What I've learnt

I am back to the position I was in sometime last semester, where I am beginning to doubt my abilities as a mathematician. Given that this is a passing phase (I hope!), I decided to make a list of some of the things I have learnt since I got back from India in June.

C* algebras :
- Semi-projectivity and its relation to Shape theory for C* algebras
- Asymptotic morphisms and Shape equivalence
- Bartle-Graves selection principle and its relation to asymptotic morphisms
- C* bundles and C(X)-algebras
- Dauns-Hoffman theorem about bundles over the primitive spectrum
- Dixmier-Douady's results on local triviality of bundles of compact operators
- Inductive limit representation of bundles of semiprojective algebras
- K-theory sheaf associated to a C* bundle over the unit interval
- UCT and Kunneth theorem and the usefulness of geometric/projective resolutions
- Brown-Douglas-Fillmore theorem
- Generalized homology theories for C* algebras
- Mod-p K-theory and associated invariants
- Construction of Hochschild/Cyclic homology
- Construction of the (non-commutative) Chern character
- Finally understood Stokes' theorem

Unrelated to C* algebras :
- Structure theorem for finitely generated modules
- Presentation of modules and canonical forms of matrices

Hopefully, reading this sometime in the future will help me feel better about myself :)

Birthing Blues

I turn 26 tomorrow. I feel like I should be excited, that there should be people jumping with joy at the thought that I am a year older, that there should be fireworks and various alcohol-induced escapades. Needless to say, none of that is happening. Funny thing is, I don't really want any of that. I don't particularly like being the centre of attention in any room of people, so being -the dude- for a whole 24 hours might cause some serious stress.

I do plan to go get a beer or two with some good friends. I had cake a day early. I am now listening to Pandora play me some Massive Attack and Pink Floyd. Things could be worse. I could be YOU!

The Walls

She put down the phone, and made sure it was safe in its cradle, before walking back into the living room, and up the staircase. She entered the room - the walls stared back at her.

The room was as it always had been - clothes strewn on the floor, a playstation in the corner connected to the television, showing some game she had never seen before. She smiled in the memory of when she tried playing Mario Bros. for the first time and was so good at it the she almost beat him - and of how mad he had been that he didn't speak to her for an hour!

She looked up, and saw the Flag. Its beauty framed against the wallpaper. And she remembered.

The bookshelf by the side were filled with Alaistair Mcleans, and Louis Lamour - all of them dog-eared from use. Those stories delighted him! - tales of exploration and adventure, of sailing to new lands and to discover unknown treasures - to fight the good fight!

The picture on the wall of him in full armour for a school play - and she remembered the reasons.

On the bedside, a framed picture of his father. The medals of honour shining bright in the sunlight streaming in through the windows. A picture of heroism and honour! But .. what was that look in his eyes?

A guitar at the foot of the bed - such a treat to listen to! He had real talent! The guitar, painted in shades of black and khaki, its strings taut, ready to play the most melodious music, or the most terrible, ungodly wailing noises that she was starting to hear.

And then it hit her - all the pain came flaring back - all the pent-up loneliness and bitterness, almost blinding ... this agony! The anger when he left, kept up inside in the face of his happiness and excitement. The feeling of impotence when those nice men in suits had convinced her that they were doing their best to find him. The raw rage at that spineless general who came back home leaving them on their own. Those bastards!

Dating Rocks

This is a rather interesting article by BBC - about the most recent attempt at dating Stonehenge. The pomp and show associated with this article has me wondering about its authenticity.

On the one hand, one cannot be too sure that the scientists are doing real science, and not just making up numbers that fit the popularly held belief - so that they might be able to get more funding for the project. Their academic careers probably depend on making this project work (the University they presumably work for has given them a sabbatical to work on the project, and would definitely not want to see them return empty handed.)

On the other hand, there is the question of the media's integrity as well! Anyone who has watched the flood of news channels these last few years will have realized that there is a lot of money to be made in the making News - clearly the way they make money is by sensationalizing an issue to the extent to which people would pay money to watch other shows (in this case, Time-Watch) on one of their sister channels - and in the process doubling their revenue off the story!

