Don’t look back

As I described in a post earlier, I started running to gain physical strength and boost my self-confidence. But not any more. I run because I love the activity. It gives me the kick; the kick that Mathematics gave Erdos, the kick an abuser gets from his weed. And that’s why I run, even in extreme conditions. I run without seeing the hour of the day. I ran when it was pitch dark and when other runners wore their reflective safety jackets. (must get one for me too). I ran in extreme weather, in rain and wind, also when it was snowing. Even when there was no crazy gora/gori runner in sight for the whole two-and-a-half kilometer long trail. I have run till I got a blister on my foot. I have swallowed an insect while running and still ran back home. But today was different.

For most of the past week, the temperature hardly went above zero. White layers of snow and ice had accumulated on trees, rooftops and cars. There was only one colour outside – white. So when yesterday night’s thunderstorm brought a downpour melting all snow, it was awesome. The temperature soared to 11 degrees above zero (which is “warm” compared to winters here) and I set out to run.

Lake on the way to the trail (cf. anomalous behaviour of water)

The snow had melted partially overnight  so the trail was marshy. But it was good compared with yesterday’s condition, when the whole trail was covered with snow and ice and you couldn’t distinguish the trail path from the  woods. In fact, that was the reason I skipped the trail yesterday and ran to the ‘Happy Hollow Park’ and was delighted to see little kids sledging in snow; but that is another story. So, here I was on the 1.5 miles trail jogging and enjoying the weather. As I came across the bridge, I could see and listen to the water from the molten snow dripping off the bridge.

It was all good until I came upon this layer of ice which I realized was but snow melted into water and frozen back into ice. One wrong slipped foot could bring my bones cracking down. I carefully trudged the ice layer. As I ran further, there were more such layers of black ice and marshy path. Umpteen times I got that mini-heart attack as I slipped on snow. I realized the trail was too risky and decided to follow a different safer path, the footpath (sidewalk) on my way back.

As I was nearing the end of the trail, the sight ahead froze me dead. I don’t really remember whether my life flashed before me, but you do get the idea, don’t you? I saw a huge layer of black ice covered all along the path. Usually when it rains, this part being shallow gets covered with water, but today the water had frozen back into ice. It was a thick blanket of transparent ice laid over the entire path and beyond. Skidding on the ice meant a sure bone-fracture and the way back was no different. It was the devil-and-deep-sea situation. Slowly and cautiously, I stepped on the ice. The friction was near zero so I soon gave up. I tried crawling also but even that was not so feasible. I waited there for a couple of minutes thinking, some of the longest in my life. Going back was not an option. Finally, after summoning some mental strength, I set out for the woods thus by-passing the ice mass. It was a wet mucky lowland and my shoe would sink in but I soon learnt to step on the fallen twigs. I balanced myself over two fallen (chopped) tree trunks as I passed the layer of ice below. Foot by foot, I crawled ahead and after a long struggle, finally made it to the other side! At last, I lived to tell the tale!

The situation was so terrifying that I forgot to take a picture of the ice-path after conquering it!

Even though this little tale of mine might not be so exciting as that of the crazy people’s in this video , its my adventure story and recollecting it gives me that “kick” which makes it all worth!

Some thoughts on Class Field Theory

Hi readers,

I have been studying Class Field theory this semester. Since I didn’t take the Algebraic number theory course offered in the previous semester, I am facing difficulty following the course. But this in no sense makes the course less interesting. Here in this post, I pen down a few thoughts on the subject, which are just my understanding of the subject. Note that WHAT FOLLOWS MAY BE INCORRECT, not to mention imprecise. But I will try and update this as my understanding increases over time.

In Class Field theory (CFT), the mission is to understand which is horrendously difficult, so they study , where is the maximal abelian extension of . By that, I mean such an (infinite) extension of so that its Galois group (which again is infinite) is abelian. Now for infinite Galois extensions the correspondence between subfields and subgroups is no longer true, so they do what they always do — change the definitions to make this correspondence work. One defines a topology on and now instead of subsets of this huge (uncountable) set, the correspondence is between closed sets and subgroups.

