Kibber to Tso Moriri pictures

The trip up to the western Himalayas went well.




The trek passed thorough some seriously beautiful and intense territory. The scenery was beyond comparison, in parts reminding us of something familiar, but always with the qualifier that we were experiencing things at double scale. We all had some trouble with the altitude (except Chirag, who did 50 pushups at 18,500 feet), but somehow everyone survived.

I'll be wrapping things up here in Mumbai for one more week, and then I'm headed back to the US.

Cats again

Being back in Mumbai is strange. I'm really only here for a short time, in another week I'll be headed up to Ladakh to explore the mountains and valleys of "little Tibet" and this seems to be a lull time in general for TIFR. I get the impression tha not so many people come to visit during monsoon season and people often go abroad or back to their home city during this time, so unless one has a project that is really engaging, there's a lot of down time. I seem to be suffering from not so much a lack of engaging projects as a disengagement from my projects, but the result is the same. The sails are somewhat slack this week.

I decided to hop on a bus because I was walking past as it was leaving, and ended up getting off in Colaba and walking back towards TIFR. On the way back, I met Narayan, the old man who feeds the cats. Narayan is 79 years old, and moved to Mumbai from Bangalore. He retired from work as a telephone operator with the government telecom, and relocated from Bangalore to Mumbai when he was young because the football (soccer) was better here. I guess you can get cricket anywhere in India, but somehow football is only slightly more popular than in the US.




On a tangent, I was wearing my Brazil t-shirt today, the one with "Order and Progress" replaced by "Q.E.D." and Nirtin commented on how he held the standard Indian view of Brazil, that it was the anti-India. I wasn't quite able to figure out what he meant by that. I've never been to Brazil, but my impression is that Brazilians on average know how to party a lot better than Indians, and while both coutries have a macho complex, Brazil's tough guys are a lot tougher, and their women are somewhat more empowered. And that they play football a lot better than Indians play cricket. But for various reasons, when given the choice between IMPA and TIFR, I picked TIFR. I guess India has its favorable points as well. The Himalayas and all...

Yesterday I gave a reprise of my talk from Lun-Yi's show, somewhat expanded to include a bit more math. The occasion was a VSRP colloquium, VSRP being TIFR's version of an REU (research experiences for undergraduates) - too many damn acronyms. Anyway, it wasn't as interesting as the first time, largely because I wasn't able to establish much of a rapport with the audience. I sometimes get the feeling that some of the people here are just waiting for me to explode into some sort of monster or suchlike. I don't really know how to describe it. Its like I'm a dancing bear who can also talk about algebraic geometery.

And, since I'll be leaving TIFR before long, I caved in and signed up at Flikr to host my photos.

Also, there are some videos (about 7mb each, so only download if you have a rather fast connection) of the rain as viewed from my apartment here and here. When I went over to campus later in the evening it was raining a good bit harder, but even these movies are rather impressive.

Monsoon

So, I went back to the US, had some adventures, and probably visited most of the people who read this journal, so I won't write about them. I had a little bit of trouble getting back to India, but that's because I seem to have forgotten how to count, at least as far as airplanes and dates are concerned. But the results of that were more good than bad, so I'll take it as it is, and now I'm back in India.

The rains took there time getting to Mumbai, but now they are here. When I arrived, there was rain that evening, and a few more times during the week that followed, warm showers that turned the dust on the streets to a slick layer of mud that made its slow way into the gutters and out into the sea. The sea, which previously had been so utterly placid that it seemed strange to look out and not see the next bit of land, had suddenly taken up a healthy show of activity. The waves still didn't crash, but the two person fishing boat no longer made a notable contribution. Then, two days ago, after the solstice, the rain stopped. The skies cleared and the waves sunk back below the tide. The monsoon is late. "What is this, what kind of a monsoon are we having?" people exclaimed.

This afternoon, at around 2, the wind started to pick up. I had been thinking about going out and finding a book, since I've finished all the reading material on my shelves that isn't a math book or the Lonely Planet, but I decided to head up to the roof and see what the clouds were up to first. Huge grey clouds emerged out of the hazy mass to the west and swept past as if in a film played at double speed. Cracks of lightning shot out to the south. It began to rain, lightly.

I sat down with my back to the low wall around the terrace, shielded by the fact that the wind was blowing steadily off the sea. Clouds raced by overhead, and the raindrops grew slowly fatter. Anupam appeared on the terrace as I stood to move under the cover of the hallway, and we stood for a while to watch the growing storm.

As the lightning grew closer, I decided to come downstairs and unplug my computer. The rain kept picking up until it was a full downpour. I stood in the doorway to my balcony and watched the sheets pass by. The area around the entrance to TIFR has poor drainage, and an ankle deep puddle quickly formed. The truck delivering tankfuls of well water to supplement our ration from the dwindling municipal supply splashed through on its way out.

I decided to postpone my book buying adventure. And my plan to go out for dinner. The rain slacked off for a little while, but then started to pick back up at around 6. When I went over to the institute for dinner, the wind had picked up, and was blasting through the open walkway that makes the only opening in the five stories of building facing flat against the sea at gale force. There was at least twice as much water coming out of the sky as I have ever seen before. It has been like that for a few hours now, and the lawns are turning into small lakes.

On the road again

Last night I had a beer with Rachel and Nathan. Rachel I know from Santa Fe, and Nathan is her bike messenger boyfriend from Sarah Lawrence who is about eight months into his Watson Fellowship to explore bike culture in various cities around the world. Bombay is on the list, along with Shanghai, Tokyo, Sydney, Curtiba, and some other interesting spots. So now there are perhaps two fixies in India. Nathan commented that arriving in Bombay produced the most significant culture shock that he experienced since arriving in Shanghai from New York.

Rachel knew that I was here in Bombay, but hadn't been able to get in touch with me, since I stopped checking my email at UW very often because of the spam. So instead we just happened to bump into each other on the street. I guess I do kind of stand out in this crowd, and India is known to produce magic. Still, the two of them running into me while I've been in moderate recluse mode in a city of 15 million is some pretty potent juju.

But the really interesting thing that is going on right now is that I will soon begin my 36 hour long May the 5th, with a little bit of May the 6th thrown in in the middle just for good measure. This feat will be accomplished by flying to San Francisco, via Singapore. It's been since September that I've been here, and I'm ready for a break from India and some time to reengage with my life and my people in the US.

And I'm ready to see Jill again, who, as this picture undeniably proves, is seriously hot.


(photo by Jose)

Flamingos

I made it back to Sewri yesterday. This time I went by train and in the late afternoon. The tide was pretty far out, but I did see that there were quite a few pink birds out there.



Wandering past the rusted hulks next to the pier where the kids were playing in the water the week before, a trio of young guys called me to come up and join them on the boat. I climbed up, we watched the birds, drank a little beer, and taught each other how to curse in our respective languages.

Waiting on the platform on the way home and inspired by Denny, I tried a little cameratossing.

Flamingos?

On Thursday night I joined the Ducrohets at a gathering of the French expats in Mumbai. It was held at a restaurant close by TIFR that Laurent had told me about, but that I had yet to explore myself. Like the parade of masochistic devotees last weekend, the cat feeder, Sunil the shoe shine guy (I've met him again, and discovered that he actually has legs, they are just rather small and not much good for walking on.), and TIFR itself, this place is one of the amazing incongruities that Bombay hosts. We stepped inside and into high-ceilinged, low-tabled rooms, with walls thick enough to block the street noise, and some low key techno playing on a good sound system that could have just as easily been in New York (or perhaps I'd be better to say Paris, since I've actually been there and since everyone who showed up that night was French).

I was struck during the course of the evening by how children are often treated so much more generously in India. While we were having our beers and Pizza Capricciosa (it seems that cheese does exist in India, if only in limited distribution) seated on low couches covered in raw silk, Brieuc was making the room into the jungle gym that is any room to a 3 year old. In between serving drinks and lighting Laurent's cigarettes, the waiters played with Brieuc, tickling him with the bolsters that he'd removed from the other couches as they set them back in place and relighting the candles when he blew them out. Though I've heard that places the don't allow kids exist in Mumbai, I've never encountered one, and the places like this one and Peshawar (where the manager once came out and scolded Laurent for keeping Brieuc from running amok while we were waiting for our dinner) are more common.

Yesterday, I went to an evening of short films on the roof of one of the hotels along Marine Drive. Yogi had mentioned it earlier in the day while a few of us were standing around outside, and though there were no plans fixed, Sreekar and I found ourselves on the same TIFR bus there, and when we found the roof of the Oceania, Yogi, Pablo, and Pablo's wife Anita were there, and Shoba was on her way. While we waited for the sky to darken enough for the films to show, Yogi and I watched the fruit bats cavorting in the twilight. "Are they showing off or what?" exclaimed the suave young Mumbaiker sharing our bit of terrace wall. A tree's canopy reached to a couple stories below the rooftop, and in it a dozen or so of them were congregated, close enough that we could see their pendulous acrobatics as they explored the branches for fruits. And when they floated in the evening breezes above Marine Drive, the streetlights shone through the thin skin of their wings, showing spindly finger bones splayed against the currents of air.

