Tuesday, April 29, 2008

One of my Turns

Chop.

Feels light. I like it.

Chop.

It shines so! The light makes little shimmering patterns along the sides. Oh!

Chop.

The colours so vivid. Flowing into each other. Red against silver. Silver against Red.

Chop.

Moving this might pose a problem. What will she say?!

Chop.

Well, I could move it in pieces. To the barn, maybe. But she won't be happy. No, that won't do.

Chop.

Wonder if the suitcase would be big enough to hold it all. Bring me my suitcase will you, dear? Heh heh. I made a funny.

Must clean it up though. Can't leave a mess. No, she won't like that at all. No No. I could use the dress to wipe it down. Yes, that will do it.

It's a nice dress though. Her favourite wasn't it? The blue one that she wore to dinner the other night? Oh well, what's done is done. She won't notice.

Heh heh.

No, she won't notice, will she?

All the red, on the bright blue. And no one to notice! What a pity!

Oh what have I done?!

She told me to be careful with the axe. She won't like this at all. No No, this won't do!

Monday, April 28, 2008

Small World

Reading about the history of 20th century quantum physics is slowly becoming one of my favourite ways to kill time - am always excited by it because I feel like I might one day contribute to these thoughts as well!

Just found a nice, easy-to-read article on some of things which I /do/ understand - John Von Neumann's interpretation of the early theory in terms of the notion of a Hilbert space. As I read this article I found myself nodding along saying 'yes, yes, of course' and that is always a nice feeling - to know what the fuck is going on ...

Quantum Mechanics (Stanford Encyclopedia of Philosophy)
Mathematically, the theory is well understood; we know what its parts are, how they are put together, and why, in the mechanical sense (i.e., in a sense that can be answered by describing the internal grinding of gear against gear), the whole thing performs the way it does, how the information that gets fed in at one end is converted into what comes out the other. The question of what kind of a world it describes, however, is controversial; there is very little agreement, among physicists and among philosophers, about what the world is like according to quantum mechanics.

Monday, April 21, 2008

Escher and Geometry

Have just been reading Roger Penrose's big fat ouvre The Road to Reality, and thought I should post about something I have learnt.

Here is a picture called "Circle Limit IV" by M.C. Escher which very beautifully describes a certain kind of geometry that is alien to us regular folk, but one that appears completely naturally in the known universe - the so-called hyperbolic geometry. This "representation" by Escher explains how this universe behaves - if it were compressed inside a circle.The idea is, as an object tries to get closer and closer to the boundary circle, it gets smaller and smaller in the usual sense of the word in such a way that its size at any point in time completely prohibits it from ever reaching the circle (Think: Zeno's paradox, but this time it's for real!). This was exactly the idea that Einstein used to describe the behaviour of bodies that are going really fast - the speed of light behaves like an "infinity" - it something concievable but not actually attainable.

Of course, for one of the angels/devils shown above, the universe looks just like ours does to us - ie. completely flat and the far reaches of the universe (ie. the boundary circle) just as unattainable.

Penrose, of course, just like any other popular science author, goes to great lengths to explain to the reader that this is not just a figment of his imagination but something that is just as real as you and me. However, I have always wondered at the rationale behind such an effort to convince - it seems to me that those people who think this is "dumb math" are probably not going to be reading a 4000-page tome on science to begin with - and for those who are actually interested, what you are doing is going to great lengths to be pedantic - something almost every thinking individual utterly detests! Solution: say it like it is, and those who want to understand will do the necessary self-convincing.

Thursday, April 10, 2008

Today

Today was a great day! It was one of those days that you dream about - not too vividly though - you don't necessarily want to live it. No, it was one of those it-would-be-great-if-it-happened-to-someone-else kinda days.

It all began with me waking up from the dead, wandering zombie-like into the shower only to realize my towel was in my room, wandering back zombie like only to discover it was actually in the bathroom because I had just taken it there you blithering numb-skull, and then wandering .. oh you get the picture. I was wandering a lot.

Then I met R., which is an exciting experience if you want to simultaneously feel proud to know someone like her and feel pity for someone who works so hard and whose students don't give an iota of a shit.