One also studies the field extension L/K where L and K are number fields instead of K/Q, as in a basic number theory course. Initially, I had difficulty assimilating the results and finding which results true for K/Q go through to L/K. For example, it every extension K/Q, at least one prime ramifies (in fact, all the primes dividing the discriminant). The units of Z are just 1 and -1 but there are lots more units in (given by Dirichlet in his Units theorem). As a consequence, it is possible that in an extension L/K of number fields, no prime of ramifies in . When the discriminant is a unit then no prime ramifies and the extension is called “unramified”.

To be continued..

SF Vacation

Since the focus of the last few posts has shifted from Mathematics to my life in the US, the stats show an increase in number of visitors. But I must add a word of caution, that soon enough, Math posts will be seen more.

A couple of months ago, Moka invited me to his place at Mountain View near San Francisco in California in December. (This is the link to his blog where you can find crazy stuff, although many good posts have been deleted). Winter in the south (southern parts of US) are much warmer unlike that at Purdue so many Americans throughout the country go southwards for Christmas and New Year.

I stayed there for a little more than a week and I could meet Ameya, who returned to India as I left SF, just in time for his birthday back home. At Ameya’s place, I went for “jacuzzi“, which is a bathtub with massaging jets. It was a Godawesome experience and hopefully I will be able to enjoy it again some time. The five of us, Moka, Ameya, Vartak, Lala and me had a great time pulling each others’ legs. The bakra however, was Vartak as usual.

Moka took me for local sightseeing on weekends and although he had seen most of the places, he didn’t mind accompanying me again. I visited the Golden Gate, the fisherman’s wharf, Burns State Park, Stanford University and more. We also went to the elegant Ghirardelli factory where I grabbed as many dark chocolates (only for me) as I could. Then there were the Cheesecake Factory where Penny of The Big Bang Theory works (I had hoped to get a glimpse of her ) and the Bubba-Gump Shrimp Co of the Forrest Gump fame. Photos have been uploaded here –

https://picasaweb.google.com/abhishekparab/SanFranciscoVacation

But the part of California I enjoyed the most was that I could run without heavy winter clothes, in bright sunshine along breathtakingly beautiful trails. I ran almost everyday, taking Ameya too with me when I could.  The last day there, I knew I was going to miss running so frequently in Purdue winter, that I beat my previous running record. Within an hour and a half, I ran along the trail from near Moka’s home to Google HQ at Mountain View and back, covering 8.5 miles! That is over 13 kilometers! You can have a look at the iPhone running app’s page here.

I returned to Purdue today and the snow has shown its true colours, rather colour – White! Roads, grass, treetops all are covered with pure white snow. And I am now gearing up for the cold winter, the vacation at SF has been a great refresher to begin the new semester with.

Running my first π miles

Running those first miles changed my life forever. I am no longer the chubby out-of-shape couch potato that I used to be.

I always wanted to run. So many times, I had the urge to run and keep myself fit. I would call up Jimish and we would decide upon the time and place our jogging would start the next morning. But no sooner did I begin running than I would give up. It wasn’t much fun. I would puff and pant and gasping for breath, would start walking, sit down on the park bench and decide never to run again. After running for two or three days, the health-conscious side of both of us would again die away and things would soon turn back to usual.

But it was in Chennai last year that Jonathan came to visit IMSc that I became serious about running. He and Sachin were regular runners at their institute – the IISc at Bangalore. Both used to run on the service road outside IMSc and I was again hit by the running bug. During the starting days, I recollect being unable to run even half a kilometer without stopping. I didn’t think I could run half as much as they could. I hadn’t the body of a runner. Turns out, a meticulous running plan, their supportive encouragement and some control over my food habits was all I needed to tap the inner runner in me.

With a steady running schedule, I could run back and forth the distance between the two railway stations there. Just in two months, I lost around 8 kilos. All the stuff they show in those gym ads actually came true for me without pumping any weights, only by running! But the joy was not in seeing myself on the weighing scale every fortnight but the fact that I could actually run so much distance in one stretch. I was amazed that my body could actually endure it.

Back in Mumbai too, I continued to run, increasing distance periodically. When Pushkar visited India, I was surprised to see he too had lost pounds. On questioning, he replied he too started running, and we nodded in total agreement. In Pushi, I found a run-buddy! For the one week he was in India, we ran together on the Eastern Express highway.

