff. But the exceptionally poor customers who travel on these trains in the dark corners of India have little time for legality and will be content buying just about anything that lets them survive this horrific train journey. (..even among the uptown urban Indians or its best of research institutes, legality is anyway not a familiar concept!..) Given my sophisticated urbanized instincts, I was at my wits end at such nightmarish traveling conditions. I can only wonder how they do it those who do this regularly. At some point of her life, my mother, a doctor, used to do similar travels regularly, albeit a little shorter. There more than the need to hold on to her job to raise her children, I guess she was more motivated by the fact that the village where she was posted was so far away from the mainstream that her one day's absence might mean death for someone.

But at the end of this terrifying train journey, lay the most beautiful sea-beach in the world. A seemingly endless and totally empty and completely clean sea-beach. Conflict couldn't have been stronger!

One couldn't be sitting blind to the images that pass by as the train passes through the outskirts of these abjectly poor regions of Bengal. What unfolds outside the window is a chilling story of systematic government failure and of people leaving in subhuman conditions. The houses one passes by are pretty typical. Its basically a cubicle of dimensions 4ft x 6ft x 6ft and this too will have two floors and will be accommodating anywhere between 5 to 10 people. These cubicles are made mostly of bamboo pasted together with mud and the roof is basically a thatched roof overlaid with a sheet of plastic on which is put up a matrix of old rubber tyres. The living conditions inside these houses is abysmal. The stench is unbearable. No lights. Nothing is clean. There is so little space to breathe that there is surely no space to think. The only question for its inmates is that of survival and the only slogan is to be able to do just about anything to make both ends meet. They are barely protected from any of the slightest of natural disturbances. It won't take much of a strong wind or a drizzle to bring everything tumbling down. The state of the people living in the 2nd floors of these cubicles gets only worse. They could only be lying on some old tattered horribly unclean mattresses on broken beds and rain and wind would be blowing in water and dust into the completely unprotected rooms. They can hardly do anything to protect themselves from anyone. But the bizarre miracle of this conniving world is that when it couldn't provide them with even a sense of respectable life, this mockery of a civilization does bring to these tattered homes cell-phones and televisions. It would be a common meal time scene to see all the inmates sit semi-circularly around a single plate of food and facing the television. The food would hardly be anything more than may be a mound of rice and salt and lemon and chillies and may be a cup of dal (lintels) for everyone.

Looking at these lives, one is soon left searching for even life.

The absolute wonder of seeing the mangrove forests at the edges of Bengal did help forget the pathos that had inevitably shrouded the mind. One is only strongly inclined to put into action in one's daily life the philosophy of the terrific book, "The Life you Can Change" by Peter Singer. At the mangrove forests, nature is playing its own beautiful games of survival albeit with a touch of beauty and comforting grandeur which hasn't ever been the forte of the humankind. One would be fascinated to see stretches of mangroves lean deep into the water and the roots to be rising upwards out of the water. At about the age of 14, I had first read about these pneumatophores and it took so many years to be actually seeing this fascinating natural phenomenon. They are a cradle for a very unique mixture of creatures ranging from cranes to deers to wild cats ("Baghrolls") and various forms of wild boars and other animals. I was still only at the fringes near the sea-beach and the deep interiors which I could see far away are known to be the home to some of the largest tigers.

Since I was putting up in house near to the beach/mangrove itself, nights were no less exciting with all kinds of odd sounds. Sleep would be hard to find with the naive mind's untrained imagination adding connotations to the unfamiliar sounds of the forest!

At a certain erosion edge of the mangrove forest, I did spot the natural phenomenon of a lagoon formation. It was hard to spot from anywhere nearby given how beautifully it had curved inside remaining hidden from the forest cover but I could see it from the top of a tower. These eroding edges are vivid signals of approaching natural disasters. Its clearly because of the rising sea-levels in south eastern Asia which is disturbing the critical salinity levels of the water. One is surely going to feel a chill run down the spine as one gazes at these fields of dying mangroves whose only remnant are the breathing roots sticking out of the mud at various places in clumps of various sizes.

Around these one could keep spotting other small water body formations and if like me one can go down inside the mud in hope of spotting something interesting then one would surely not be disappointed. Initially my efforts were paid back with just a sight of a few snails lazying around in the shallow muddy waters but soon I could spot, a "Mud Skipper". Its a very unique animal whose lungs are disproportionately large compared to its lizard like size and structure. And not just big, the lungs are pretty transparent and they bulge out clearly evertime it breathes outside water. It can also live under water. Mud Skipper's are evolutionarily very important since they are the "missing link" between the life that evolved first in water and when it started to come on land.

These still couldn't take away the show from that of a sunrise on this vast, empty, open and sparkling clean beach. It was a sight to see. Just at dawn the sea-anemones would be curled up and as the sun rose they too seemed to pull up their tentacles. I didn't care whether it is harmful but I did touch the slimy sticky tentacles. Just for the experience! One couldn't but help feel connected to a pantheistic emotion as the sun shimmered across the white and golden sand smeared flat and seemingly endlessly around. I walked towards where the red crabs lived and most ran inside their holes as soon as they heard human footsteps albeit from very far away. But still I did manage to get some photographs of their crowd and some of them individually. When they are collectively out, they would make stretches of the sand looks red from away! And pretty much ubiquitously one could see the much smaller and colorless hermit crabs scurry between the legs. Here there would also be dogs who seemed to manage to sniff from outside whether a certain hole in the sand had a crab and could dig it out and maim it. But it didn't seem to have any intentions of eating them. As the sun kept rolling higher up behind me, I crossed these regions to walk to the eroding edges of the mangrove which I described earlier. Here the land would get tricky and marshy and it turned out to be beneficial to pull down some of the long branches of these trees and use that to test the land stability before setting foot any further.