But the story has definitely caught my attention. The results do sound cool!

BBC NEWS | Science/Nature | Dig pinpoints Stonehenge origins

Until now, the consensus view for the date of the first stone circle was anywhere between 2600 BC and 2400 BC.

Strictly speaking, the result was rounded down to "between 2400 BC and 2200 BC" - but 2300BC is taken as the average. .....

"It's quite extraordinary that the date of the Amesbury Archer is identical with our new date for the bluestones of Stonehenge," said Professor Darvill.

"The date of Stonehenge had been blowing in the wind. But this anchors it. It helps us to be secure about the chronology of events.

Communication Breakdown

This last week has been a rather pleasant one - giving a talk to some friends on Thursday about a subject that's dear to me was very exciting and very liberating in itself. Have found myself a little under-used this semester because of the lack of teaching, but this talk gave me something to think about when my mind was bored. That kind of thing helps a lot!

This upcoming week is going to be similar - Need to plan a 2 hour presentation to my advisor and sundry classmates about what I've been working on these past few months - continuous fields of C* Algebras. It is going to be quite tough, especially because I don't know if I understand things well enough to explain it to anyone else! That takes a whole new level of knowledge, and I am just beginning to scratch the surface - Help!

But hopefully, enough work and I should feel comfortable enough to give the maiden presentation - building on it might be harder because of a complete lack of perspective (why AM I doing what I'm doing?!)

Oh well, time will tell ...

Reproach

Ahh .. the beast of insecurity raises its ugly head again!
Begone, Begone thou foul fiend!

Disconnect

Read Upamanyu Chatterjee's English, August this week for what is probably the 10th time. As before, I was struck by the deep melancholy of the protagonist stuck under all that humour and bravado. It is a great book, especially from the eyes of someone like me, who has grown up in India, speaking English with a Hindi accent, reading Oscar Wilde while listening to Rafi, and at the same time being completely out of touch with the realities of rural India.

Often have I wondered about my right to call myself Indian - agreed, much of who I am is because I have grown up there, eating Pav-Bhaji and chasing BEST buses while decked out in gum-boots in the pouring rain in Bombay. But my outlook on life is very heavily influenced by Western ideas - the idea of premarital sex does not pose any ethical dilemmas, the thought of living in an English-speaking country for the rest of my life does not leave me muttering to myself about my fate - so who the hell am I?

Ever since I landed in Madras in 2000, I have given this some serious thought. Fortunately, the struggle to learn Tamil and French simultaneously, coming to grips with guttural Tamil (in college) and refined English (at home) and many other things I went through during those years have together left me feeling rather good about myself! Most importantly, the interesting mix of people I have met in Bombay, RV, Madras, Mysore and finally here in America have left me with a rather malleable cultural perspective. I enjoy listening to different accents and trying to catch turns-of-phrase which are typical of a certain community. There is a perverse joy in looking at an obviously stoic Indian girl and wondering how good she would be in the sack.

Yes, This is the kind of thing I do in my free time - think about, and write about myself. I do need a life.

Happy Birthday!

This might just be the first time I have remembered in nearly a decade. Go me!

It now seems appropriate to post what is possibly my favourite poem -

Where the mind is without fear and the head held high
Where knowledge is free
Where the world has not been broken up into fragments by narrow domestic walls
Where words come out from the depth of truth
Where tireless striving stretches its arms towards perfection
Where the clear stream of reason has not lost its way into the dreary desert sand of dead habit
Where the mind is led forward by Thee into ever-widening thought and action
Into that heaven of freedom, my Father, let my country awake.

- Rabindranath Tagore

The future of interfaces

So while checking the usual tech news this morning, I came across a fabulous collection of pilot videos from Mozilla Labs on their futuristic concept of a web interface known as Aurora. Now although it seems like the desktop is far too cluttered in these videos, it is exciting to realize that one day, we might have a 3-d interface by which we access information - an interface where things can be grouped together on the desktop more visually and also moved around the desktop more intuitively.