Eventually, the films started, and we made out way to the blankets set out in front of the chairs for the overflow seating. It seemed that we had happened upon a film club whose meeting night had been discovered by a weekly paper and suddenly the club had to deal with a few times the audience that was expected. The guy who introduced the films was effusively excited about the turnout, and promised to have more chairs over the weekend (there will be more films showing tonight and Sunday).

The first film was the best, a documentary on the flamingos that I didn't see last weekend. Apparently, high tide is not the best time to go and see them as we had thought, but instead about an hour or two before, when large parts of the mud flats are still exposed. I'll go this weekend and see if I can find them. The documentary described how sometime around 1994, 10,000-20,000 lesser and greater flamingos decided to converge on the Sewri mudflats. I don't know what Sewri means in Marathi, but it sounds like Sewery, which is an accurate enough description. However, it seems that the mix of sewage and industrial effluent creates a concoction such that the algae on which the birds feed really flourish. Unfortunately, there are also significant amounts of heavy metals being pumped into the water (ten times what India considers safe in many cases), quarrying operations that are rapidly changing the shape of Thane Creek (where the mudflats are), and there is a giant bridge going up soon that is slated to pass right through the mudflats. The film and the response that it garnered form the audience did quite a bit to shift me from my sour mood regarding the existence of environmentalism in Bombay, though Yogi and Shoba did have to explain to the old woman sitting next to us that seeing the birds in real life would be even better than seeing them in the film.

The rest of the films were more like what I was expecting; a comedy based on the difficulty of finding change, a spoof on the "separated at birth" theme that is rather popular in Hindi cinema, with a moral of national integration, a blundering mess of a mystery about a young couple found dead at the bottom of a cliff, and a story about a homeless guy who doesn't understand the concept of money, but happens on a briefcase full of it. After each film, the director would have a few minutes for questions. This was fun, and added to the film club atmosphere. Yogi, Shoba and I were amused that the only question the evening's anchor seemed to be able to ask was, "How much did the movie cost to make?" This was especially ironic when he asked it of the guy who made Paise...?, the film about the beggar who tried to eat a suitcase full of money and came up frustrated.

After the film, Yogi, Shoba and I went for dinner at the Tea Center. The food was great, but we ended up with more than we could eat. I find that this happens often when I go out to eat in India. It is a given at a thali place like Joshi's, but even at a regular place like this, food in Bombay seems to be feast or famine. It is hard to turn down a few more mouthfuls of a beautifully spiced dish, and easy to tip past the saturation point.

And in other news, I've been amusing myself and my streetside friends of the minute by letting people ride my bike, or at least try. When I first started out riding around in Bombay, I was really hesitant to let anyone take my bike for a spin. Other than one kid who I met on the very first day out, I tended to fend off any requests to take a spin. But after a certain point, I realized that there was no real reason for this, and that it is more friendly and more fun just to warn them and then watch. It turns out that the size of the bike and the fixed gear really do make it pretty much impossible for someone to just get on and ride.

It usually works about like this: I pass a group of guys hanging around on the sidewalk, or they gather when I stop somewhere. One of them is the most forward, and after a few questions about the bike, they ask if they can go for a ride. I show them the fixed wheel, and they nod like, "yeah, whatever, Gora, I know it's a bike." With some effort, they swing their leg over the seat which is at least four inches too high for them. On their tip-toes, straddling the top tube, they put a foot on a pedal and prepare to push off. Generally, the pedal they are putting weight on is not forward enough to carry them all the way into the seat, which they usually can't reach anyway, or for them to get their weight onto the other pedal, without passing the bottom of the arc, at which point they still have most of their weight on the initial pedal, and it stops the bike. Since they aren't really moving yet, they don't fall all the way over, but it is also not really a graceful dismount. At this point, the crowd of friends who I am standing with starts laughing and everyone is trying to figure out what is going on.

The experiment often ends there, and the bike is returned in a flurry of head wagging, but sometimes the would-be rider has more perseverance, and manages a few wobbly turns of the pedals. A few weeks ago, I spent a Sunday afternoon letting some people figure it out, and some of them did eventually. I had noticed a bike with an unusually large gear while out walking the day before, and the owner, Chandrakhar, asked me to come by and show him my bike. He was able to ride it pretty well after a little while. We went for a ride around the city that afternoon and last week I stopped off and though he wasn't there, I left him one of the copies of Cranked that Jill sent.

Solar powered tricycles, and where they might lead

A few years ago at Burning Man, I met Bob. Bob rolled into our camp in his solar-panel-and-windmill-powered RV with a fiery-crested stained glass bust of a horse at the prow. Bob's RV was neat and orderly on the inside, with a design aesthetic inspired by a small ocean going sailboat. His controls were a joystick on a cord that was long enough for him to be able to drive from anywhere in the vehicle. When driving into the wind, a properly timed jet of flame from the horse's crest would be caught by the windmill and split into a triple helix.

The next year, I ran into Bob again, and he was driving a giant tricycle that looked sort of like a praying mantis on a hang glider and hallucinogens.


(Photo by Waldemar Horwat)

I stopped in to chat with him one day while wandering around the playa. We snacked on guacamole and chips that the previous visitors had left, and Bob told about his life as a technician and engineer building devices at Stanford Medical School. We talked, among other things, of the future of transportation. Bob was convinced that the Lithium-ion battery was going to power the first successful electric car. His observation was that battery technology is increasingly driven by consumer electronics, and the threshold weight to cost to power density ratio to make a reasonable car is pretty much where we are now. These cell phones and laptops that we all can't live without now suck up a fair amount of juice, and one of the biggest factors in making them sell is making the batteries small and lightweight, while still being powerful and long lasting. These are also, of course key features of a battery that would power an electric vehicle, since in addition to moving the fat ass of the driver, it must move the batteries. In previous eras, the market impetus to make such batteries was a lot less significant than it is now at a time when 300 million Indians have mobile phones.

So anyway, at around the same time that Bob and I were eating guacamole, some folks in Silicon Valley (including the head of SpaceX) were starting a company to follow up exactly this idea. Their car is quite close to production, and it looks and sounds pretty damn sweet. The concept of the Tesla Roadster is to make a high end sports car (it is very similar in design to the Lotus Elise) that uses ability of an electric motor to blow the pants off of similarly designed gas powered cars. Now, these are stupidly expensive toys, but there are plenty of people who want to buy these stupidly expensive toys, and Tesla's plan is to make the money they make off of the Roadsters finance the development of a more practical version, and eventually get the price and models more in line with what the rest of everyone is interested in, car-wise. (The Tesla apparently does 0-60 in 4 seconds, has a 200 mile range and recharges in three hours from a wall outlet, and there are plans to sell it with a solar panel that will provide about 50 miles per day of charge.)

I personally still prefer the bicycle for an advanced technology, high fuel mileage, low emissions vehicle, and with products like the Stokemonkey coming out, it increases its usefulness and car replacing ability. I'm certainly not one of the people who disagree with technology like Tesla on the grounds that it is still a car. That sort of idealism doesn't allow for much compromise. The Tesla is a really neat next step, and I hope that they succeed. Tucker and DeLorean may have been knocked out of the car business by the big establisheds, but things really are different in today's market. Mostly because of the internet, distribution of information is much faster and wider. Also, this is a new product in a way that the Tucker and the DeLorean really weren't.

And since I mentioned the Stokemonkey, so I should say a little about how cool I think it is (cooler than the Tesla in many ways, but less likely to grab the attention). I've not actually seen one, much less ridden a bike with one, but I can still be excited about them. The Stokemonkey makes a bicycle into a human/electric hybrid vehicle. They are powered by NiCads instead of Lithium-ion (Lithium-ion is not the only battery technology that's being advanced by the consumer electronics market), and a compact electric motor provides a power assist, basically helping you pedal like the stoker on a tandem, putting out a good deal more power per pound than Lance Armstrong (of course, Lance eats sandwiches, not burning coal). Hybrid electric bikes aren't all that new, but this little device is the coolest implementation of the idea that I've seen. My favorite application that I've seen a picture of is this Sycip from the North American Handmade Bike Show. It is that little red thing.


(Photo by Alex)

Speaking of the NAHBS and of projects like Bob's praying mantis tricycle and fire-shooting horsehead chariot and the Tesla cars, I have to say that it makes me really happy that all of these smart and creative engineers and builders are working on projects like this and figuring out how to get people and their stuff from A to B more stylishly and more efficiently instead of getting jobs at Los Alamos and Sandia or Lockheed or Raytheon and figuring out how to be more efficient and stylish while killing people, or even just at GM, figuring out how to make cup holders more stylish and not giving a crap about efficiency. Of course, there are plenty of people doing the latter sorts of things, but my hope is that the bike builders and rocket scientists are enough cooler and more inspiring that the pendulum will continue to swing in this direction.