It was too hard to leave this most miraculous sea-beach and return to the shackles of this unfair world of the only war-mongering form of life.

Is evolution necessarily eventually suicidal?

Wednesday, April 20, 2011

My Buzzes on Indian team's winning the Cricket World Cup 2011

As and when my project with calculating some queer notion of "cohomology" in some funny superconformal theories gets stuck, I get back to Buzzing about various stuff. Lets me take my mind off. And surely I was documenting the run up to the cricket world cup win by the Indian cricket team.

For me the important thing was not just that the Indian team won but that the final was almost single handedly won by Gambhir and Dhoni. I was especially delighted by the title clinching contribution of Gambhir. What a game to watch and it asserted so many confidences I have had about these two people inspite of the criticism launched at these two people by the crowds in general.

So here are my Buzzes on this historic event listed in reverse chronological order,

* Documentary on Dhoni

* About Gambhir

* Bharat Ratna for Sachin

* Nehera on this last over against South Africa

* The last moments of the world cup final

* Amitabh breaking his superstition with the world cup final

* About Gambhir and Dhoni

* My mother's quip about Dhoni

* About Dhoni and Kirsten

* Why cricket connects so well with Indians
* Reactions of player's families

* The day the Indian cricket team won the world cup

* As the Indian openers collapsed during the final

* Before the India vs Sri Lanka final began

* Someone cycled 1500km to watch the final

* India defeating Pakistan in the semifinals

* Shahid Afridi

* Before the India vs Pakistan semifinal

* Frenzy about the India vs Pakistan match

* India defeating Australia

Monday, March 7, 2011

Buzz on Rabindrasangeet

Almost as a matter of principle I don't write blog articles of small lengths. (anyway I hardly write anything that most people will call short! Most of my regular emails to my regular contacts are at least 1 page long and not so rarely much more longer :D) I try to ensure that all my blog articles are some accumulated thoughts (hopefully coherent!) about some topic over a long period of time. But in the process of writing blogs over these years I found that apart from these accumulated thoughts there is a continuous stream of thoughts of short lengths which get lost without appearing in public. I believe that every thought which is not expressed at least in private to someone is basically wasted and its best if every thought is made public. GMail Buzz provides a good recording spot for all these and its been an year since I have been Buzz(ing).

Hence if someone of you wants to be tuned into these they can read my Buzz as well. So let me link you to that using as a cue a recent Buzz I wrote about Rabindrasangeet.

As you can see by following up on that link that the Buzzes after that have been on various other topics. Some have been with the intention of highlighting some news article or to advertize for someone's paintings or blogs or on supersymmetric Chern-Simons theory (something I am pursuing these days) and the latest one is about Zorn's Lemma.

Saturday, August 21, 2010

Festival of geometry

These are those rare occasions in life when it becomes possible to concentrate on things completely surreal  without getting too much affected by the mortal issues. In general I do find it difficult to concentrate on doing my science after I have a had a walk along say the streets of Mumbai and seeing people living on them in abject poverty. And I have no reason to feel optimistic that any science I ever do will help them. This depresses me at some sub-conscious level. But then probably my love for ethereal surpasses my mortal pains. This ICM Satellite meet at IISc on "Geometric Topology and Riemannian Geometry" that I happened to be selected to attend was not free of such aspects. The key facet was the intensity of the mathematics and the opportunity to meet people with similar interests. (as I have never done! It is quite a rejuvenating experience to spend hours at a stretch talking to people who are all interested and intrigued by the same questions and issues.) The palpable thrill of being able to discuss geometry with professional geometers did help me take my mind off such nagging issues like the food which was unhealthy enough to make me and some others sick (looking at the correlation of events the suspect is the restaurant called Nesara inside IISc), that the bathrooms very often had no soap and that for some queer reason students from Princeton in similar stage of their PhD as me were put up in hotels. (whereas I got a student hostel to live in which was at least way better than the terrible accommodation that I had gotten when I last visited IISc as a KVPY fellow some 7 years ago) I have no clue why this discrimination was done but when I pointed out this seemingly racist arrangement to one of the organizers I got back some gibberish like "you are not equal to them" and "foreigners are not allowed to live inside the campus" etc. I was almost being tried to be given the impression that my fellow Princeton student was paying for his hotel (clearly this is false as I found by cross checking with them) whereas I on the other hand was being given some 800Rs as DA. (with no harm to me I could have easily returned back the 3500Rs odd of TA/DA but given the scenario such an act of mine might have been considered indecent!) As far as I can infer from experiences (may be I am wrong) even TIFR probably as some policy like this whereby every random grad student from outside India when lands up here will get a guest house room in the campus which is almost always out of bounds for similar standing Indian student visitors. Anyway when I first visited TIFR as a summer student I was given an accommodation so far away from the campus that I found it more beneficial for academics to spend my nights sleeping on the sofas and taking bath in the night-guard's bathroom.

The conference did start with some very dubious facets like an Internet arrangement that was yet to be set-up when I arrived. (apparently I was "very early" by arriving one day before the start). The travel instructions somehow seemed to say that there will be someone waiting to receive the visitor at the airport if one arrived by plane. Of course people like me who can't afford to travel by planes had to struggle around to get to the conference location. (Interestingly 7-years ago KVPY organizers had arranged for a pickup when I arrived on plane for the summer camp} {some fancy for the "sky-people"? (Avatar!)} Even when the Internet facility was set-up it was under lock and key! So there was no way I could have accessed the Internet without first wasting quite a bit of time running around to figure out which volunteer had the key. Clearly at night it was impossible to do this. By the time the lectures ended and I got some breathing space to check my emails the mathematics office considered it to be the end of working hours and hence locked the computer room meant for the visitors! Thankfully some of the volunteers after a day or two realized that I am the only one around who is using the Internet facility and they let me keep the key. (Most others had laptops who connected using the wifi in the conference hall)

Some students in IISc apparently mistook me for a prof! (happy to know that somehow my face didn't look like some teenager's to them like many strangers think!) and some people observed to me,

 "Why are you so happy the whole day? Why do you always have a smile?"