This seems to lead back to this incredibly cool demo by Jeff Han of a multi-touch user interface which gives, in my opinion, the best possible way in which one could interact with a 2-dimensional device.

Now, the neat thing about these things is that the world now seems to be in a position to provide the computing capabilities to make full use of these technologies - for instance, there is D-Wave's Orion quantum computer which can recognize images and tell one from another by being able to harness immense amounts of visual data.

Plus, there is this Microsoft-promoted visualization tool called Photosynth, which is able to collate photographs from flickr, tag them with meta-information and club them together to give a panoramic view of the object/place in question.

All this might seem too much like science fiction, but with the rate at which technology is going forward, I wouldn't be surprised if we had something like Aurora in action in another 5 years.

Protection

Just reading The Fifth Elephant by Terry Pratchett - The book begins with the death of a man named Wally Sonky, who was stuffed into a barrel of molten rubber. You see, Mr. Sonky was known for making, among other things, little "wallies" - a rather life-threatening business in a city full of orthodox dwarfs who don't even allow their women to shave, let alone use a condom.

So it seems appropriate that I blog about something similar - an effort by the National Aids Control Organisation (NACO) in India to spread the use of these wallies among the traditionally backward (and hence vulnerable) social groups. They have gone about giving condoms to the women of a rural community north of Delhi, and have educated them as to its benefits. The male-dominated society has responded well, and seems willing to take these measure to prevent the spread of STDs and unplanned parenthood.

This, to me, is a big deal. I very strongly believe that, whether one uses it or not, the option to use a condom without any social stigma associated to it should be available to every living human being. Unfortunately, though, there are a great many places in the world where using a condom is considered a sin, and a prevention of natural (ie. god-given) functions of the human body. Of course, they don't stop to think about the economics of raising children, or, for that matter, getting Aids.


BBC NEWS | South Asia | Condoms help tackle Indian taboos

"We first began marketing the female condom primarily among sex workers three years ago," he says.

"We then decided to introduce this among rural women, since they are also a vulnerable group with little access to public health services.

Fallen

The leaves rustled. A dog barked.
The buzzing of the crickets and the broken shrieks of the wounded lemur.

The forest was alive tonight.

Ruan was alive tonight!

The torn carcass was lying before him, evil red poison pouring from its veins. He had done what he wanted. His nemesis, lying before him in a puddle of his own piss and blood. But why wasn't he satisfied? Why had the burning desire to kill not been dowsed? The rage that had pursued him for days (oh! the torture). It was still there, lying in wait for the body to catch up with itself. Soon it would return, this hunger for human flesh. Soon, the very thought of the ripe chubby flesh falling off the bones of a helpless manling would be enough to send him into a frenzy of rage!

But he wasn't like this, you know. Ruan remembered days, now seemingly in the distant past, where he was merely another wolf, sharing the world with the tasty homo-sapiens, but where the anger and delirium had been missing. And then he remembered ...

Coming home that night after a leisurely stroll through the bog, the smell of his cave had been different. He thought nothing of that, though - just a stray rat, he said to himself. But then he saw them, oh the pain!

They were his cubs! His little cubs, you spineless bastards! You waited till I was gone because you knew I was too strong! Oh you swine ...

And then the madness took over again. Diving through the thicket, Ruan plunged towards the only place he knew he could find fresh human flesh.

In the distance, the eastern sun rose over Beijing.

Void

There's a place
In the darkness of your soul
In the depths of your mind

What will you do?
When the world begins to search
When they begin to find?

How do you explain?
The seeds of lust in your heart
The words of rage in your mind

What will you do?
When you begin to search
And you begin to find?

Philanthropy and Bill Gates

As is common knowledge, after 30 years of heading one of the most power-hungry corporations in the world, Bill Gates has decided to (at least superficially) throw his energies into bettering the lives of the down-trodden peoples of the 3rd world.