Clearly, a big part of the change that is happening is due to the new sexiness/practicality/popularity that environmentalism is finally acquiring in the US. Since perhaps the largest export of the US is desire, many of the changes in this regard that happen in the US eventually make it out into the rest of the world. The foreign money that is pouring into India in the form of outsourcing jobs is often spent on toys. As was recently commented on in an editorial over here, India's wealthy should really take a look at their own logs before demanding the right to growth at any cost because India consumes so much fewer resources compared to the West. The carbon sink of India's rich is India's poor. (In addition, I'm interested how these ecological footprint numbers are calculated, because there's a hell of a lot of polluting that goes on at the local level here because of nonexistent or unenforced laws that I'm not sure makes it into these guilt trip numbers that tell us how many times over we use up the planet. I just took one those tests with the data from my life here and my life in Seattle, and I apparently use 1.5 hectares here, and 26 in Seattle. There are supposedly 1.8 per person for the world. But I sure do like breathing the air and being outside better in the US than I do here, except when I'm up in the Himalayas...)

It is true that 80% of Mumbai uses public transportation, but that figure is falling, and that still means that at least 5 million don't. The local trains are famous for being crowded (over 6 million riders per day), but a good part of that is because the system hasn't been updated for decades. On the other hand, there is a growing number of SUVs on the roads here. I was talking about this to one of the other guys who lives in my apartment building last night, and he observed that (1) even a poor American probably has a car, and (2) Indians are comparatively less likely to make any sacrifices in terms of providing material goods for their family. (This guy has lived outside of India while he was a student, and he strikes me as an intelligent, open minded, somewhat conservative person. He is married and has a one year old son. His wife almost never talks to me, and if I am on the roof and she comes up there with her son but not her husband, she leaves immediately.)

Anyway, my point is that many people in urban India have bought or at least coevolved some significant parts of the 1950s era American Dream as far as consumption is concerned. But while there are many things that I wish people would do differently in India, most of them having to do with attitudes towards the environment in one way or another, one of India's main problems has been outsiders telling them how to run things for the last 300 years, and the last thing they need is another idealistic white guy who thinks certain attitudes should be reevaluated...

No Flamingos

An afternoon out on the streets of Mumbai tends to inspire at least a mild headache. If the dehydration from not being able to drink enough water doesn't do it, the sun will, or the horns and the general stress of being in the midst of so many people, or the dust, or the constant assault of smells - these days it's mostly garbage, sewage and truck exhaust since the dry season doesn't lend much moisture to the greener smells that filled the city when I first arrived. And then there is jar and chatter of biking on these roads if I chose to ride. For the most part, I'm keeping a low profile these days, holed up at TIFR and eating at McRajan's or the canteen, heading out just one or two times a week.

But today, I was lured out by the promise of seeing hundreds of flamingos who had stopped off in their migration at the mud flats of Sewri, just a few miles north of my part of Bombay. Arvind and Yogi went there this weekend and took some pictures. The theory was that if I went at high tide, I'd have the best chance of seeing them up close. Theory didn't pan out, but I did encounter some kids swimming off the end of a pier,



and a parade of people holding up buckets of water on long steel poles pierced through their cheeks,



and towing cars attached to hooks through the skin of their backs.



I also played in traffic on the way out. The string holding my tripod to my bars came loose, so part of the time the camera was looking at the ground, but you get the idea.

Demonstrations

One of the things that I'll be doing in Seattle next month is part of an amazing project that Lun-Yi has put together exploring the connections between mathematics and art.



I'll be giving a short talk in which I will try to convey some of the ideas underlying the process by which a mathematical theory turns a geometric object into abstraction, and then given an example of an abstraction of the sort that is produced by this process, reconstruct the geometric object. The analogy that I will be using is the process by which a cartographer draws a series of maps, and then how someone looking at a map develops a mental image of the land itself. My goal is to use the second part of this analogy to describe the so called Minimal Model Program, which is one of the largest industries within algebraic geometry.

I just came from our weekly seminar, where we have been working through a recent paper by Hacon and McKernan proving a very key step in the program. It is a technical result, and though I'd seen both of them give talks on it, I really had little idea of what was happening. Yogish, Narjmuddin, Amlendu and I have been taking turns presenting parts of the paper, and because Amlendu is going out of town next week, the length of our talks has gone from about 90 minutes (which is already almost twice as long as what I am used to) to a full two hours. At this time on Tuesdays we are all generally pretty burnt. But, with my lectures this week and last, we have finished working through their proof, and though I can't say I see it all perfectly, the picture is much more clear.

Game Over

NYT article on the Olympics being used to successfully put pressure on China regarding Darfur.

Hopefully this will be the first in a number of effective moves to get China to listen more to motivations other than greed and paranoia.

Quiet

As in, I haven't been posting.

That's mostly because there hasn't been anything worth posting about. It's warmer, hence I'm more lethargic, and less prone to being interested in going out into the city. This isn't that bad, as I have about one more uninterrupted month here in which to focus on math. Beginning when I come back to the States in May I'll suddenly be rather busy and then my schedule stays pretty chaotic until it ceases to exist.

But when it gets interesting again, I'll let you know. And maybe when I need something to procrastinate with, I'll let Team Red down from Sandakphu (though I hear that they like it up there).

Vancouver 2008

So I've been getting a steady trickle of rejection letters from places where I applied for a postdoc, but yesterday morning I got a bit of much more positive correspondence. It sounds like the next place I'll be heading after TIFR will be the University of British Columbia. The position won't start until January, and funding is potentially on somewhat shaky ground after the first six months, but I think it will work out well.

Besides, everyone loves Canada, eh.

Inaugurating the treadmill

This morning provided one of these interesting moments when the curtain parts just a bit and I get to remind myself that I am in fact, somewhere else entirely.

My latest means of countering the fact that my office, my apartment, and the places where I eat are all within three minutes of each other, and everything outside that bubble involves lots of honking traffic, hence activities other than sitting in a chair or walking back and forth along the seaface or in the open area between the atrium and the auditorium tend to be limited has been (appropriately enough for India) some yoga in the morning. At first I was doing this on my own up on the roof of Jagdish, but then I learned from Costis that the sign on the bulletin board proclaiming "Gents Yoga Class, 7:30-8:30 AM" did in fact refer to something extant. It isn't really a class at all, but there is a guy who comes in every other week to provide a list of poses and some guidance. Other than Costis and I there is only one other young guy there, and he's on some totally other scheme of exercises. There are two other guys who come in, but they are older and seem to be following specifically prescribed regimens such as staring at a candle for twenty minutes and then doing some yogic breathing/snorting for a while.

So this morning, our yoga-wallah came in and asked us to come join him in the other room where the weight machines are for an "inauguration". What was to be inaugurated was a new treadmill. In contrast to the existing treadmill, this one is set up looking out the window, so that those who prefer to walk in place using a machine can stand on the second floor and look out and see what they are missing rather than be tucked into a corner under the stairs and stare at a wall. I guess that during the rainy season it can be nice to take a walk indoors, but I generally don't see the point. Anyway, when we came into the room, the Star-Trek-esque control panel was draped with a garland of orange flowers, and our friend had a couple sticks of incense burning. One of the men present was given a dry coconut, which he cracked open on a dumbbell. Some sweets were passed out and the guy who cracked the coconut tried out the new machine.

(The sweets were of the extremely sweetened pistachio flavored compressed milk product variety, and however good it may sound, it isn't, and I had to cut out of yoga early because the thought of suddenly ejecting that little blob of sugar with last night's dinner in tow while standing on my head was all too present.)

Apparently this equipment inauguration thing happens every so often. On telling this story I heard about a little bit of drama that came about when someone in the (string) theory group got a new piece of office furniture and deemed it necessary to acknowledge this fact. It seems that some more secular members of the department found the sanctifying of an office chair or filing cabinet rather offensive and there was a little bit of tension for a while. I'm certainly ignorant of much of the associated baggage, but as a ritual to acknowledge gratitude for getting a new thing, I thought it was pretty neat. I suppose it isn't all that unlike cutting a ribbon on a new bridge, just on a much smaller scale.

Solar eclipse

(picture links to a 1.6mb movie)

One rare occasions, the smog comes in useful.

As I was about done taking this a shoe shine man with no legs by the name of Sunil Kumar manualed his hand crank tricycle up to me, and inquired about my nationality, marital status, and lack of a rear brake.

Adventures

I sat with Nirtin Nitsure, current Dean of the school of Maths, during lunch today. Nirtin is a loquacious and lively character, by turns interesting and obnoxious conversation, drawing heavily on the desire to always play Devil's advocate to the greatest possible effect. A few days ago, we were having lunch and Yogi (who was Nirtin's student) sat down to join us. Seamlessly integrated into the conversation was Niritn's immediate and insistent question to Yogi, "Would you rather have an elephant's trunk or no nose at all?" A few seconds earlier we had been talking about Western and Indian attitudes regarding historical preservation, but anyway...

The point of this digression is that today Nirtin asked me what sorts of adventures I had been on recently or had planned.

"Only mathematical ones," I replied.

Which is pretty much true. So far, I don't feel like I have produced that which would very unambiguously indicate a successful career as a research mathematician, and this suspicion is confirmed by the paucity of job offers that present themselves to me. In May, I'll be back in the US for a conference on rational curves, a thing central to my research. So my plan is to do as much as possible between now and then to ensure that I have something to talk about with the other experts, and to use my experience at the conference as a sort of touchstone to help me figure out what the hell to do with a PhD in algebraic geometry. Clearly there are plenty of options, but the obvious one, academia, seems to have the feature that the exit is a one way door. I already promised Sándor that I wouldn't be a taxi driver with a PhD, so that old fall-back is out.