Never heard that from anyone!
  Anyway coming from a formal background in Physics it was an interesting experience to attend a mathematics conference for the first time. It was fun being the only Physics student in the midst.
It was quite an experience to attend a Hindustani Classical music (on Clarinets) concert by Narsimhalu Vadavati with a bunch of some of the best mathematicians. (weirdly enough the Japanese people seem to have been visibly enjoying what looked quite cacophonous to me!) The very low quality of the music left me depressed. Definitely India has far far better music to showcase to the world. Add to that the fact that the acoustics of the hall at National Institute of Advanced Studies (NIAS) were pretty bad with the ear splitting at the higher pitches. And then the power fails for a few minutes during the concert drowning us all in total darkness. Though not the first time. It happened the same way when Hutchings (from U.C.Berkeley) was explaining to a full packed hall the mysteries of the geometries of soap bubbles. (Interesting that we still don't have even a conjecture about what the shape should be for more than 4 bubbles together!) Such organizational fiascoes from the Indian side leaves me pretty much embarrassed while sitting in the crowd amidst an international crowd.

Hutchings amazed me by his conspicuous silence throughout the conference whether during lectures or during tea-breaks. It is hard to find someone who so rarely ever talks! He never asked a single question nor did I ever see him interacting with many others. But it was endearing to see his childish enthusiasm and smile when on stage explaining even utterly complicated stuff like his recent discoveries of new obstructions to symplectic embeddings in 4-dimensions.

I had a quite interesting conversations with Fernando, a Riemannian Geometry prof from Brazil. (After all one of the standard texts in the subject was written by doCarmo, a Brazilian). Fernando's talk was very neatly organized which made it very appealing to beginners like me.

I had some very fruitful conversations with this guy Aron Naber . He did his bachelors in aeronautical engineering from Penn State and then did a PhD in Riemannian Geometry at Princeton under Gang Tian! During his PhD he completely classified all Ricci Solitons on 4-manifolds. He is just 1 year into his post-doc and he has been invited to speak at ICM satellite meet!

Interestingly he wanted me to explain to him what are sigma models! That is a very exotic QFT thing. Wonder why is he interested in it. He tells me that people are smelling that the good old idea of sigma models in QFT have some deep Riemannian Geometry hidden in them! I explained to him whatever I knew about sigma models. 
Aaron's knowledge of geometry is awesome and I gained a lot from him.

He shared with me his various insights about Ricci flows and solitons.
I got pretty much charged up to follow up further on this topics.

Interestingly Shiraz (with whom I have very regular interactions in theoretical physics) had some insights about what are called rotationally invariant gradient solitons years back in this paper of his. It seems that there quite a non-trivial interest in being able to see if there is a cause-effect relationship between existence of a Kahler-Ricci soliton on a manifold  and flat (in any sense) metrics on the cone over it. There are some technical conditions on this base manifold like it has to be
compact complex manifolds whose first Chern number is positive (Fano Manifolds)(examples being the projective space probably)     Apparently if the manifold is Einstein then the cone is probably Calabi-Yau and that is apparently of interest in physics.

Some other examples of interesting open questions which excited me were,

{not that I understand the exact issues but something tells me that these are interesting}

* If you start with a negative sectional curvature metric then is/when the constant scalar curvature metric in its conformal class also of negative sectional curvature? The problem seems to be that being of negative sectional curvature is an open condition and hence it is not clear as to whether it is preserved under Ricci Flow.

* Are there hyperbolic 3-manifolds with a foliation whose leaves are minimal surfaces?

* Seems to me that there is quite a serious problem in finding an analogue of Heegard-Floer homology for 4-manifolds. (The motivation being that Seiberg-Witten invariant for 4-manifolds is analogous to the Alexander polynomial on 3-manifolds)

* People seem to want to know whether a hyperbolic 3-manifold is always finitely covered by a fibered 3-manifold. 

* It seems that there are some topological restriction to putting hyperbolic metrics on spaces and it is not known whether one can put an hyperbolic metric on surface bundles over surfaces.

I hope that at some point in future I will get time and opportunity to spend time thinking about these.

Here I mention some basic issues that I discussed with Aaron and gained clarity about,

* Transitive action of the isometry group on the tangent spaces does not guarantee that it will take an orthonormal basis to another. In some vague sense the number of orthonormal basis in a vector space grows exponentially with the dimension and just transitivity can't match up. Being "maximally isotropic"  or "maximally symmetric" (both meaning that they have n(n+1)/2 Killing fields or that is the dimension of the Isometry group) is necessary to make the isometry action be transitive on the set of all orthonormal basis of a tangent space (and make sectional curvature constant). Thats what happens for the euclidean planes, spheres and the hyperbolic planes and also for the FRW metric in usual cosmology.

Basically the idea is that homogeneity and isotropy is not enough to get constant sectional curvature. Homogeneity alone gets only scalar curvature constant and isotropy at a point gets only Ricci curvature constant. (it basically maps every 1-dim subspace isometrically to another and Ricci basically depends only on a basis)

Homogeneity and Isotropy together hence give only a constant Ricci curvature manifold.

* If you can act on a constant curvature (probably in any sense) by a discrete subgroup of the isometry group then you end up as a quotient another constant curvature Riemannian manifold whose fundamental group is isomorphic to the discrete subgroup you started with. But whether or not the quotient is compact and whether what its genus will be (if definable) are much harder questions.