When I came to America, I could see people running everywhere in all weather at all times of the day. This inspired me greatly and I expanded my running paraphernalia to include sports tees, a pair of running shoes and a GPS enabled cellphone with a running App (Runkeeper) that tracks your speed, location etc. Its much fun running here on a jogging trail with trees and river around. The air too, seems cleaner.

When Pushkar described his -mile run at Georgia Tech, I was amazed. Being a lover of mathematics, the word “-miles” stuck in my mind. I knew my next mission. Inspired from Pushi, I set out for running miles. I had never completed the trail and my cell App told me that it was 1.5 miles. I continued further until it showed 1.57 miles and then turned back. Pacing steadily, and varying my speed regularly, I ran till I reached the end of the trail, … miles it was! In just above 30 minutes! A couple of months back if anyone would have told me I could run so much, I’d have mocked at him.

There have been many difficulties I faced while running, for example, one day I swallowed a bug and it was real sour. I thought I was going to die for sure! But apparently, it is quite common among regular runners. I saw this blog and realized how crazy people can go.

Winter is setting up and running at near-freezing-point temperatures seems difficult. Tougher the challenge means more the excitement! Geared with woolens now, I am preparing myself for this challenge. “Whatever doesn’t kill you makes you stronger”, they say. Lets see how this goes, I will write a sequel to this post by the end of winter describing my experiences.

 

10 things about America

Things a new desi in Amreeka will find amusing:

• Everything is topsy-turvy – from light switches to car directions.

• Everything is huge. Corridors, classrooms, vehicles, roads, footpaths – they are so massive! If you have difficulty walking, then Walmart offers you a little car to move around for shopping. (Such huge is Walmart, and other supermarkets!)

• Its all so clean – Trust me, no Indian in the America has ever or is likely to pee or spit (sh*t) on these roads, or similar actions they wouldn’t hesitate in India.

• Taps are like joysticks, as in the latest Batman movie. For the mechies, they have two degrees of freedom; for others, you can control the temperature and water flow with a single knob.

• There are machines for everything. I saw two trucks in the campus, one crushed twigs into fine wood powder and spew it into the other. I even saw a machine for sweeping roads!

• My house doesn’t have a ceiling fan, but there is an AC and a heater.

• Buses have seat belts but no clutches. The bus I went in had an automatic load lifter, the driver just put the luggage on the cart and it automatically lifted and placed it in the bus! They also have strange abstract things like hand-sanitizers and route maps.

• Buses also have inbuilt GPS so you can track their location from your cellphone. This technology is actually useful when during hasty mornings, every minute counts. Also during winter so you don’t need to wait out there freezing yourself.

• Speaking of tech-freakiness, weather apps on your cellphones (unlike the Met department in India) are reasonably accurate, so you need to carry your umbrella only when it says high probability of rains.

• All notes from 1$ to 100$ have the same dimensions! A dime (10 cent coin) is smaller than a cent and a quarter (25 cent) is bigger than a dime!

• No one breaks rules, a biker will halt on an empty road in the dead of the night waiting for the red signal to go green. So do pedestrians!

• Its the rule of the (Indiana) state that vehicles should yield to pedestrians. That makes it possible (and fun) to cross the road when a speedy car is approaching us and we can continue walking without the fear of being run over.

• Its impolite not to hold the door open for the person walking behind you.

• Squirrels here have no stripes on them, guess they haven’t been blessed by bhagwaan Shree Ram!

Overall, things might appear exciting and “cool” for a newbie (fresh-off-the-boat is the term) but soon, you realize life is totally predictable. I miss the uncertainty of Mumbai – those sporadic torrential rains which have served an excuse for the delays of millions of office-goers, the traffic-jams which teach you what patience is, and the crowd in the morning local trains that teach you what life is all about – Survival!

The American Sojourn – Job Fare

Its been more than a month since I have been in the US and things are pretty much falling in place. I happened to experience a fantastic thing that occurs every semester in the American universities, which I am going to describe in this post. Its called the “job fare”. Companies – big and small – come on predetermined days to universities where they are given places to set up their stalls.Graduate students in search of jobs or internships submit their resumes and the better ones are called for interviews and stuff.