On a less personal but still meta-mathematical note (or meta-meta-mathematical note for those who keep track), a couple of interesting articles showed up on the arXiv recently. The first, cross listed in math.AG and hence noticed promptly, is math.HO/0703427 is an article titled Mathematical knowledge: internal, social and cultural aspects by Yuri Manin, one of the few who has the impressive distinction of a mathematical object denoted by his name hyphenated with that of Gauss. (Incidentally, I have a hard time mentioning Gauss without being annoyed that he gets his name attached to inventing hyperbolic geometry along with Bolyai and Lobatchevsky - clearly he worked out some of the important formulae, but it isn't so clear that he understood what he was looking at - and this was the essential feature of that discovery in my opinion. I feel that when Gauss, who was clearly one of the best mathematicians ever, gets his name tacked on to the discovery it belittles the work of the other two, and also the other work of Gauss himself.) Anyway, Manin's article rambles a bit, but in the rambling style of someone who has a lot of interesting things to say and wants to say all of them. It seems interesting and probably worth looking at if you are interested in what mathematicians think about mathematics. The second article came out last month; math.HO/0702396 by Terrence Tao is a discussion of what characterizes good mathematics. Just the list that he starts with makes an interesting prompt for thinking about this question.

More math movies

I made a couple more math movies with surf today.

The first is a family of curves that is only mildly more complicated than the Mobius strip.



And the second is related to the Hopf fibration on the three sphere.

Holi Technicolor Batman!

Sunday was Holi, the festival of color, a holiday of ambiguous origination, a bit like a Hindu version of Easter. There are elements of a spring festival in the picture, and then there are some dubious religious stories pasted on top. The TIFR colony's version of the holiday begins the night of the full moon with a brief bonfire and passing out of sweets. A brief trip to Gokul for dinner and we missed all but a few embers surrounded by a lot of empty chairs, and someone using another fire to burn some leaves and make a lot of smoke.

The festivities began the next morning at around 10am with a few people milling around near the cricket pitch, smearing powdered color on anyone within reach. I wandered out and soon found myself tinted. There wasn't much to the coloring ritual beyond a "Happy Holi" and a smear on the face. After a little while, a hose was passed up to a first story window and a mud puddle was constructed. People gave up color for brown with varying degrees of enthusiasm. Sreekar made a good show of resisting, but he too joined with the mud people. I lingered until I had to fend some of the revellers off lest they pick me up and carry me into the mud. Instead, I went and took my bike out for a spin around town.



I started with my usual route out to Marine Drive and up to Malabar Hill. On the way past the slum near Cuffe Parade a bucket of lavender colored water was thrown on me, and riding through the city as it evaporated off my shirt was quite pleasant. I figured I'd check out Banganga tank while I was on Malabar Hill, and found the standard cricket game going on, except that everyone was painted purple. A couple of times I stopped and let someone give my face a bit more paint.

Here's the view from my handlebars:



From Malabar Hill I cut east and North across the city and then turned left and headed north, perhaps as far as Dadar, I'm not sure. Traffic was really light, even for Sunday. Occasional groups of people milled about in chai shops, restaurants and doorways with varying ammounts of paint. A few of the sidewalk dwellers were taking baths as I rode by. It was nice to almost blend in for a change. Being painted purple partially hid the fact that I was ferengi. On the other hand, I was clearly one of the only ones exerting myself on this afternoon. It seems that in Mumbai, everyone takes the afternoon of Holi even easier than a normal Sunday, which is dead slow by Bombay standards. What that is by rest of the world standards I may have forgotten. Eventually, I decided that I'd had enough and turned around. It took a while to get the paint off my face, and the shirt is not going to be white again. That's okay.

In other news, this is an interesting article about the place of the slums in Mumbai. Specifiically, it talks about how all of the recycling that is going on as under the radar business.

And not related to Mumbai at all is this article on one of the more interesting biofuels on the horizon. It is lots better than ethanol.

A universal curve

What follows is a rambling example attempting to explain some mathematics. I didn't really have a well defined audience in mind when I wrote it (or rather, I had a number of well defined audiences in mind and all of them pulled in different directions) but hopefully it is interesting and intelligible to some anyway. I clearly need to draw some more pictures and insert them to break up the ramble, but until I get around to it, I'll leave that bit of work as an exercise for the reader.

I'll probably try to work this idea into a general audience talk, perhaps one introducing the minimal model program, so if anyone has any thoughts, I'd be glad to hear them.

Families of curves are rather interesting objects. Consider the set of all curves in a given geometric space Z and call this set Curves(Z). Then we can consider the universal curve, which is the subset of the Cartesian product Z × Curves(Z) containing pairs of a point in Z and a curve containing that point, namely

UCurve(Z)={(z,[C]) ε Z × Curves(Z) | z is in C}.

It turns out that with some reasonable restrictions on the type of thing that we want to consider as a curve, that Curves(Z) and UCurve(Z) have the structure needed to be considered as geometric objects in their own rights. A family of curves in Z is a subset of Curves(Z) that fits into the same language of describing geometric things that we use to describe Z, the curves on Z and Curves(Z).

A simple example of a family of curves is the set of lines through a given point in the Euclidean plane, E. Call this family H. It is a subset of Curves(E). H is by definition the real projective line, i.e. the circle, parametrized by slope, where a vertical line is said to have a slope of ∞. The universal curve, which will have the name F and sit inside UCurve(E), is relatively easy to see - it is quite similar to the plane itself. Using polar coordinates centered at our given point to describe the plane is almost the same as using the universal curve. The problem with polar coordinates is that when the radial coordinate is zero, the angular coordinate is meaningless. And standard polar coordinates use angle instead of slope, which forgets that we are interested in lines through a point, not rays coming out of that point. To get lines, we need to remind ourselves that x denotes the same line as x+180, which is a bit ad hoc.

So what we are looking at is a parametrization of the plane E by a slope coordinate and a line coordinate. For non vertical lines, we might as well use the symbols y/x for slope and the r for the line coordinate, reminding ourselves that y/x=∞ and negative values for r are okay. When we use these coordinates for the plane, there is ambiguity at the points where r=0. But the points (0,y/x) are on different curves, so they are not the same point on the universal curve. This difference between the universal curve and the plane is the key to what is going on. The universal curve coordinates work fine to describe the plane, except for the point where all the curves that are collected into the universal curve come together. On the plane, this is one point, but in the universal curve, there is a different point for each curve in the family - that is, there is a copy of H sitting inside of F such that the whole thing gets contracted to a point. This phenomenon is called blowing up a point, and F is called the blowup of E at a point. The copy of H that gets collapsed is called the exceptional curve.



F is topologically a Mobius strip. There is a picture of this in Hartshorne, conveniently reproduced on Davis's backpack for all you Seattle people without a copy or two lying around. But better than looking at a picture, draw your own. Draw a disk around the point that gets blown up instead of the whole plane and make a Mobius strip with a stapler or some tape. Draw the circle that follows the middle of the strip of your Mobius band (this whole circle is going to correspond to the point) and and a few lines across the strip perpendicular to the central circle, in both cases, press hard enough or use dark enough ink or use tracing paper so that you can see the line on both sides. You should think of the line that you draw being equally visible on both "sides" of the strip, so when you draw it, the ends will join through the paper. Right now this is just the way we'll do things. We aren't doing noncommutative geometry yet. Label these lines with slopes starting with ∞, then move into big negative numbers, increase up to 0 and then up to positive slopes and back to ∞. Trace your way around the central circle and mark the correspondingly sloped lines on the flat plane to convince yourself of what I'm rambling on about.

The Klein bottle shows up if we look at the family of complete geodesics through a fixed point on a sphere, say the south pole on the earth, in which case we get the meridians. The universal family is again very similar to the space on which the curves live, in this case the sphere. In this case, there are two places where we need to resolve the indeterminacy about which line we are on at the north and south poles all the lines come together. We do this by by blowing up these two points.

This corresponds to what is going on topologically when we look at a world map, for example with a Mercator or cylindrical projection. Latitude and longitude provide the location at any point other than the poles, but at the poles, the longitude is irrelevant information. But it is still a coordinate that we can read off of our map, so it must parameterize something. These somethings are the exceptional curves, one middle circle for each of the Mobius bands of the Klein bottle. At first glance, this comparison should seem sketchy, since we all know that a map makes the upper edge of the map collapse to one point - the north pole, the sides stitch together, and the bottom edge collapses to the south pole. So why bother with this intermediate step that seems to needlessly complicate things by introducing a Klein bottle? The advantage of the intermediary step is that one keeps an intrinsic picture of the geometry at the poles.

Without a labeling indicating that the meridian at x extends through the pole as the meridian at 180+x, there is no way to tell what the geometry is at the poles. This labeling is exactly the labeling that identifies the map as a Klein bottle.

So what is the point of this example? I thought of it in the context of two connected ideas. The first is the minimal model program (MMP) in algebraic geometry, and it relates to the interpretation of a map that appears to be a Klein bottle as in fact depicting a sphere. One way to understand the goal of the MMP is that it seeks to understand the right geometric object that corresponds to a given map. In this example, running an appropriate version of the MMP would tell us to take our Klein bottle map and blow down the two exceptional curves and recover a sphere with all the geometric data at the poles and elsewhere described as the mapmaker intended.

