Climate change

So, here is the story of last Sunday's adventure. Anupam, Arati, Alok and I met up and took the early ferry (6:30 early) over to Mandwa, where I had gone before. They took the bus and I rode th 20 km to Alibag. We had breakfast at a hotel in the middle of town and got directions to Kashid beach, about 35km away. (Breakfast included a "paper dosa" that covered about a third of the table.)

I set off out of town, asking directions frequently. I stopped by a pond covered with amazing lotus flowers, huge and pink standing on stalks at least two or in some cases three feet out of the water. I need to fix or replace my camera soon. I stopped to admire them for a little while, and watch the women in their bright saris washing clothes at one end of the lake. As always, a small crowd gathered to inspect the ferengi and his bicycle. Among the six or so things I have learned how to say in Hindi (which is close enough to Marathi that a large number of people speak both), "Mai cycle kud banaya hai." (I built my bike myself) is one of the more useful, since it answers or diverts a number of questions that do not have answers like "America" and "yes". After a few kilometers, I was instructed to turn off the main road to the right. The new road passed through some swampy areas and then wound through villages that kind of merged into one another. The road was quite bad.

After about 17km of this, I came to a big bridge over a river that was letting out to the sea. On the other side was a police checkpoint, but they were not interested in me. I turned right onto a much nicer road that wound along the coast and up and down a couple hills. It was a very pleasant ride. Quite a few cars packed full of beach goers passed me, and most of them slowed down to look and take pictures.

I arrived at the beach at around 11:00 and found the others sitting in the shade of some trees at one of the tables set up by a concession stand. They had not been there long. I had a coconut and we decided to head down the beach a little away from the crowded part. The water was nice enough to swim in, and the slope was very gradual. The others could not swim, so they didn't venture far out into the water. I swam out a fair bit and was surprised that I could still stand with my head out of water and my toes on the sand. We played in the waves for a bit. Anupam and Alok were quite excited by the fact that one could duck under a wave that was about to hit them.

By 1:00 we headed back to the cover of the shade, had some more coconuts, and moved our chairs to try to stay in the shade of the scraggly beach pines. Some neighbors moved in with a car stereo and really bad taste in music. Eventually they switched from whiny sap to Eminem, and while this is certainly not what I would like to lounge about on the beach listening to, it was infinitely better.

At about 3:00 I started back. I was not really full of energy, but the first part of the ride was nice enough that I enjoyed it. The second half of the ride to Alibag, the part after the bridge, was probably the hardest 17km I have ever ridden. This was entirely situational; the combination of the villagers burning trash, the exuberant horn use (probably 20% of people passing me in either direction honked before and while doing so), the bad road and my lingering cold combined for a less than fun ride.

At 5:00 I met the others in the restaurant where we had breakfast. They had just gotten there, the bus having beat me but only just barely. They had had to stand the whole way. So we were all a bit dazed and tired. We had some tea and snack, and at about 5:40 I started back towards Mandwa to catch the 6:45 boat. By the time I was getting back near to Mandwa, the sun had gone down and the 15 minutes of twilight were gone. By the time I realized that I had made a wrong turn, it was pretty clear that I was going to miss the boat. When I finally got to Mandwa, it was 7:00, and it appeared that the last boat was gone. A group of motor rickshaw drivers stood around saying, "No boat, climate change." I didn't understand the second part, but no boat was clear enough. Alok, Anupam and Arita were not there, so I assumed that they had gone ahead without me.

One of the drivers offered for me to stay at his house for the night, and I figured that this was my best option, since I didn't really want to ride back to Alibag and look for a hotel. I loaded my self and my bike into the seat of his trike and was annoyed and amused at myself for taking a wrong turn, but glad that things seemed to be working out. I was a little annoyed when he decided to name a price after driving me a few miles down dark unfamiliar roads, but since it was only mildly exorbitant in the local economy and not at all in dollars, I didn't seem worth it to care.

At his house there were two more trikes parked. I was introduced to his family (who then stayed in the other room for most of the rest of the time), drank some tea, and watched cricket on TV. I was exhausted, and I find televised cricket as boring as televised baseball, so I went to bed quite early. (Not that I don't enjoy going to an occasional baseball game, but the enjoyment has more to do with having an excuse to sit around outside than the details of the game. Cricket seems to take this picnic idea even further. Instead of innings, there are breaks called tea and lunchtime.)

Anyway, in the morning I got up and caught the ferry back to Bombay. I met Anupam and Alok in the hallway outside my office. It turns out that there was an unseasonal storm on Sunday night in Bombay (where I was there were dark clouds and a bit of wind) and the 6:45 boat did not leave without me, it had been canceled. The bus that was going to take them from Alibag to Mandwa was canceled as well. They thought that I would figure this out, and so they waited until about 9:30 for me, and then took bus and train the long way back to the city. I guess that is what the motor rickshaw-wallahs meant by climate change, no boat.