The two articles linked to below are the latest in a series of debates on the hypocrisy of it all, and also on the possible good things that might come of his new-found altruism. The difference between these and any other article on the subject is that these tend to focus less on Mr. Gates' abilities/inabilities and more on those of the entire free market economy - as they point out, philanthropy is becoming a much more marketable word now than it used to be, so the question is : "How are the large corporates going to incorporate that thinking into their business strategies?"

Making Capitalism More Creative - TIME

Creative capitalism isn't some big new economic theory. And it isn't a knock on capitalism itself. It is a way to answer a vital question: How can we most effectively spread the benefits of capitalism and the huge improvements in quality of life it can provide to people who have been left out?

The Audacity of Bill Gates - TIME

There is something deeply wrong with a system that allows extremes of inequality, these people believe, and creative capitalism is just a way for the corporate élite to put off making the necessary changes.

Swamp Thing

Just began reading Alan Moore's rendition of "The Swamp Thing" - a horror-fantasy comic about a creature that is a traumatized plant-like monster that spends its life trying to understand itself and its past.

The original story arc revolved around the usual super-hero mythos - something along the lines of The Hulk - the creature was born in a lab experiment gone bad, where an explosion results in the mingling of the scientist's mind with the boggy marsh surrounding the laboratory. When everyone thinks he's dead, he arises phoenix-like, and begins to hunt down those responsible for the explosion and for his wife's death (obviously, she was conveniently disposed off by the bad guy's henchmen).

But Alan Moore takes the original script and gives it a twist - in #21, "The Anatomy Lesson", the reader finds that the Swamp Thing has been located and shot down by the Military Special Corps and now a doctor who moonlights as a half-plant mutant himself is performing the autopsy. In a beautiful interplay between the panelling and the story line, Alan Moore bores into the tortured anatomy of the Swamp Thing, revealing that it is not really a man who has been turned into a plant, but merely a sentient plant, that believes itself to be a human!!

This outstanding revelation now leads into the creatures deepest darkest nightmares, and reveals it as a desperately pathetic animal looking for salvation. Wonderfully illustrated, Alan Moore made his mark with this series, and it certainly is a brilliant read.

There is a wonderful line in one of the comics at a point where the Swamp Thing has visions of running from the plant world into the Human plane of existence while being advised by his humanity. It says : "This is the Human Race, You have to keep going, or you will get disqualified"

Work? Surely you jest!

Well, I've been getting progressively more and more excited about work over the last few weeks - It all began sometime 2 weeks ago, when I started reading Dixmier's book on continuous fields of C* algebras. Something about the cohesiveness of that theory excited me - especially the facts about the ideal structure being recoverable from the fibers. Reading Nilsen's paper seemed to fix those ideas, and then getting to Dadarlat's paper was just like seeing daylight again! So beautiful, this idea of asymptotic morphisms, and the way they tie up with continuous fields!

Anyway, I could wax eloquent about this for hours - but the point is that I find myself actually doing some minimal "research" for the first time. I am reading papers and books interchangeably, and wondering about the grander perspective so that I don't get lost in the trees and miss the forest.

Trouble is, and this just might be me torturing myself for no rhyme or reason, I find it hard to communicate this to others. Maybe I am not trying hard enough, but it seems like everytime I start talking about this people shut off and go all bleary-eyed on me. This, of course, led me to consider the value of such communication - it seems like one of the most important aspects of research : to be able to exchange ideas freely and to get excited about what other people are working on. Maybe I am an idealist, but I feel like I should put more effort into this.

Add to this: the rather disturbing conversation I had with my advisor today - about misdealings and dishonesty in the profession. He's a nice guy, and the events we discussed obviously left him feeling very annoyed and offended, and I could totally see it from his point of view. So the question is: at what point do you stop this idealistic free exchange of thoughts, and begin to work towards publishing your own papers without running the risk of someone stealing your ideas?!