The second idea is the construction of the map as a universal curve. First of all, this has nice philosophical implications, because the way that a map is drawn is by first exploring the territory along paths. Perhaps a more vivid example comes from the knowledge we have that comes from astronomy. All this information has essentially coming straight at us along some sort of geodesic through spacetime. Sitting here on Earth can do little more than collect the information as it converges at our south pole of the universe. But philosophy aside, this idea of using a universal curve for a family of relatively simple curves through a fixed point as a map of some object to be studied is central to the proofs of many results in algebraic geometry. In particular this idea can be used to prove a result due to Shigefumi Mori, one of the key architects of the minimal model program, namely that a variety with ample tangent bundle is projective space.

It is here that what I am researching makes connection to this example. I believe that families of (rational) curves through some fixed point that are as simple as possible, given that I want my families to contain a curve pointing in every possible direction, should make a good enough map to reconstruct what sort of space these curves are living in. My particular tack is to try to simplify the problem even further by working with approximations to the family of curves, approximations that I call minimally indicating rational arcs. The trouble is, I'm not sure if these approximations actually make anything any simpler, but hopefully we'll see.

Gas!

For dinner last night I had four of the most delicious grilled cheese sandwiches ever created.

Joshi Bhojanalay

I've been meaning to write a post about food for a while. It seems that I've finally gotten tired of the canteen food here, so perhaps now is a good time.

As far as the canteen food that I'm sick of - it is actually not bad. There are two canteens, the west canteen looks out over the lawn with the amoeba topiary and is open for lunch except on Sundays, as well as breakfast during the week and tea and tiffin (generally something deep fried in the afternoon and the same as what was for breakfast in the morning). The lunch varies a certain amount, but often includes attempts to create some sort of non-Indian cuisine. East canteen is open for lunch and dinner every day but Sunday, and the food is always the same. It is roughly what people from Maharashtra would eat at home: dal, rice, chapati and some vegetable. It is vaguely spicy, but only very vaguely. For institutional food, it isn't bad, but it is always the same, and eventually almost everyone gets tired of it.

This happened to me, and I've been going to Kailash Parbat more often. It is nice to be a regular at a place like this. When I show up I get a friendly head wobble and last night I heard one waiter tell another, "hey, the cycle guy is here." Even the grumpy head waiter smiles and asks me about my bike. I almost always get a fresh lime soda (lime juice and club soda) and some sort of snack (like Pani Puri - crispy deep fried pockets that one spoons a watery chutney into and eats in one bite) and then a vegetable curry (there are dozens of choices, and everything is vegetarian) and some naan and rice to eat it with. I drink a cup of tea and sit for a while to digest before riding home.

I've also been trying to get a gas canister. My quest for a kitchen pretty much ended when after I had acquired a few basics, I tried to make a cup of tea, and I had exactly enough gas left between two canisters to boil one cup of tea. When Jill came there was a brief flurry of getting a kitchen knife and a frying pan, but getting a new propane canister is not as easy as it should be. I started trying again last Wednesday after Bill and Yuko had people over for dinner and Bill shamed me for being so lazy until he realized that it was not so easy for those who are living in one of the apartments and not the guest house. So in the past week I've spent a total of about two full days waiting around my apartment for the gas delivery tricycle to show up, but they never come when they say they will, or even within an hour or two of this time. So until then, a grilled cheese sandwich remains an unfulfilled longing, and I eat out or go to the canteen.

One of my favorite places to go is Joshi Bhojanalay, aka Friends Union Joshi Club. Places like Joshi's are nestled in corners all around the city, and many are quite old. Joshi's dates back more than a hundred years, and though the owners changed from one family to another at one point during that span of time, the food is still a straightforward Gujarti thali. (Gujart is a state in India, and thali is a style of meal, where a variety of dishes are served together. Ilangovan discovered the place and introduced the current TIFR crowd. (Ilangovan, or IG, is a mathematician of Keralan extraction who has been in Bombay for 18 years and has been my local guide to all of the best restaurants that I have found with the exception of Kailash Parbat. IG also was the one who finally dragged me to a Bollywood movie.) Anyway, IG showew Pranab, and Pranab took several of us there once, and I was hooked. I went there with Jill, Sreekar and the Ducrohets, and have never seen Jill enjoy a meal so thoroughly. Tonight I took Bill and Yuko.

The walk there from the TIFR bus stop is always moderately exciting. After a walk along one of the few relatively unobstructed sidewalks in Mumbai, one must navigate the big open place where traffic crosses haphazardly and various construction projects are underway - in other places one might call it a square - by Metro cinema, and this is always interesting. And the street between there and Joshi's is one way unless you are a bus or a pedestrian (or six pedestrians pushing a handcart twice the size of a car), which makes for interesting navigation. It is also perpetually heavily under construction. But eventually, one makes it to the arched entrance leading to the courtyard and the stairs leading up to the restaurant on the first floor. This is truly not the sort of place that can be found without a local guide.

Upon entering Joshi's, one sits down at one of the two-seat tables. One side of each table is open to the aisle where the waiters circulate. First, they bring a cucumber and tomato salad, raw red onion, small green chiles, a little bit of mango pickle, and scoop each of a red and a green spicy condiment. Then come buttermilk and water to drink. There is a choice of two dals, one sweeter than the other, or a sweet yogurt or coconut based dish. Usually, they give me all three, because I don't seem to be able to pick one fast enough. After this, the specific menu changes with the days of the week. On the day I went with Jill, Sreekar and the Ducrohets, we got a little fried ball with stuff inside and some sauce to go with it. It was quite tasty, and I think Jill had three or four by the time the meal was done. The dry vegetable was a wonderfully spiced cabbage and green pea thing, and then there was an aloo palak, some bright green stuff, and a paneer in curry. Crisp papad goes well with the spicy chutneys that come with the salad at the beginning. The roti guy came around with his ghee-drizzled disks, regular chapathi and the kind with a tumeric yellow tint. There were the hard, cookie like biscuits and a darker puffy roti, spiced with some combination that didn't get a chance to be critically examined before being consumed. Then the sweet nutty yogurt sauce came out. Jill liked this one. I turned to ask her what she thought of the place and she bubbled, "I keep going from this green one (the condiment that came with the salad and onion) to this white one (the sweet nutty yogurt sauce). The spicy one is so good, but it hurts, and then this one makes it better, but then I want the spicy one again..." Her eyes glazed over and she reached for another morsel of delicious fried thing with stuff inside.

A thali at Joshi's is a proper Indian meal, and most of the eating is done sans utensils. The rotis are torn into small pieces and used to scoop up the other foods. After a bit of practice, I am able to do this without making much of a mess, but there is a learning curve, during which the sauce often makes it well past the first knuckles. Especially in the south, rice is also eaten with the fingers, after adding just enough dal or curry so that it sticks together. I've tried this a few times, but doing it generally leads to a big mess, and I prefer to use utensils. There is a sensuality to eating with one's fingers that is missed when food is mediated by spoon and fork. Like the cacophony of spice that goes into most Indian meals, it isn't something that I want to have all the time, having not grown up eating like this, it is a bit overwhelming to have every meal be so intense. But the experience of eating a good thali like at Joshi's is one of the acmes of food experiences.

Harishchandragad

Saturday's trek up Harishchandragad was my favorite of the past three. (Comparing it to the green trek up Manikgaht is difficult, because this place is so different in the rainy season.) On the trek were Antiaji and Yogish, our expert guides and Yogish's wife Shoba. There was Sreekar and I from the math department, as well as Bill Casselman (who is visiting the math department from UBC) and his wife Yuko. Sam, Kevin and Tanaka (who is visiting from Japan) joined from physics, and Girish from astronomy. Travel was long but straightforward, involving only a train ride to Kalyan and 90 km bus ride.

We got off the bus at a wide spot on the road and set off across fields towards the cliffs a few miles distant. A local priest, barefoot and wrapped in an orange robe walked ahead of us. He had a string tied around one ankle, a reminder that he had said his prayers, or perhaps that he needed to pick up a loaf of bread at the store. An ox cart trundled along the road with us as well. A plastic bottle full of dark liquid was tied to the axle and hung down like a scrotum. My guess is that it was full of oil for when the squeak of the bearings (if there were any, which is questionable) became noticeable over all the other rattles associated with taking a wooden wheeled cart on a dirt track.

It was early morning still, and a lot of birds were about. A pair of black and white kingfishers were looking for fish in the stream. The way that they would hover they looked like gargantuan hummingbirds.


(Bill's picture)

We arrived at a village after about an hour, and stopped for tea and some breakfast. Supposedly the place where we stopped made an amazing poha, but I didn't get a chance to find out what this is, because Yogi was justifiably worried about getting such a large group up and down the hill in time to catch the bus and the train back to Mumbai. On the way out of town, we passed a woman washing dishes at a well, which was deeper than I thought it would be, and the water did not look good.