Then went to class post-lunch, which, for those of you who may not have tried it, makes you feel like the aforementioned iota. Doubly so when the lecture is in complex analysis.

Following that was an intense conversation with one of my students on what a similar triangle is. The kind of conversation where the primary speaker discovers that removing one's liver with a pair of scalpels is not such a bad idea after all.

Then I gave a talk - the less said the better.

But now comes the genuinely cool part - between 4.30 and 8.00, apart from a conversation with S. I don't remember doing anything except work. It was ridiculous the amount I ended up getting done. Discovered this crazy "expectation" function, an extended Fourier series, and proved that a certain algebra (goes by the name of Cuntz) was as simple as they come!

Ended the day by proctoring an exam, where the aforementioned liver was officially removed.

Friday, April 4, 2008

Social Web

This idea has been haunting me for a few months now. I spend a lot of time online - mostly reading, listening to music and watching videos. I read a few blogs, and even among the news websites, find myself greatly attracted to what other people are saying about the news of the day. Digg and Reddit, for instance, have taken this idea to its logical end - news stories are only posted there if there are a million people interested in it.

I find it intriguing that so much who we are and what we know depends completely on the people around us. But today, in this exciting global village we live in, the number of "people around us" suddenly includes everyone with a modem! It boggles the mind to think of the number of people reading the same news I read everyday, and coming up with completely different conclusions, and those conclusions influencing my conclusions and so on ...

The link posted here talks a little bit about this interesting social interaction we have developed over the web. I'm not sure how good the idea is, but it does merit some thought, so I decided to post it.


TED | Talks | Jonathan Harris: The Web's secret stories (video)
Jonathan Harris wants to make sense of the infinite world on the Web -- so he builds dazzling graphic interfaces that help us visualize the data floating around out there. Here he presents "We Feel Fine," a project that scours blogs to collect the planet's emoti(c)ons

Wednesday, April 2, 2008

It's awesome to be me

This is another one of those posts again ...

Yes, it's frickin' awesome to be me. I am wonderful, and truly fantastic.

So here's the story, after I get back home in May, wallow in food and wine for a month, and then come back and do jack-shit for 3 months (yes, I don't have to teach this summer), guess what I do next?

Oh yes, I get to be a TA peer mentor! For the uninitiated, this means I get to meet all the new TAs (read: chicks) and tell them how to teach effectively and do all the things I (yes, that would be me) do so well. I get to give them some presentations during their orientation week, have them visit my classes next semester to get some tips and attend "debriefing" meetings. Always wondered what those were - just hope that involves the aforementioned chicks and a distinct lack of briefs.

Just got a letter from Miss BustMyAssIfIFuckUp this morning offering me this position, and I feel great. Especially because lately I have been getting more and more frustrated with my students and the apathy with which they approach the stuff I teach them. It's all their fault, of course, because (and you might have figured this out by now) I can do no wrong :)

Tuesday, April 1, 2008

Note to Self

I periodically find myself questioning my abilities as a mathematician (not to mention as a human being), but I am in one of those up-swing times right now - everything seems possible, and I just feel very very excited at the thought that I am going to get to do math for the rest of my life (inshah allah). So I thought I should list out some of the cool things I've learnt this semester.

(Oh btw, my blog-editor (Scribefire) has an on-the-fly spellchecker which flagged "allah" and "learnt" but not "oh" :)

Here goes :

1. Montel's theorem, Zalcman's lemma, Picard's theorem and the other awesome compactness conditions for meromorphic functions.
2. Covering spaces and their correspondence with the group of deck transformations.
3. Rudimentary notions of a Riemannian metric, and some wishy-washy stuff about the hyperbolic metric on the unit disc.
4. Weyl-Von Neumann theorem about self-adjoint operators (crazy!)
5. Definition of the extension of a C* algebra, and the introduction to Brown-Douglas-Fillmore theory.
6. Nuclearity, exactness, c.p. lifting theorems
7. Amenability of a group and its connection with nuclearity (together with a cool proof of amenability of an abelian group).
8. Just yesterday, some homotopy techniques in computing the K-theory of pull-backs (still fresh!)

So that's that. I hope, in times of desperation, I look back on this note and feel good again.