I am in two minds about this, and it will require some careful thought - but in the meantime - onwards with semi-projectivity! :)

Vagabond

Discovered a new Manga this week - called Vagabond - written by a gentleman named Takehiko Inoue, and I must say, I am really enjoying it! It tells the tale of a self-obsessed Ronin, who spends half his life fretting about the fact that he is not the world's greatest Samurai, and the other (concurrent) half challenging the greatest Samurai to duels. He goes from being a total wuss to being something of a deified legend - and meets some really cool people along the way.

The nicest part about this is the art work - Inoue sets a rapid pace for the book, but contrastingly, likes to pause every once in a while and reflect on what has just happened. For instance, this page is preceded by a long and tough battle between our hero and some soldiers from the Imperial Army who are out to kill him. He has just spent the last 15-odd pages massacring them - an impaled neck here, gouged eyeball there - the usual excitement - but now the author takes this page to pause. The middle panel is that of a mercenary who was killed when a rock was hurled on his head, and that is framed by the moon on either side - it obviously is meant to have many interpretations - but there is a certain serenity and a foreboding about this page that has me all a-twitter!

Real nice comic - I've just started so I hope it stays this way.

The Omniscient One

God : I think I'll get rid of Norway.
Satan : Why, O Gracious One?
God : Never did like the fjords. What the fuck is a fjord anyway? I gave that one to Slartibartfast, and look what he did. Amateurs!
Satan : Hey! I like those little things! You can't get rid of dem phyordz! (Aside: Hey Azazel, what's a phyordz?)
Azazel : It's a prehistoric turd, boss.
Satan (to God): Hey! I like toids! I fuckin' protest!
God : Ok, that's it. I'm done with you (Kicks him into hell). I decree that you will now be known as the Fallen Angel!

(Now really mad, Satan rises rubbing a bruised rump, while Azazel is laughing heartily and kicking around a piece of meat).
Satan : Hey Azazel, what's the bald piece of flesh you're playing with?
Azazel : It's one of His rejects, boss. He calls it a homo-erectus! (chuckles).
Satan (rubbing his chin) : Reject, huh? Well, no longer! Let's mess with Him - throw that critter in Africa and give it hair only on its head and its crotch! This'll be fun. Oh, and just for fun, teach it to play with rocks like you do, will ya? Maybe one day it'll throw rocks at Him!

(This was the not-so-coherent thought that popped into my head while reading this)

Snowblind

In other news .. I just found the link I've posted below, and loved it! The cover for Snowblind is frickin' unbelievable - it seems to capture the original song, and at the same time reflect the fact that it is being sung by this dude.

The Covers Project » Black Sabbath

This is fucked up ...

I had a feeling this might happen someday, but this is happening during a time when India is doing well as an economy, and just when people like me (and many others) might start considering coming back to India because the standard of living is now comparable to the west - Why in fuck's name does the government do shit like this? This is preposterous, and my complete impotence in this matter is the worst part!


HRD orders faculty quota, IIT directors livid-India-The Times of India

The lecturer’s post in the IITs is a contractual one and the basic salary is Rs 10,000 per month. Usually, fresh PhD candidates are taken in at this level.

If their services are found satisfactory, they are promoted to assistant professor and get onto the permanent rolls of the IITs. But now, almost half the posts - 49.5% to be precise - will be reserved at both these levels.

Comic delights

So, I've been reading this blog for a while now, and find her very very amusing. But this was frickin' awesome - laughed me ass off.

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!

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.

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.

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.

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

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 :)

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.

Supa Dupa Fly

I was just revelling in the joy of Pandora, and felt like posting something in praise of it. So here's a few hip hop songs I've discovered in the past few months :

Missy Elliot - The Rain (Supa Dupa Fly) - I frickin' love Missy Elliot.
Wyclef Jean ft. Missy Elliot - Party to Damascus - Nice fusion
The Roots ft. Jill Scott - You Got Me (Live) - Sung by the original songwriter, quite a bit better than Erykah Badu.
Mos Def - Ms. Fat Booty - A tribute to the booyah! Need to find out what the hell an "idaho potato" is :)
Talib Kweli - Get By - Pretty slick production, methinks.