Simple as this may sound, you may wonder what my role here might be, since I am a research student and not really looking for a job. The previous day, I went to Walmart with Aditya. I looked up at an insulated cup and exclaimed, “I’d buy this but its too expensive.” He asked me to wait until tomorrow, the day of the job-fare.

Inside a huge lush green garden in the campus, there were about a hundred colorful companies’ stalls and thousands of job-seekers all formally dressed up. On the tables were kept fancy stuff, which you were free to collect. Those interested in jobs / internships had to stand in huge queues and one-by-one reach the stalls, submit their resume and convince the company representatives to recommend their CVs up above the pay-line. Well, I wasn’t interested! And that gave me all the time in the world to collect the freebies. They ranged from pens and pencils to iPhone covers and mousepads.

I was brutal in garnering this free stuff. What could I do, had to prove my Indian-ness out there! Plus, my roomies were standing in those long queues hoping for jobs, so I further had the onus of “dhaap”ing stuff for them too!

After a while, my pockets were full of pens and paper clips and sanitizers so I started filling out my bag with heavier items like insulated mugs and water-bottles and more bags. When my bag too gave way, I went to my office and emptied the bags and pockets and went anew! Later, I got bored (sick, actually) of collecting pens and mint and got a little embarrassed too. But soon enough, I saw a 2x2x2 rubik’s cube (my favorite in the entire loot) and a yo-yo and suddenly my embarrassment disappeared. In fact, I was embarrassed about having gotten embarrassed and started “dhaaping” with a new vigor.

When I went to the Amazon counter, the lady eyed me suspiciously when I tried to grab a torchlight. Hesitatingly, I asked her if I could pick up the torch. She asked my major, I replied Mathematics. Both of us knew Amazon doesn’t hire mathematicians so finally, she was dejected and said, “Go ahead, and take the box too, it contains the batteries”. Well, it was awesome!

At another counter, there were cute little computer mice kept and I couldn’t resist saying, “Oh, a mouse!” The girl there replied, “No, its mint (packet) in the shape of a computer mouse” and I, dejected that it wasn’t a mouse, replied back, “Ohh, its a decoy!” Man, I can’t forget the annoyed look she gave me! Must be really proud of the company she belongs to.

The guy from Michelin tyres was cool. He asked my major and I replied back saying I really wasn’t out there looking for a job but going around, taking pics and.. “… and collecting freebies”, he completed the sentence. “Well, now your publicity is not restricted just to Formula-1 cars”, I said and he agreed wholeheartedly.

With three (free) bags full, I returned to my office. When I brought “some” of the stuff back home, my roomies were overwhelmed especially after I gifted them a SanDisk pen drive, a Schlumberger water-bottle and a John Deere cap. Tomorrow, I have a new MATLAB shirt to wear before going to the second and last day of the job fare!

The American Sojourn – 1

The whole flight journey from Mumbai airport to Delhi and then to Chicago was an exciting period of twenty odd hours wherein I kept thinking of all of you in India who would have made my journey much more enjoyable. As I absorbed all the jazz and hype around, I also penned down some thoughts while in the plane and at the airport. It may not be a great fun to read and definitely won’t make into any bestseller like “The inscrutable Americans” but its “my” version and soon will find a place on my blog. (It finally has!) So here I go…

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The aircraft is descending to land, I look out of the window and see one of the fifty United States of America. I had expected to see tall skyscrapers, like the ones I had seen in American TV serials like Prison Break. Instead, I saw greenery everywhere! (Perhaps the sky-scene in the TV was New York, I thought. In retrospect, Anurag tells me that the “other” side than the one I landed is mesmerizing, with the tall buildings and all). There were well-planned buildings giving the whole landmass a geometric shape. The insides of these shapes were painted green, by the immense vegetation. (Back in India, before landing to CSI, one sees Dharavi, supposedly Asia’s second-largest slum). I was impressed.

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The immigration formalities all have been done and I’m here inside Chicago airport waiting for the bus to Purdue. Its scheduled after an hour and will take three more hours to reach Purdue.

I sit here looking all around, dazed by the surroundings wondering whether or not to spend my first couple of dollars at the MacDonalds nearby. I finally decide not to, and start writing this memoir.