For the next 90 minutes or so, we gradually ascended through forest to the sound of singing bulbuls and rollers. The canopy provided shade and there was a pleasant breeze blowing. At one point, the trail split. Antia wanted to take the upper route because he thought it would lead to a shortcut. I expressed my reservations about following anything that Antia termed a shortcut, recalling the other two times I'd been on a trek with him. It isn't that breaking trail isn't fun, it's just that I was really enjoying the peaceful walk through the woods and didn't feel the need to add unnecessary adventure just yet. Yogi soon caught up and confirmed that following the upper path would be just fine, and we continued. Antia in the woods is almost the archetype of taciturn mountain man, but I think that he cracked the mask looked a little smug about the fact that we went his way. In any case, everyone was amused.

The trail led us up to a col where we rested and drank some water. A rock had been carved with a simple bas relief of a monkey's outline. This had then been painted bright orange. A bell hung from a tree branch above the rock, and the breeze ruffled an orange pennant. Following Girish's lead, Bill, Yuko and I gave the bell a ring as we left.

From the col, we ascended a trail that wound back and forth across a steep face. Large parts of the trail were carved into the rock, but there was nothing as steep as the staircases from Goragad two weeks ago. As we rose above the canopy, I spotted a few monkeys jumping about, mostly hidden by the foliage.

The trail topped out onto the plateau after 45 minutes or so, and we were able to look back over the valley we had crossed this morning. A long dam made half the valley into a reservoir that was used to irrigate the other half. After a short rest, we were on our way towards the other end of the plateau, where the Deccan plateau upon the edge of which Harishchandragad stands drops off to the plains of the Konkan coast in a massive cliff called the Konkan Kada. (Kada means wall.)

After a few miles of up and down through scrub and across dry washes, at about halfway to the Konkan Kada, we came to a temple. We stopped here to look at the carvings and to collect a little water from the spring fed tank that was in the temple. Only Yogi, Shoba and Antia were willing to drink the water. It was still quite nich though, because by this time the the sun was being rather assertive, and a few of us to the opportunity to rinse the sweat from our faces. I wet a handkerchief to cool my neck and keep the sun off.

Near the temple was a cave carved from the rock and full of water. A Shiva Lingam (a fairly common sort of shrine representing the god's penis) stands in the middle of the pool, and is bracketed by the remains of four pillars. Only one pillar still stands, signifying that we are in the fourth age, Kali Yuga (a Kali that is not the godess Kali, but some other Kali that doesn't sound different in English). Anyway, that pillar also falls when the age comes to an end in a few tens of thousands of years.

The path continued up and down, crossing dry washes that are sure to become impossible torrents in the monsoon rains, until it came to the edge of a lot of air. The cliff arced around to the left and right, and dropped what was certainly in the hundreds of meters. The edge on which we stood was overhanging, so looking out over the edge induced quite a bit of vertigo. A hot breeze drifted up from the plains below, and we amused ourselves tossing bits of chaff and watching them float on the updraft.

3.4 M avi of the edge of the cliff



Lunch was had in the shade of a tree. Shoba's chutney was once again the star of the show, but the boiled eggs, potatoes, tomatoes and flatbreads that it enhanced were quite welcome in the hot afternoon. Lunch was finished by a little bit of chocolate that Kevin had thought to bring. Unlike chocolate made for consumption in cooler climes, Indian chocolate is made with a smaller proportion of cocoa butter and does not melt in the mouth, or more importantly in the backpack. I caught a few minutes nap while my companions talked about cricket or Bollywood or something.

Our return was via the exact same route by which we came, only the light and our energy levels had changed. When we at last came back to the place where we had had breakfast, we found that to our pleasant surprise, there was a refrigerator full of orange soda and half frozen mango juice. It was one of the best orange sodas I've ever had.



The most notable feature of the long trip home was the fact that most of us were able to sleep on the bus. I was lucky and had a seat near the front, but still had to constantly fight the centrifugal forces that wanted toss me into the aisle or into the lap of the guy next to me. Somehow by clasping my fingers around the bar on the seat in front of me I was able to find a set of stable points that didn't disappear when I relaxed and went to sleep.

Legos+Math

Neil pointed this one out to me.

http://www.andrewlipson.com/mathlego.htm

Happy cycles and Keralan trike tricks

After his talk the other night, I introduced myself to Greg Roberts. Learning that I was a mathematician and would be in town for a while, he told me to email him and that perhaps we could for a cup of tea at some point, or that if I saw his motorcycle outside Leopold's that I should stop in. I did email him, and mentioned that I'm more likely to be found at Kailash Parbat than Leopold's, and that if I was there, the only fixed gear bike in India would be sitting outside. (That may be an exaggeration, but I'm not so sure. According to a recent report, India's only velodrome, near Delhi is, "full of bumps and cracks, and more often visited by snakes and rats that humans.")

Roberts told me about Hamu-bhai, his friend and a bike shop owner in Colaba. I stopped by there Sunday on my way to lunch. Happy Cycles is on Third Pasta Lane. (There are at least three Pasta Lanes; Kailash Parbat is on First Pasta Lane, two blocks down.) The shop was a typical looking Indian bike shop, with an array of wheels hanging in the doorway, and an ordered clutter of tools and parts filling the small room. Work stands don't seem to exist here, at least not in south Bombay. I guess that there is too much a premium on space. Hamu-bhai's two mechanics were working on bikes in the street, occupying space that would otherwise become parking. One was adjusting one of the standard workman's bikes - a double top tubed black frame built to haul heavy loads and last like a tank. I rarely see them well maintained, but I also rarely see them broken. The other mechanic was changing the seat on a kid's BMX. The bike was so badly rusted that a considerable amount of hammer usage was being employed to extract the old seatpost. I rode up and introduced myself, telling Hamu-bhai that Gregory had told me about him, and that I was just stopping by to say hello. He heard Gregory's name and looked at my bike and smiled, pulled out a chair and asked his son to go and get us some tea.



Happy Cycles sells and repairs both bicycles and motorcycles. (Note that both motorbike and motorcycle are short for motorbicycle, which is no longer a word.) There were a few almost shiny new hero brand bicycles leaning against the building on the sidewalk next to the shop, and an array of motorcycles and scooters, many of them covered against the constant abuse that is being outside in Bombay. I parked my bike at the curb and took the offered chair. Hamu was the first Indian I met who knew what a fixed gear was, and he explained the lack of rear brake to his mechanics, who set aside their tools to take a look at the American bicycle. Sitting on the sidewalk and sipping tea, I answered all of Hamu's questions about my bike, and about what I was doing in India.



His curiosity about me satisfied, he pulled out a picture book of the sort that one can have made at a photo studio these days and showed me some of his finer creations. The artistic bicycle is not a much existing thing in India - the only human powered vehicles where much attention to aesthetics is ever paid are the tricycle rickshaws and cargo haulers (more on this later). But put a motor on some wheels and Indians go for detailing like the best of them. Hamu-bahi was into restoration and customization of classic Indian bikes, mostly Enfields. Classic is a loose term of course, because until recently the models were pretty much the same year to year. When you think about it, redesigning a working device and updating one's manufacturing plant is an expensive and somewhat wasteful task to do every year. Mostly for this reason, Indian bikes changed rather slowly compared to their counterparts in other parts of the world, and Enfield Bullets are still rolling off the assembly line looking a whole lot like they did in 1947. Now the UK even imports "brand new classic" motorcycles back from India. In any case, some of the bikes in the Happy Cycles stable are restored 50 year old gems. The pictures in the book depicted the conversion of a few of these aged finds into sleek machines. A significant enough chunk of my formative years were spent being enamored with the combination of steel, tires, and motor that is a muscle car that I stiil love an artistically done machine. (I used to have one of these, but of course, mine was black.) The motorbikes that Hamu-bhai showed me were in this category of vehicle as art. Two of the bikes from the picture book were parked outside the shop, Hamu-bhai's own in red, black and silver, and another apinted in black and green and heavy on the chrome. Gregory has restored this bike for Johnny Depp, who plays Shantaram in the movie of the book. My favorite bit of detailing was the pressed tin grips, kickstart and foot pegs, textured with chromed vines and flowers.



I took my leave of Hamu-bhai, and made a few notes in my mental picture of what sort of Indian bike I might be tempted to build. As I said, a decorative bicycle is pretty rare in India, but it could certainly be done. The cycle rickshaws in West Bengal were often nicely decked out in bright paint, though often maintenance was seriously deferred. A smaller number of the cargo trikes were similarly decorated, including the one that I took a ride on in Kerala. We were walking back to the guest house where we were staying in Allepuzha and I stopped to admire a shiny new trike. The owner was resting in the shade and wagged his head, smiling at my approach. He made a gesture that I didn't understand until his friend said I should get on and go for a ride. This proved tremendously amusing. An Indian bicycle is not a light thing to start with. To make a trike, the frame is often modified to include not just a double top tube but a doubled down tube as well. The rear triangle is removed, and in place of the chainstays, a wishbone of angle iron extends back and spans the axle. Rebar seat stays are welded in, and an angle iron frame is made for the wooden box that sits behind the rider. The wheels are special heavy duty things, often forgoing tensioned spokes for solid bars of rebar welded to hub and rim. The drivetrain consists of a standard Indian set of cottered steel cranks on a chainring (perhaps with "Atlas" or "Hero" stamped into the steel), about eight feet of chain, and a cog bolted to the middle of the axle. I estimate about at 2:1 ratio of chainwheel to cog.