And now, back to Pandora ...

Firefox goes Places

Have just downloaded and installed the new Firefox 3 Beta 4 and found myself reading the Release notes rather in awe of what we have in store for us. Understandably, Firefox is a surfer's wet dream. It has great features and add-ons which make it so user-friendly it's ridiculous. Have just been blown away by the new bookmarking setup in this version: Places.

It is a great way of bookmarking pages, minus all the pains of bookmarking. So bookmarking, the way I do it, is have a bunch of folders on the Bookmarks toolbar folder (called "Important", "Blogs", "Comics", "Reading", etc) , each of which contains a list of links to related sites. Now the problem with this is two-fold: If the number of such folders gets out of hand, the Bookmark toolbar is too long, and now has a little arrow on the right telling me there is some stuff out there. So now you have a folder called "S" for "Stuff". It contains everything from Youtube videos of kids playing rad. guitar, to news about a local book fair next week. ie. kinda stuffed.

The other major problem is having too many links in the "reading" folder : everything from a BBC article on shell-fish to a random blogger's take on Calvin N Hobbes. Not so good if I need to scroll through 15 sites before getting to the one I want to read.

In short: the problem would be solved if I just had a way of searching my bookmarks from the location bar. ie. the new Places "Tags"! All you do is, when you bookmark a website, just give it a tag, like "blog, shark, miniature". Now if you type any of those 3 words, the bookmarked website will show up under the location bar! Love this!

More importantly, the list is sorted in decreasing order of "frecency" (frequency+recency). Just found all of this, and am extremely impressed. Now I don't have to worry about limiting the number of websites I bookmark ever!

Firefox 3 Beta 4 review : Mozilla Links

New in Beta 4 is adaptive learning: Firefox will keep an eye of what you type and what you select. After a few repetitions Firefox will understand what you’re trying to do and provide better suggestions. This should address the case where frecency (a combined frequency and recency index) didn’t provide the best results.

Free, as in Beer

Now Rann the Kite brings home the night
That Mang the Bat sets free—
The herds are shut in byre and hut
For loosed till dawn are we.
This is the hour of pride and power,
Talon and tush and claw.
Oh, hear the call!—Good hunting all
That keep the Jungle Law!
Night-Song in the Jungle

Oh yeah! Just found The Jungle Book as a free ebook. Love the fact that these authors have been dead so long that even their estates are sick and tired of leeching the little pennies from every book lover on the planet. Go dead people!

On a not-so-legal note, I also found the new Artemis Fowl Graphic Novel as a torrent file. Am waiting for it to download so I can continue to procrastinate and avoid work through the rest of the weekend. Excited!

Facade

Just found myself re-reading some old Sandman comics - something I find myself returning to every now and again to feel that euphoric I-am-seeing-real-art feeling. The comics always border between extremely good fantasy and extremely disturbing horror and it's often hard to distinguish one from the other.

This specific comic, called "Facade", talks about the faces people wear when they go out into society, the tragedy of seeing someone's true face, and finally that of mortality (a recurring theme in these comics, in the guise of a cute goth girl representing Death). The following excerpt (minus the image, unfortunately) is one of those times you stop to wonder what the author was thinking when he wrote this, but then you stop wondering because you don't want to know the answer :

I hate making faces. They give me dreams.

I have only two kinds of dreams : the bad and the terrible.

Bad dreams I can cope with. They're just nightmares, and they end eventually.
I wake up.

The terrible dreams are the good dreams.

In my terrible dreams, everything's fine. I'm still with the company. I still look like me. None of the last five years ever happened.

Sometimes I'm married. Once I even had kids. I even knew their names. Everything's wonderful and normal and fine.

And then I wake up. And I'm still me.

And I'm still here.

And that is truly terrible.


PS: The use of bold lettering is originally part of the comic, and although it seems superfluous, a second reading makes you realise that it actually gives the passage that extra dimension. Neil Gaiman is a genius, he really is.