As I was figuring a way to call up Shaunak asking him to pick me up and to call aai informing her of my safety, I noticed the nearby phone booth. I was curiously looking at it, since I didn’t have any change coins. Soon enough, a fair guy with dark black Indian hair called me and offered to help. He gave me his cellphone and I called up dabad. He turned out to be an Indian from Indore working here.

He soon left for his bus and I sat there looking around. Everything is spotless clean. Not a spec of dust anywhere. Even then, the gore janitors are driving those little vehicles with mops at their bottom, cleaning up the place. “So what, its equally clean at CSI and Delhi airports”, my patriotic mind defended. (CSI is Chhatrapati Shivaji International airport, for those of you who don’t know). I continue thinking what to write.

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Bikash Shakya from Nepal and his family are waiting for the Purdue bus. He is starting a PhD in Biology at Purdue. And he has a wife and a kid daughter to support. This would have been outrageous in India. A man’s foremost duty there would be to fend for his family; personal interests come later. That is why Mr. Raman (name changed because I forgot) is doing his PhD in Electronics at IIT Bombay now after retiring at 60 from his engineering job. In this respect, America is good. Bikash and his family and I are about to board the bus, and I pause writing.

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For some reason, I ain’t feeling like changing the Indian time on my wrist-watch to the local time. I prefer calculating the current local time every time I look at it. “This watch will always show IST”, some patriotic whim in my mind screams. The watch, with the UK flag on it, shows Indian time in the US. Is it globalization? Never mind.

I get into a bus and watch American roads. Its perfect, superb, just ideal! Its a superhighway, all vehicles follow traffic rules. Yet there are cameras installed at tollbooths. I passed a construction site and it was pretty much the same as in India. Except that the workers were all in safety-suits and with their helmets donned on. Some time later, I saw a large flat area with thousands of vehicles and a huge signboard that read – America’s auto auction. Pretty cool, man! A few minutes later, I saw a wind-energy-power-plant that went on like miles in both directions. Yeah, miles, gallons, pounds, Fahrenheit, a new Indian will go crazy with the mensuration units here! Wind, solar power, nuke energy and all.. impressive!

A few hours later, I landed at the Purdue airport and Shaunak’s friend came there to pick me up. He was an American and when I told him its my first visit to the US, replied something like “No sh*tting”. I had a tough time following his accent but it was not that bad. Regretting not watching movies in Avdhut and Mali’s room

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The above was a part of an email I sent to my near-and-dear ones, my friends in India, who I wished time and again would be with me. It would be an altogether fun to experience this with you guys!

Republic of India

My friend Swapnil is preparing for his Civil Services exam. A recent discussion with him convinced me how we Indians are totally ignorant of so many things about our country. As an example, how many of us know Operation Cactus? It was a (successful) military operation the Indian government initiated against armed mercenaries who tried to overthrow the Maldives government. Where does India rank in terms of geographical area? Can you describe the preamble in the Constitution of India? We as Indian citizens are ignorant about our history, geography, scientific achievements, politics, international relations, our military prowess…

The country is run not so much by politicians in power but the IAS officers, those brilliant civil servants who formulate critical policies that have secured our democracy. The civil services’ exams are considered to be one of the toughest in the country. Aspirants totally devote many years in knowing so many facets of India, a crucial aspect in studying for the exam . They are expected to know obscure facts about our country. Not just that, in the interview one is also judged by her/his ability in dealing with real-life case scenarios such as ‘How would you tackle the Maoist situation?’ A lay answer might be, “Just bring in the military and shoot out the mischief-mongers”. Thankfully, the country is not left to such Hitlers or Mussolinis.

In the recent sabbatical, I am currently reading about India as much as I can lay my hands on. Unfortunately, Wikipedia gives only a superficial view or so to say, a fact-based perspective as against an opinion-based perspective. As far as documentaries are concerned, hardly any documentaries are made on important topics like the Indo-Pak wars or the Operation Blue Star. Our news channels are constantly busy in lifting their TRPs by breaking news everyday. Nevertheless, some interesting Wiki-links are given below:

• India
• Operation Cactus
• Operation Blue Star
• Kerala (You see, I’m not biased towards Maharashtra!)
• Zero Rupee Note
• Corruption in India
• Right to Information