I had come across this concept while I was trying to understand some paper of Witten's where he seemed to be creating solutions of Einstein's equations by acting on the hyperbolic plane by discrete subgroup of isometries of that.

One more interesting piece of insight from Fernando's talk that I ruminated over during these is that from the Gauss-Bonnet it is not so hard to see that on a torus if the sectional curvature is always non-negative then it is surely 0.

Now it seems that this kind of "rigidity" theorems also hold in higher dimensions but they get enormously harder and only work case by case.

The statement for n-dimensional torus was due to none other than Gromov and Lawson.

A particularly interesting generalization of this is by Schoen and Tau who showed that "mass" as defined in General Relativity always has to be positive. (intuitively this should always be true but this was far from obvious from just the Einstein's equations). Apparently there is a more sophisticated proof of it by Witten using Penrose's twistors. (I guess this is the same Schoen who proved the famous Yamabe conjecture that on compact manifolds every conformal class of metrics has a constant scalar curvature metric)

A general idea behind these rigidity theorems is that given a manifold with a metric a compactly supported metric deformation cannot change the scalar curvature. This is something that I would like to understand further.

I also met this very eloquent PhD student at Princeton called Nick who is looking into Conformal Geometry (under Wang). I got along very well with him. He happens to be a batchmate of Arul (he was one year senior to be at CMI). Among the many interesting quips he made about Maths and doing a PhD, one was, "If you really like someone then you should get married otherwise one marries either before or after a PhD". {Of course getting a PhD is simpler than that!} This came up in the context of Aron having already married while only 1 year out of his PhD. (of course there were rumours about who will get the Fields but now talking about them is pointless, but definitely it is completely exciting that half the Fields medals have been given for proving conjectures in condensed matter physics and one can read a short very insightful review of them here by none other than Terence Tao, another Fields medalist himself) Though Michael Usher said, "Fields medal? Who cares?" (Usher gave a very nice talk with lots of motivations!)

Interestingly Nick tells me that given the hugely depleting number of geometry students in his place he is very lonely in his working. (On my side geometry definitely looks almost extinct!). And he tells me that many students in Princeton work for long hours alone and rarely ever talk to others. (interestingly he says he is one of them though I found him quite loquacious!)

Good to know that I am not the only lonely one around. (as one often feels in TIFR where the rest are always huddled into groups doing some calculation which I don't find interesting)

Nick and I chatted about everything under the sun from windmills to conformal metrics and a lot about student-advisor relationships and the hiccups about beginning research. We talked quite a bit about the issue of building pre-requisites for research. (so many things in Riemannian geometry end up being questions in Cartan's classification of semi-simple Lie Groups. How many geometry PhD students know the proof of Cartan's classification? Nick tells me none!)  It was nice to find someone to talk to about some of these issues which have been also puzzling me off-late.

Nick did his undergrad from Washington-Seattle.

Nick tells me that at Princeton many people work completely alone and since people don't have to attend classes together there is very little bonding between the people. He says that people at U.Chicago form a very well-knit group since they go together to classes. We talked about which is better, to have regular classes and courses or to be left alone to read as in Princeton. 

Aaron's wife works as a counselor in some "Residential Home" for "crazy teenage girls". They are basically taking care of lunatics and helping them rehabilitate them. Aaron says that such social work is simply horrible life since there is lot of work and she gets paid zilch for it. He tells me that he would for nothing on earth take up social work as a career. Apparently it has been listed at the top of some recently brought out "never take up" jobs list. Apparently Mathematics is at the top of best jobs in the US! He didn't lose chance poke at me by pointing out that Physics features somewhere in the 6th or 7th position.

I met my CMI prof KV at the joint dinner between the geometry and the representation theory conference. He asked about my whereabouts and seemed pretty friendly to me. He has also been following on the Vinay Deolalikar stuff and he says that people are apparently convinced that the proof doesn't work but something interesting might be going on.

I also got saw the legendary Kashiwara around. Though I didn't talk to him.

On the mathematical front I was quite enthralled by the talks given by Ron Stern and Ron Fintushel. Awesome people. It was quite exciting to talk to them too. Stern tells me, "One learns Seiberg-Witten Theory if one really wants to learn it". And anyway one upshot of many of the talks was that I should get excited everytime I hear of a lagrangian submanifold of a symplectic manifold. Apart from just a rewriting of good old classical mechanics I had not taken symplectic forms that seriously. Seems I should. And also I had never taken a keen interest in spaces where the dimension is not constant even on connected components. These are of course not manifolds. But then they are very exciting in Riemannian Geometry. For one thing these don't have a well-defined notion of "tangent spaces" but have "tangent cones". And more curiously these might not even be unique. From whatever Aaron says it seems to me that these are known in Physics as "orbifolds". I wonder if they are the same things. Aaron has proved some rate of growth theorems about the dimensions of these stuff for lower bounded Ricci curvature spaces and the formulas looks like Holder Inequalities. (strange!)
 Andras Stipsicz made this very thought provoking statement while analyzing the path-breaking work of Sucharit,

{Sucharit and 3-manifolds have become almost synonymous now!}

"3-manifold are like prime numbers" 
Sucharit's talk was one blitzkrieg of intelligence overflow.

He made his intentions very clear by his opening lines,

"All this is very interesting to me but will be either known to some of you or will be simply too overcomplicated. Hence I will go fast anyway"

He set up an algorithm by which any link could be written as a grid diagram (like Tic-Tac-Toe) and a set of moves on it which basically mimicked the Reidmaster moves and showed that all his moves give cobordant links. Then he constructed a hugely complicated derivative operator which sums over some very queerly chosen blocks inside that grid and miraculously its composition with itself is 0! And hence you have invented a homology theory.