So, it was a bit of an adventure, and I'm going to finally put the bigger tires on my bike. I seem to get some points here for having ridden 100km. Cycling for fun is almost unheard of for many Indians, especially the wealthier sort. Bikes are seen as transportation for poor people and toys for kids. Of course, this philosophy exists in the US too, but it seems more entrenched here.

So, what else...

Today I got a bank account at the branch of the bank that is here in the institute. It only took two and a half hours. Plus whatever time I spend when I go back to pick up my checkbook and ATM card. I'm hoping that this will be not much.

Srinivas has arranged for me to go and spend a week at the Chennai Institute of Maths, to meet Paranjape. I'll go on Sunday.

Dipankar pointed out this article by Terrence Tao titled Perelman's proof of the Poincaré conjecture; a nonlinear PDE perspective. It seems somewhat unreasonable that looking at anything from the perspective of nonlinear PDE would clear things up for me, but this paper is quite lucid, and I feel like I understand something deeper about these ideas after an initial reading.

As I mentioned earlier, one of the things that fascinates me about mathematics is how some very interesting structures are particular to three dimensions. My favorite easy example is that this is the only place that one can tie a nontrivial knot in a piece of string (two or fewer dimensions and there is no room to cross the strands, four or more and there are enough dimensions to untie anything you like). Clearly, there is something special about three dimensions, because this is apparently where we live.

The string theorists Andreas Karch and Lisa Randall seem to share this fascination of mine. Their work explores the idea that somehow the universe starts out with lots of degrees of freedom (dimensions) and then, following the basic principle that the universe is essentially lazy, reality relaxes, folding dimensions into each other until something stops up the process. This something is a collection of structures that happen to exist in three dimensions. I'm probably horribly misrepresenting their argument already, so I'll say no more.

Another thing that three dimensions does with its weirdness is make proving the Poincaré conjecture a lot harder. Some of the reasons that this basic topological problem is so difficult are similar to the reasons why tying a knot in a string works; there is just enough room for really tricky complications to arise, but not enough room to avoid any of them easily. In three dimensions, the topology (that flavor of geometry in which a donut and a coffee cup are the same - a point made the other way by Vivek this morning when the cart carrying the cups was late coming to breakfast, but there were plenty of savory Indian breakfast-donuts) is really entangled with the geometry (that flavor of geometry where one actually measures things) of things, and the geometry is sufficiently complicated. This is the basis of Thurston's geometrization program. It says that any 3 dimensional topological manifold has a canonical decomposition into a set of parts with specific geometric structures, and that understanding the topological structure can be achieved by understanding these geometric structures. Problem is, understanding the geometric structures is rather hard.

Hamilton's idea was to write down a differential equation, the Ricci flow, which would take an arbitrary geometric structure and relax it to the canonical one. The equations of Ricci flow are similar to the ones that describe the tendency for heat to flow from a hotter part of an object to the cooler parts, but instead of flowing heat, it flows curvature, sort of like when a squashed balloon bounces back to round. There are some problems with this process, like the fact that regions can develop where the curvature is infinitely high, like a balloon that wants to lose all of its air until it collapses to a point. The plan was to use some sort of surgery-like procedure to cut those parts out and replace them with more well behaved parts in a way where the topological information that was hopefully to be extracted would not be affected. The problem then becomes finding information capturing quantities that scale perfectly, so that as the singularity develops with all of its infinities, the quantity is not changed drastically.

Perelman's accomplishment is that he did this.

Tao's paper caught my attention because he focuses on this idea of a critical quantity, one which scales perfectly in the presence of a singularity. I've been thinking about moving information across scales a bit lately. My brain wants to build an analogy between space-time relativity and scale-observation relativity, but exactly how this analogy looks is somewhat elusive. Stuff that is very far away runs into the observational problem of it being seen closer and closer to 14 billion years ago, and hence outside of our concept of time, and stuff that is very small exits our observational paradigm. So then a critical quantity would be one that would pass through the too-small-to-understand barrier and tell us something interesting. Of course, I immediately thought of the stories that my dad would tell me while we were on road trips when I was a kid. The incredible shrinking man was a scientist at Los Alamos who started shrinking, and every so often, he would pop through a quark or into a black hole and out into a new universe.

I tend to think about a lot of this stuff sort of like I think about science fiction stories. I don't know enough physics to really separate possibility from nonsense, but perhaps enough to come up with lots that sounds like it might be one or the other. It's sort of like how I play with installing software on unixy machines instead of playing computer games. In that case, I tend to know just enough to make something good and broken if given sufficient time.

Anyway, back in reality, I wasted far too much time today paying attention to American politics, which was spouting better news for once. I hope that some worthwhile changes are in the works.