My first attempt at getting started consisted of me lifting myself off the seat by pressing down on the pedal. It seemed that one of the wheels was in a bit of a divot, and lifting the contraption out of the hole took more force than I had in just mass. I pushed the trike forward a foot to get all three wheels ready and started slowly forward as I looked for another opening in the light afternoon traffic. I knew that quick and agile were not going to apply to the handling of this beast, so I waited for a good sized opening, slowly moving forward all the time. There was a car parked by the side of the road, and I swung wide to pass it, still waiting for the trickle of auto rickshaws and motorbikes to stall for long enough for me to make a u-turn. The way the vehicle was pointed moving forward would lead up and over a bridge crossing a canal, and into more traffic, so I needed to get it pointed the other way.

Suddenly, the trike stopped. I had misjudged how wide the rear axle was, and the right wheel had scraped along the bumper of the car. I jumped off and hoped I hadn't caused any damage to car or trike. The trike was fine, but there was a minor but noticeable scratch on the car, which was a fairly new model. Fortunately the car's owner, who was standing nearby, was laughing so hard that he had no ability to be upset. The trike's owner was having a blast watching the giant white guy try to pedal his trike, and insisted that I continue when I tried to give up in embarrassment. Trike backed up away from car, I found my opening and eased out into the street. With a lumbering turn, I was headed back the the other direction. I pedaled along, feeling a bit like an elephant, turned back and returned the trike to the very amused owner.

Some books

One of the ways that I have been getting to know this place is by reading it's books, both books about the place and just books by Indians.

The first one I read was Suketu Mehta's Maximum City. It has its fans, but I found it only so so. By the author's own admission, his chosen topics are ideally suited for 14 year old boys, or others with a love for the life stories of mobsters, prostitutes, religious fanatics and others similarly extreme. I must admit that it gave me a little apprehension to be reading this book in Seattle, preparing to go to this place where Suketu made it sound like people got taken out in broad daylight by thugs hired for a pittance on a daily basis. I've yet to see a gangland murder, or even anything looking particularly violent. (I don't think that the rock throwing mob ever actually got around to it.) Not to say that the violence isn't real, it just isn't what I'd fill three quarters of a book about this relatively nonviolent city with. Not to say it didn't teach me a lot about Bombay, it contains a wealth of interesting anecdotes, and certainly helped me to orient when I showed up here.

On the night when Sukhendu, Ilangovan, Chan and I went out for dinner and Ramzan sweets at Muhamed Ali Road, I picked up Yann Martel's The Life of Pi. The protagonist is Indian, but the book is not so much explicitly about India as about exploring the Indian way of mixing fantasy and reality. This is of course also manifested in Bollywood, but shows up (from what I can tell) in the literary tradition going back to ancient times. Lots of storytelling in India is unabashedly fantastic. In a collection of stories adapted from old sources (they all predate the Muslim influences), gods and magic show up as frequently as they do in Ovid. It seems that if it would be more interesting to mix things up a bit, the storyteller will more likely than not mix them up. And of course Indian food is the great metaphor of the culture, and the unchecked cacophony of spices come together with the same flexible attitude towards consistency.

In Madras, I acquired Midnight's Children. I could have read this book before I and I can read it again after I have spent the rest of the year in India and again after many visits to this place and all would be different experinces. The book is as thick with sideways description and cultural reference as the city is thick with humanity.

At a party at an apartment building in downtown Seattle full of artists lofts, Jordan (who I made the digital sundial with) told me about Shantaram. I had just learned that I was coming here, and he was all jazzed up about this book. I put off reading it until last month, when I found it in Darjeeling and wanted to have something to read while curled up in my sleeping bag against the cold. It is a bit of a door stopper, but I tore through it in little more than a week. I completely understand how Jordan found it a great story even without my particular reason for being interested in this corner of the world. But a lot of it happens to be set pretty much in my backyard. After I read it and Jill started reading it, we would go for walks from my apartment and I'd point out the slum where Shantaram lived and set up his clinic, Leopold's bar, the Taj Hotels and so on. We went for drinks at the Oberoi, and every time we went to the airport, we passed by Haji Ali Mosque, lit up at night in decrepit splendor.

Shantaram's description of the experience of a Westerner becoming Indian illuminates many things about the culture that I find confusing. Like Maximum City, it is a book about gangsters, but it is written by a (former) gangster, and the stories are somewhat autobiographical, rather than presented with the excitement of a hotel room interview. And there is a lot more to the book than a gangster story. When I arrived in India and began my journey through this culture, I was very aware of the shifts in resolution that I experienced culturally. Incomprehensible sound focused past accent and I began to understand Bombay English, gesture and affect began to distinguish the individuals who had previously been instances of a smaller cast of actors. I've slowed down now, the newness of the city has worn off and I am less likely to venture out from TIFR than I was at first (Kevin and I were talking about this at lunch today - it is a bit frustrating how disconnected from the city this place can be). Reading Shantaram, I followed the story of a similar path, retracing some of the steps that I had taken, and then going much further.

Shantaram is the name given to the book's author, Gregory David Roberts, when he went to live in a village in northern Maharashtra. When he goes there in the story, they get off at Jalgaon, which is where Mike, Rhi and I hopped off on our trip to Ajanta. After the events of the book, he was captured and served the prison time that he had escaped and was living on the run in Bombay from. He now lives in Bombay, near Kailash Parbat, the restaurant where I am most likely to go if I go out to eat. He still helps run the free clinic in the slum where he lived and is involved with a number of other humanitarian projects in Bombay and otherwise. Roberts spoke last Sunday at the arts festival, and I went to see what he had to say. In the book, one of the characters takes some time to explain a philosophical system based on an advanced layman's understanding of physics and a belief that the general tendency of the universe is to order itself, and that mind is the current acme of our understanding of this process. In any case, he's a smart guy and a competent speaker, and it was interesting to hear him out.

In other news, I've bought my ticket to come back to the States in May. I'll be in the bay area for a week for a conference, and then up to Seattle and down to Santa Fe. I'm looking forward to the trip. The conference in San Jose is an AIM workshop on rational curves, which I'm supposedly developing some formalisms to help describe. Hopefully I'll have something concrete in time to share with the experts in May. I certainly have a clearer idea of what is going on, but that also means that the obstacles and dead ends are more defined.

The slew of job applications that I sent out over the past months have begun to send back echos, and so far nothing positive has turned up. I'm not really willing to stay another year in India (and it isn't clear that that's an option anymore, because of the housing allotment). I've been meaning to make another set Freelance Mathematician business cards anyway...

The 12 megabyte ideal

Math has funny ways of unpacking itself. I was playing with a fairly simple example, the surface defined by x^3+y^3+z^3=1, and suddenly the answer the question I asked the computer was not an a handful of one line equations, but a list of equations that made a 12MB text file. It didn't shed any light. The feeling was not unlike missing a turn on a mountain bike and going ass over teakettle into the bushes.

The old man with cats gives me hope. Everyone else, ...

Last Saturday there was another trek. It was much shorter this time. Pictures are here:



After the trek people got together at Gokul. Fun, but something seems to have followed me home lodged in my gut and is causing general unpleasantness. Regardless, the most memorable thing of the day was meeting the man who fed the cats. Yogish and Shoba had told me about him earlier that day, and we came upon him walking from where the taxi dropped us (everyone else had a desire to go home and take showers that somehow overpowered the desire for food and beer). The man who fed cats is an old man, and according to Shoba, he spends about 150 of the about 200 rupees (approximately $5) that he makes every day on fish for the city's stray cats. We stopped to watch the cats eat. There were about a dozen, tabby, calico, a couple not yet full grown teenager-kittens, all of them looking sleek and tough. They devoured the bombil fish that the man would pull the bones out of and tear into small pieces that he gently tossed to these cats. Shoba tried to pet a tabby who was devouring a piece of fish on the recessed part of a wall, but the cat didn't seem so keen on having its back pet while it was eating so she let it be. I learned that the cat feeder has about fifty cats that come to the three or four places where he regularly brings food. He knows them all, and they recognize him.

Sunday was a slow day. I eventually made my way into the office to check the internet. (I still don't have a connection for my apartment - which wouldn't be such a big deal if I had a phone that could make outgoing calls, but my "phone" is really just an intercom that can receive calls from the outside world. I could also get a mobile, but the general hassle of getting one is a common topic of discussion for other expats, and I'd rather avoid it...)

Anyway, I ended up reading this article in Rolling Stone about Tibet. I visited Tibet 20 years ago. I remember Lhasa as a place where I ate momos and fried bread from the market, drank tea with butter and salt with a family who adopted Eric and I just because. In the Bharkor market I bargained with thumb and pinky for a brown corduroy chupa (and then acquired the nickname "Khampa Chunchun" when I wore it) and some leather glacier goggles. I remember hitchhiking out along a dusty dirt road towards the valley with caves where one version of a Tibetan creation story holds that the monkeys decided to come down out of their caves and become humans. We camped in a field by the side of the road and woke up in the middle of the night as a herd of yaks wandered by. In the morning we climbed the ridge of rock and sand. I made it about 100 feet from the top and couldn't keep going because I felt altitude sick for the only time in my life. I read the article's description of what things are like there now and my eyes swam with tears. That place where I was is gone. Tibet is consumed, and with the spoils of the carnage, China creates missiles to move an arms race into space, fighter jets to sell to those who can't get them from the US, Russia, Great Britain or France, and building the largest dam in the world.