Now the biggest miracle is that this is precisely the Heegard-Floer homology.

Sucharit says,

"The definition is too complicated but it comes out naturally"

Except probably Andras and Siddharth nobody asked a question and the entire talk ended with the same eerie silence as it went with.

Anyway on a larger scale it does seems to be quite a big thing to do to be able to see in absolutely unexpected places interesting dimension lowering maps whose self-composition is 0. Thats the name of the game. You have discovered a homology theory! Things are miraculous if that gives a finite process of counting in the space of maps in some other well known homology theory.

Pursuit of geometry does bring one to very endearing events in life.This guy Nick from Princeton was very nice to me.

He said to me "I think you should definitely meet Gabai" and he introduced me to David Gabai! It was quite an opportunity to get to talk to this legend.

I have been startled by the exuberance and energy of Gabai. I don't know of of many students in their 20s who are so excited about mathematics as this some 60 year old guy! He always had a sparkling smile on his face and was always scribbling on with something or the other in mathematics. I was just stunned by this guy's never ending energy to talk about mathematics and always so with a huge smile on his face!

I also saw "Mahan Maharaj" around apparently one of the very famous "swamis" at Ramkrishna Mission/Ramkrishna Mission Vivekananda university. He allegedly secured a very high rank in the IIT entrance exam in 1987, the same year Rajesh Gopakumar topped it. Rajesh did his PhD from Princeton and Mahan did his from Berkeley. As far as I hear after some more years around as post-doc he gave up normal life and took "diksha" and became a "swami" living that stern life.

Mahan is pretty famous for his work on hyperbolic manifolds and what are called "ending lamination spaces". I have heard a lot about him from 2 of my acquaintances who have studied under him during their undergrad. He has apparently been working very hard with the organization at his place to make subjects are differential geometry compulsory for Physics undergrads and subjects like Conformal Field Theory and Classical Mechanics compulsory for maths undergrads. He has had partial success.

Finally I saw him around here. David Gabai seemed to be very fond of him. Mahan has an awesome physical built!

He gave his seminar wearing that typical saffron coloured kurta and beneath a saffron coloured wrap around dhoti.  His talk was about some partial solution of the Hilbert-Smith conjecture. His was clearly the best Indian talk. (compared to unspeakably bad talk by Ramesh Sharma and add to that his distractingly irrelevant mention of some calculation tricks in "ancient Indian mathematics" at the beginning of the talk) Mahan had an awesome level of confidence and a charismatic speaker. His intelligence was almost palpable. Fintushel one day came up with a question as to whether every involution on the product of two Riemann surfaces of different genus splits as a product of involution on each. The very next day Mahan went up on the board and gave a proof for it. In fact he proved a stronger statement that it splits for any discrete group action. (or something like that). Interestingly it was Fintushel's birthday on which Gabai said ,"This is Mahan's birthday gift for him" Gabai said that "I won't reveal Fintushel's age but he now qualifies for medical aid"

Gabai led the congregation to sing a "Happy Birthday to You" song for Fintushel to which he replied, "I thank you all from the bottom of my heart" The camaraderie between these stalwarts in geometry was very inspiring.

I am not just irreligious but anti-religious but it doesn't stop me from appreciating Mahan. This guy can go around as a brilliant mathematician and except for his dress there will be no reason to see or know of his such queer affiliations. Thankfully he doesn't wear his religion on his sleeve.

I planned out a dinner with Nick and I was wondering if he would make it to the appointed spot treading through this so complicated campus with innumerable lanes and forests. And I was overwhelmed when around the meeting time I saw Nick standing by the side of the nearby jungle poring over a map of the campus!

I went up to him and saved him further trouble to what already he had taken up to find his way through this labyrinth to come and meet me.
I was simply overwhelmed by this gesture. I don't remember the last time I was at the receiving end of such efforts!

Over dinner we managed to talk about a myriad of topics. Nick asked me about my family and he wondered "So does your entire family do mathematics?" !
Then he asked me whether I have brothers or sisters and whether they too do mathematics. He told me that he has a brother who is also a maths undergrad at Washington university. His father is a chemist who "works with fishes for the government" and his mother apparently used to check car license certificates but gave up the job after he was born. And his mother was 42 when he was born and he also a brother! (My mother is currently 42!) He gave me a long lecture on what he sees computers to be able to do by 2050. In this context he explained to me how using ZFC one can code every mathematics proof as a sequence of symbols drawn from a finite set and how using some simple rules a computer can be made to check in finite time whether this proof is correct and how this implies that in principle a computer can also come up with a proof given a statement. And how this entire thing relies on Godel's incompleteness and how this is impractical because of time-complexity issues. Apparently Russel was the first person who showed that this can be done and using this coding technique he took 77 pages to prove that 1+1=2! (But this is important since that is apparently the only way known by which a computer can be made to understand the proof of 1+1=2. It is also apparently the first example of a computer comprehensible mathematical proof and very few such examples are known) Then he went on to explain to me how using the axiom of choice coupled to this technique one can make the computer understand statements like "take any 2 points in the topological space". And how this connects to "Model Theory"

Interestingly he has picked up all this while he did philosophy courses as a maths undergrad. This is very interesting that philosophy courses end up teaching so much of deep mathematics. (Philosophy courses as I have seen some Indian students do in Indian colleges is just pathetic nonsense)

He imagines that the time-complexity issues of coding proofs will be the next big thing computer technology is going to achieve. All this while he was so excitedly and animatedly explaining it all this, he seemed to clearly forget that there are other people around in the restaurant! We went on to talk about Avatar, Harry Potter, Lord of the Rings, Celine Dione and Crisswell and Golem! (comparing the similarity of the technology between how Golem and Avatars were created)  Then the discussion shifted to cooking and had a laugh comparing each other's astounding cooking skills. (He has gotten addicted to Chicken-Tandoori and Garlic-Naan and thats what we ordered. I introduced him to Lassi which he found awesome) He seemed to have had a very interesting undergrad where he took 5 years to get an MSc from Washington-Seattle. In those 5 years he did some 10 undergrad courses and some 20 graduate courses. And he had the opportunity to replace the undergrad algebra courses where Artin is covered by 3 quarters of Algebra courses where Dummite and Foote is covered. And he took one full graduate course on curves and surfaces! (Its a terrible state in India that people can get BSc. in Maths never having done any theory of curves and surfaces like the ones in the book by Pressley or Singer and Thorpe). While in Washington he did 3 courses in differential geometry where basically the 2 books by Lee were done. (I have read most of Lee's second book and it is beautiful) His complex analysis course looks very inspiring to me where they took 2 quarters to do Ahlfors' book thoroughly! They spent about a month learning how to do real integrals using contour integration and doing those curious summations using complex analysis. I was mentally comparing to that the terribly unspeakable Complex Analysis course which I did in CMI where that horrible compressed book by Remmert was declared to be over in 4 months and never ever was using contour integration to do real integrals discussed and that was called a misuse of complex analysis course! Thankfully I have picked up a lot of that given the efforts of Amol to make us go through that in details, Probably the most (of the rare few) important things I learnt in any TIFR classes. It was simply impossible for me to understand from Cauchy-Riemann Equations to Casoratti-Weirstarss theorem in 4 months. (as was attempted in one of those rare bad maths courses in CMI) A first course can at most go up to Riemann Mapping Theorem or at best Picard Theorem but even that was not done (judiciously so) in this Nick's college even in 6 months.

Nick told me of his experience of meeting Terence Tao when he visited UCLA before applying there. He was completely awed by that guy (and why shouldn't one be!). Apparently Terence took him out to the botanical garden and showed him around all the curious plants they have. Expectedly Nick says that Terence was probably one of the most friendly and kind people he has ever met. They did discuss some mathematics about what Terence was doing then. Never did it become an issue that he was talking to probably one of the greatest thinkers ever. 

I had decided to pay for the bill but Nick put up an enormous protest and he wanted to pay. He was under the impression that I was an undergrad and when I told him that I get a stipend he agreed to reduce his stake to 70% of the bill. He said that he will pay the full bill if I ever come around to his place.

Post dinner we had a walk where he came up to my accommodation to see where I live.

Probably one of the best of the rare few dinner outings I have ever had.

I ended this trip by meeting an acquaintance of mine in Bangalore whom I technically know for the last 22 years but haven't met for many years in between. Interestingly while out with him I witnessed the upcoming Bangla band "Backbenchers" perform life at PlanetM. It was quite impressive.

Saturday, June 12, 2010

A life through links

In this ever resource constrained world thanks to the struggle for whatever little there is up for grabs, it is getting easier and easier to label people. It is getting harder to control the addictive simplicity of boxing people into narrow containers of  what the classifier wants to see. It has become so hard to refuse the convenience of seeing people as taking sides if one argues for a cause. It is so easy to hold the resources hostage to bargain social compliance. 

Like in the wake of incidents like Dantewada, one dare not rise up for the people in the Gadchiroli village, you might run the risk of being called a Maoist (which has become synonymous with being a terrorist probably not without good reason).  One dare not say the prof is teaching completely wrong stuff lest one faces social backlash. One better be careful to decontextualize every academic discussion so as to not hurt the egos of someone powerful but has no clue of the academic content of the discussion. (We have now new names like "diplomatic skills" or "soft skills" as euphemism for bad words like "playing politics") One dare not speak against nuclear energy if one is taking salary from the Government of India, or worse from the Department of Atomic Energy. One dare not show contempt for pro-women political smooth-talking  lest be threatened to lose potential life-partners.

In this world of threats and arm-twist bargains that I live, it is only getting harder to say the truth, blog, have a chat, publicly discuss, argue, Buzz. I was so naive when I thought that science is all about rational thinking. I was so stupid when I believed that precision and correctness though not the forte of politicians does find appreciation in science.

Growing up is all about disillusionment.

I thought trying out here another form of political smooth talking that I have unfortunately learnt being in academics, avoid the risk of having to show courage of saying something on one's own by filling up writings with web-links. 

So here I list some of the web-sites which I have been following for the past few months,

* You-tube like non-English websites this and this one.

* Homes pages of some students in Berkeley whose academic interests largely overlap with mine Kevin Lin, Schoemmer Pries, and Theo

*  Witten's QFT lecture notes, fall and spring.

* Some papers on the importance and validity of intelligence and its measurement like, this one , this Gladwell's article, on the importance of g, this blog on intelligence measurement, this article in NYMagazine, (though I have strong objection to this practice in New York schools as explained in this article), and this one about there being so few girls in mathematics.

Inspite of all the research one is still left waiting for the Indian education system (especially the Physics ones that I am more familiar with) to recognize the importance of intelligence and more importantly to recognize that "specific skills" are not to be confused with "general intelligence", the former have a lower cognitive floor and is trainable. We can't skew the system in such a way that "skills" become more important than "intelligence". Just because one can repair broken cars one is not a mechanical engineer. Just because one can do large integrations fast or use Mathematica or can write C++ programs one is not a physicist! 

* An interesting CFT paper

* Discussion on the Feynman Path-Integral at MathOverflow, one, two, three and four and the references within. 

* A writing on renormalization group

* Once in a blue moon there happens good/interesting courses in TIFR like this, one by Sunil Mukhi and the other by Shiraz and this one by Amol.