Many people in China and India have the attitude that it is soon going to be their turn to be at the top of the hierarchy of world power, and that exploiting land and people in order to get there is perfectly allowable, perhaps necessary, because that is how it has always been done. And that "getting there" largely means having lots of shallow material junk that is all as new as possible. This may be truly the way things will play out, and I've had a number of chances to hear people spell this out for me. I tend to respond with the observation that they're a bit late in the game, that the map is pretty much closed and that there's not going to be much left if they can't come up with something more creative than copying the west. If you want to live way beyond your means and exploit the rest of the world to do it, it kind of requires a rest of the world. India at least seems to have quite a bit more compassion towards than China. Not that it's a nation of saints by any means. Ahimsa is largely a myth, but there are a few cat-feeding old men and people who know that getting along is the only way to make it work in and among the noisy bustle of those who just want more flash.

Tumling to Sandakphu

How does one describe waking up to a crowing rooster to watch dawn unfold itself at 3000 meters, spilling across the southern faces of the highest mountains in the world?



I guess I can't really.

Sitting there, I thought about how distance can create beauty. From 50 miles away, the cold, the wind, the fear of a fatally misplaced step does not exist. Instead, one sees the perfect white of snow and ice, wisps of frozen crystals blowing off the peaks, and the stark profiles of the ridge lines. I feel similarly in the emptiness of the southwest, or in the few forests of thousand year old trees that still stand further to the north, or watching waves crash on to a shore with a regularity unpuncutated by millennia. In such places, observing the structure of things at non-human scales is unobstructed, and this creates a special sort of experience where it is easy to let go of the fundamental insignificance that is one's idea of the self. The basic goodness of the world is so nakedly apparent that the fear of losing something valuable by forgetting the ego falls away into the void between the human scale and that other.




But the spinning planet is of course oblivious to our amazement, and the fiery dawn soon calmed into a clear, cold morning. We went inside and had some porridge and were on our way. Within the first mile, we changed our angle enough that we had a clear view of Everest. Jill and I stopped to let Dabar catch up (he often hung back, stopping to chat with friends he met along the trail or take advantage of a spot with cell reception to send a message or make a call - yep, 15 years ago it was McDonald's most places, Coca-Cola everywhere, now it's internet most places, cell phones everywhere). Dabar pointed out the peaks to us. This was not an angle that Everest is frequently photographed from, so the profile that we were presented with was not as familiar as expected. In fact, Makalau visually dominated the group more than Everest and it was this sharp profile that I first stopped for. Later at Sandakphu we were able with the binoculars to make out some known details.



Dabar led us up a not often used path along a ridge adorned with weathered prayer flags. Small fire pits showed the ashes of someone else's stories.

After an hour or so, the trail started down to Garibas, a village nestled into a pass where we stopped for tea and some snacks. The way down wound through forests of bamboo, rhododendron and Taxus pine, or Himalayan Yew. Dabar said that a strong tea made from the needles was used as an anti-cancer medicine. Strawberry vines crept around the edges of the trail. A few times we heard what might have been animal noises and one time it was a troupe of monkeys, but the rest of the time either whatever it was never revealed itself, or more often, it was a small group of cattle browsing on the new bamboo shoots. The trail itself had been there for quite a long time. Nearly the whole thing was cobbled and then overgrown. Runoff gullies tumbled down the hillside, braiding in and out of stone staircases that were never perfectly regular to start with. Much of the trail was in shade and there was frost in the parts that never got sun.

In the village, we stopped at the Sherpa Tea Stall Garibas, this displayed painted white on a green board. Two cats sunned themselves on a shelf by a window, through which we could hear a small fire heating tea. Garibas has a cell tower. Dabar tried to make a couple of calls but the reception didn't seem to be that great, but this instigated a bit of phone shuffling among the few locals who were hanging around. While this was going on, two women, one older and one younger, and a small boy arrived. The women carried large bundles of firewood and the boy, who must have been about five, was proudly carrying an armful of sticks.

We sat there for a while. The sun was warming my back and I was not cold and neither was it particularly humid, so I was surprised to see that my breath was visible.

From Garibas, the trail ascended steeply, and then leveled out, winding around the side of a hill to Kalapokhri, the black lake. About an hour out of Garibas, the change in weather that had been heralded by the lenticular cloud crowning the sunrise on Kanchenjunga had arrived. The wind picked up and washed our trail with cloud. I stopped to watch three white prayer flags on long poles held straight by the stiff wind. I stood breathing as the clouds flew past against the blue palette of sky. Imagining the prayers flying off towards the Himalayas carried on the wind took very little effort.

After leveling out, the trail wound around on the northeastern side of the ridge looking out over shady forest. Streams of the cleanest water that we had seen in India crossed the trail, iced over when the hill blocked the sun for most of the day. It was quiet, and we walked at our own paces in silence for a couple hours until the last bit of uphill to Kalapokhri.

From Kalapokhri to Sandakphu was another 6km, much of it steep uphill, so even though it was only early afternoon, we decided to stop there for the night. The village of Kalapokhri is a collection of huts sitting at a low place in the ridge. The place where we stayed was over a small rise from the lake (more of a pond) at the intersection of a few trails. When there was a break in the cloud, we could see Tumling in the distance and were surprised by how far away it looked. We had reached the low end of the altitude range where yaks can live, and the lowland cattle were replaced by these large black and white shaggy beasts. A corral next to the guest house where we were staying was home to about a dozen young goats who constantly clamored for attention. They were very cute and I repeated my desire to have a herd of goats of my own.



In the evening, sitting around the charcoal fire in a low ceilinged room wallpapered with old newsprint Dabar and I talked about how in the US most heating and cooking is done with electricity or gas, and that wood fires are often a luxury. He is surprised that goat milk is more expensive than cow's milk. In India it is the opposite. We talked about old forests, about the small areas of protected forest in our respective countries and how sad it would be to grow up without ever visiting a stand of trees each as big as one of the houses in the village. I told him about pink fleshed salmon and he smiles and shook his head slightly, his tongue sticking half an inch past his teeth - a gesture clearly indicating that his imagination was giving him something that tasted really good.

After dinner, the clouds had cleared and the moon was not yet up. There were more stars than I have seen in a long time. At Chaco Canyon, the glow of Gallup 100 miles away on the horizon is visible, but that is probably the closest that I can call to mind. India may have far more in the way of toxic and septic pollution, but even in the cities light pollution is less than in the west.

The next morning I woke early enough to go outside to see the village before it woke up. An Indian tourist who had been driven up in one of the land rovers and had explained to Jill that it was too windy up at Sandakphu to appreciate the view, as well as elucidated a selection of his theories about the universe was awake too, greeting the crisp morning air with a cigarette. Perhaps he was from Kolkata and it made him feel more at home. In any case, I was glad that he didn't try to come say hi.

As the livestock and their keepers began to stir, I went in to wake Jill. We brought a couple of the ruled hyperboloid stools out into the morning sun and drank tea as our hosts started their morning chores. An old man with an argyle sweater vest walked by with pails of fresh milk for our porridge, and a young woman set out a dish of corn for the goats. As each had their fill and interest in eating began to wane, the head butting and rough housing that had simply been part of getting to the food became a game that started taking over the area until they were chased away down the hill to spend the day foraging.

After a lazy breakfast (they really did have to go milk the cows first) we were on our way again. The trail wound around to the west and through a village where a baby goat had just been born. It was still wet and the mother was licking it clean while nudging it up onto unsteady legs. A little while past this village we came to the next pass. We rested a little while before the trail started uphill in earnest. For a while, we were keeping pace with a young man and his two yaks, and at one point a train of ponies passed us on the way down. It was quite steep, but the clean air and the views and the promise of the view that lay in store invigorated me and I felt like I could have run up the hill.



Our trek peaked at Sandakphu, 3636 meters above sea level. Above a sea of cloud stood a panorama vanishing into central Nepal and rising up to Everest, less than 100 miles to the east. A series of jagged black ridges, behind which could be seen the distant peaks of the Tibetan Himalaya, connected the Everest group to Kanchenjunga, lying only 50 miles to our north. From here the panorama continued across Sikkim to Bhutan and Chomling in the east.



We spent the rest of the day reveling in the views. We climbed to the highest point around, a jut of rock topped with an arch festooned with hundreds of flags.



India has many ways of wearing at a person. The noise, the pollution, the poverty and the way so many people are culturally or consciously blind to these things, not to mention the constant supply of people who see a white person and perceive nothing more than a fat wallet made mobile get to be more than a bit much. Knowing that that place is there, that as I write this the moonlight is reflecting off the ice and illuminating my panorama makes all the hassle disappear, and I can remember that not all of this place is this insanity of a city.