* A beautiful article on the problems with economic reforms in India by Swaminathan Aiyar. This is website provides a good open-source collection of articles on socio-economic issues. Unfortunately not everything is open-source here. 

* Home-page of Avi Loeb and CFA
  Avi Loeb's papers are a joy to read. I recently had some interaction with him while I was preparing for this talk I gave recently. This also brought me to interact with Jonathan Pritchard.

* I was skimming through these papers from the Poverty Action Lab ,one, two, three and four.

* An interesting blog by a taxi driver in Singapore.

* Steve had something to say about Noam Chomsky here.

* A beautiful song by Greenday and this addictive one by Shakira.

* A organization called BloodConnect for organizing blood supply during emergencies. An acquaintance of mine was one of the founders of this.

* Stories by Anderson
* An article in this new e-magazine devoted to reporting on the Middle East.

* MIT OCW's Algebraic Topology, basic, advanced, more advanced.

* An article on evolutionary reasons behind psychological differences between men and women.

* Trying to understand complications of immigration from this article from here. This is another amazing open-source collection of articles on economics.

* MIT World

* Berkeley Lectures 

* An organization called "Boond" which looks promising. 

* A beautiful photoblog.

* Etingof's course on the interface of geometry and QFT

* A book on QFT which I can freely access because TIFR has subscribed to it.

* Two amazing lectures at TED on regenerative medicine and artificial limbs

* An article on possibility of space-travel

* Have been looking through these articles by Tim Gowers and Ben Green.

* Dror Natan

* Have been reading through QFT and CFT notes by David Tong 

* 3 books on Riemannian Geometry that I realized I can freely access because TIFR has subscribed to it. One be Jost, by Besse and one on Twistors. I have read mostly from the book by Jost and I like it whereas I haven't explored much of the other two. Associated to this is this recent discussion I had on MathOverflow.

* Some good articles by M.V.Ramana explaining a super-obvious idea as to why pursuit of nuclear energy should be stopped and especially India should not invest in any nuclear power and how terribly flawed is the current state of operations and possibly coming up laws on nuclear reactors in India. Its high time we come back to common sense and stop going gaga about people who were instrumental in bringing nuclear energy to India and those who have been hard-selling this self-defeating nuclear dream.

This is another beautiful article by M.V.Ramana along with my friend Suvrat explaining the problems with the cap on nuclear liability.This one is by Suvrat alone.

A  malfunctioning at a nuclear power station can within seconds put these numbers of 19000 dead of Bhopal look like a small mishap, something these days Indian media is suddenly excited about. The verdict was yet another example of the barbie-doll status of the Indian judiciary and the administration and more importantly it proves that every Indian is valued between $500 and $2000 by the Indian Government.

Monday, April 19, 2010

For Sashi Tharoor

I rarely take serious note of any political event in India. Definitely not seriously enough to write a blog about. And never have I blogged about any one single person centric event. But this time with this forced resignation of Sashi Tharoor, I am seriously perturbed.

First of all I know Sashi Tharoor only as much any lay man knows from his websites and public statements. But I have known about him since a long time from he used to be the under-secretary  general to UN and later executive assistant to Kofi Annan. More because as far as I remember he happened to have studied at the St.Xavier's Collegiate School Kolkata where I studied from Class 7 to 12. If my memory is not failing me badly I remember my english teacher there Mrs.Ranjana Bhattacharya telling me that Sashi Tharoor was in her class. I also happend to be in Ranjana's class quite a few times. A very charistmatic english teacher who started off by giving me the near failing marks in the beginning and scaring me to death with her principles but ending with giving me the highest scores in my final english exams. Getting almost full marks in her english correction scheme is not a cake walk. 

The basic point that is far from clear is, what is the crime? In no allegation that I hear people putting up against him is there a crime! I see no victim! He apparently "influenced" Sunanda Pushkar's getting a stake in the IPL Kochi team. So what? What prevents me from helping a friend of mine get something as long as I am not breaking the law or infringing into the rights of some more able candidate?

There is no clear allegation of crime against him as far as the news reports go. I suppose he probably being unfamiliar to Indian politics became just an easy target.

I believe our home minister Chidambaram is a very knowledgeable and respectable man and he has also stated that Sashi Tharoor didn't benefit from the IPL bid. This statement obviously has no legal value but is definitely important.

It seems more to me that it is hurting the deprived sensibilities of some people to see an "elite" in a high post. If this results in me being labeled an "elitist', so be it.

There is little doubt that very few people in the Indian parliament have the level of know-how of international politics as Sashi Tharoor. Goes back to his extensive involvement in the past notably with the peace processes in Geneva and Yugoslavia. It is hard to imagine a person with such extensive international experiences in the Indian government.

Now isn't the cost that India incurred in losing his know-how quite substantial?

More importantly, why are the people who have something against Sashi Tharoor not filing some police case against him and take to proper legal route if he is suspected for some crime? Why just create a ruckus in the parliament and cause personal embarrassment? 

Deplorably it isn't unusual in India for a technical problem to be turned into a personal mud slinging.
Even in research institutes during scientific discussions!
Unfortunately Sashi Tharoor hasn't been spared either.

And this isn't the first time. His tweeting has wrongfully been repeatedly pulled up against him many times. We as a nation don't seem to really believe in freedom of expression and all this hue and cry about maintaining secrecy about government policies is just arcane psychology to say the least. Wonder when people will realize that paranoid secrecy in the functioning of an administration is the perfect womb for corruption.

In India one is free to have an opinion as long as it agrees with the person higher up.

His comment about not enjoying a holiday on Gandhi Jayanti was definitely a good point and didn't obviously go down with the section of people who mysteriously feel that holidaying is a great way to show respect to a person. I think if not anything Gandhi was at least quite a hard working guy. We even give holidays for voting!

Here we see not just causing personal embarrassment to a person but a signal to the intellectual class of the population. "Stay Away".  The entire Sashi Tharoor episode casts a deep shadow on the sensibilities of the Indian parliament and its sensitivities about the upper educational echelons of India.

There seems to be a systematic (deliberate?) disconnect between every Indian administration body and the intelligent educated Indians.

It in someway comes as a very little surprise since quality education never really was in the priority list of the Government of India. It has always been focussed on opening "more" institutes than to build even a single best-in-the-world institute. It continues to live under the self-defeating delusion that quantity can substitute for quality.

We as a nation are still far away from realizing that education is NOT about being able to turn knobs of some machines or read and write or even being able to compute some Feynman diagrams! Education has to beget ability to have researched opinions. Now you cannot expect people to get more educated and yet have no opinions in the public. Civilization is essentially characterized by the extension of the means by which every opinion can get heard in the world and resulting in more and more sophisticated public discussions. Democracy by discussions is an idea championed fiercely by Nobel Laureate Amartya Sen. We have moved from speeches to posters to books to web-pages to blogs to Orkut to Twitter. The Indian administration has to realize that they cannot live under the delusion of wanting hordes of educated people without opinions!

Then let the government invest more money into making A.I and robots and not on schools, colleges and universities. They might just then have the country they dream of, lots of intelligent machines working day and night and producing results but will have no opinion whatsoever. Robots will not blog or tweet.

This episode further deepens the fatal chasm that exists in India between the intelligent educated people and the administration systems.  We are just making it threateningly impossible or people in the former class to step into the second. May be its the way it is designed to be.

Friday, March 26, 2010

A biology lab travelling on the oceans.

This is a photograph of the boat Tara Oceans on which I happened to land today by an absolute stroke of luck. 

I generally don't blog about some particular incident but almost always about an assimilation of ideas from a string of events in life. But this time I am going to change this pattern for this unique case. 

It was my first experience of meeting and interacting with an international scientific expedition group. This is very different from the life of a regular scientist. Of course I also heard accounts from these scientists of meeting with pirates near Somalia and how the French Army escorted them when while they were passing the gulfs near Arabia.

Basically this is a small sail boat on which a bunch of French and German biologists (mainly from University of Heidelberg and EMBL)are traveling around the world looking at the distribution of organisms (especially photo-plankton) around the oceans of the world. This will be a path breaking experiment which will do a comprehensive study of the effect of the human civilization on marine life. Remember that half of the oxygen that we breathe comes from the planktons in the ocean. We wouldn't be there without the oceans.

Ofcourse these sientists pointed out that world population crossed the maximal sustainable limit of nature around the 1980s! So the planet having to support a population so much in excess of its upper limit is straining the ecosystem of the oceans to dangerous limits. And this is much more fragile than the one on the lithosphere.

It is a 3-year program during which these people will travel around the globe's coasts sampling the data. Anybody familiar with biology would know that doing on-line analysis of organisms in a solution is near impossible. But precisely thats what these scientists are doing on board continuously using their very sophisticated instruments. To get a feel of the technology remember that to do microscopy one almost always needs a completely disturbance free region. Ocean waves 100 meters away from a microscope on land can be fatal to the experiement. Now comare that these people are able to do amazing levels of microscopy while traveling on the oceans! 

This team arrived in Mumbai today and their next stop will be Malaya and then to the Antarctica. The lead scientists landed up in TIFR to give a talk about it and I happened to be in that talk. I was supposed to go to my class on cosmology after that talk but then the cosmology prof (Alak Ray)  came and told me with a cheeky smile that he is cancelling the class since he is goin aboard Tara Oceans. It took some minutes for this information to sink in. And then I realized that the biology department has organized a trip for lottery selected 40 students from their department to this amazing floating travelling laboratory. First thing I was told was that I am not allowed to tag along. My cosmology prof was somehow the only non-biology person to be specially invited to the trip.

And the TIFR bus left at 5:30Pm with those few lucky biology students in it.

But then its me the desperado and I wasn't the one to sit around taking that. I came to know that at 6Pm the speed boat would leave from the Gateway of India heading towards this ship. And it was already 5:40Pm. On the spur of the moment I just packed in my camera and left with a friend of mine from the neutrino physics department. I asked the taxi to drive to the Gateway as fast as he could. But even on reaching there we couldn't figure out from where the boat was leaving. And almost when we were planning to come back,I spoted the TIFR biology crowd in an obscure corner. And I also spotted the biologist with whom I had recently done a biology project

And I hung around as the Tara Oceans sent in speed boats to take the bio people to the ship. After sunset when the last boat arrived, I jumped in. And I didn't regret it. 

Since I was in the last batch to arrive on the boat we got a longer time to move around and see this floating laboratory. And the German scientists were more than happy to show us around and explain stuff.

I am pasting below photo of this awesome sailing on the oceans molecular biology laboratory that I saw.

 One of the scientists (most probably German) explaining this crucial machine that goes down into the waters to collect samples. It can typically go inside for about 120m though they can in principle send it down for 2000m
This is where they purify the ocean water to extract out the organisms from it which is the ultimate objective of study.

This is the entrance to the kitchen and the bedroom and the living-room and the microscopy room of this floating molecular biology laboratory.
The kitchen. These French and German scientists have learnt to cook Biriyani.

A closer look at the capsule that goes underwater

The living room and library of scientists floating around the oceans. It is in the lower deck.

The store-room for the scientific apparatus and food supplies.

The other end of the kitchen with the fruit supplies hanging from the top in the net.

The scientists in front of the control room on the uppermost deck 

Unfortunately  blogger doesn't give me a method of uploading the videos I shot of the descriptive talks that the leader of Tara Oceans gave to us on board.