Angels and Demons

Just came across this beautiful picture of a naked woman tying her arms around a statue of Satan while being possessed by the darkness at her feet. Somehow wonderfully captures the moment of the loss of innocence without saying too much. Got the image off of this website, where some folks at Cornell University have compiled a whole bunch of images of the Fantastic in Literature, with a view to educate.

Have found myself lately getting more into horror fiction as well - H.P. Lovecraft and Edgar Allan Poe mostly, and some random short stories from magazines with titles like Tales of the Weird. So this is right up that alley.

Night food

So it is 2AM, and I was reading this awesome book called "A Game of Thrones" by George R R Martin, whom I was introduced to just this week. Rather ordinary sword-and-sorcery fantasy, but it has me rather enthralled. It is very much in the vein of Mercedes Lackey, whom I like a lot, so I am pretty happy.

Anyways, as usual, got hungry and ate some cereal. While eating, I did a random google search (love doing that, btw) for "night food", and it turned up the following link. Surprisingly good song by some random Calypso group back in the 50's with extremely suggestive lyrics for that time. Apparently, it caused quite an uproar in Jamaica back then. But recently, the singer passed on to the happy place in the sky, and so NPR had it as their "Song of the Day".

Thought I should share ...

NPR Music: 'Night Food' and the Corrupter of a Nation

"The room is dark / She said, 'Come and eat / This night food is very warm and sweet' / I said, 'Lady, there's no knife and fork / And how can I eat food in the dark?' / She said, 'This food needs no knife and fork / How can a human be so dark? / The food is right here in the bed / Come here, man, make me scratch your head

The Conqueror

Given Douglas Adams' fascination with Genghis Khan (refer first few pages of Hitchhiker), it isn't surprising that he wrote a nice little short story on the true history of Ol' Genghis and his pals. Here it is.

DNA/The Private Life of Genghis Khan

A casual observer would not have noticed anything remarkable about the man who rode at their centre, muffled in a heavy cloak, tense, hunched forward on his horse as if weighed down by a heavy burden, because a casual observer would have been dead.

Pandora's Podcast

I think it is a universally accepted fact that Pandora is the most awesome website around. Just found this interview of Tim Westergren, the founder of Pandora, by an AOL Podcast station. Although some of it is redundant information for anyone who has used the website (the interview is old - back when Pandora was not really all that popular yet), there are some interesting discussions towards the end - particularly one where you hear Tim tip-toeing around the question of whether Big Bad Record Companies are trying to push him around to "recommend" their own artists :)

Soul of Wit

She : "So where is my comb?"
He : "It is on yon counter top, O fair maiden!"
She: Since when have I been a maiden, O brave .. er .. warrior?"
He : "Well, it doesn't exactly have the same poetic ring to it if I said O fair one who hath once been a maiden. It's kinda like taking the soul of wit and gently beating it to death with a dictionary."

Art

Have always thought that the preface to Oscar Wilde's The Picture of Dorian Gray is probably the best appraisal of art I have ever read. Reading it again today, I was dwelling a little bit on the line

"It is the spectator, and not life, that art really mirrors."

Found that deeply insightful just now, and wanted to share it.

To boldly show

Interesting ... Found old episodes from Star Trek, Twilight Zone and a bunch of shows I've never seen. Wow!

Video - TV Classics on CBS

Reality

I was over at someone's house tonight, and one of the guys there was watching television - something I haven't done in years. I was initially curious, then amused, then left extremely disturbed at the sights I saw on TV - you see when I last saw a TV show, reality television was still not 'in'. There were a couple of shows which were trying it, but it had not really caught on as a 'fad' i guess. But now, there are entire channels devoted to reality shows. It was probably a similar reaction to what our parents might have felt when MTV came on the screen - "They are now showing this new rock n stone music on TV!" - but I definitely felt old watching these new shows to which I have nothing in my experience to compare them to and feel comfortable watching them,

anyway, this led to a series of thoughts on the natural tendency to do good in the average individual (note : the average individual who will serve as a test bed for these theories is myself, for want of a better guinea pig). question: where does the human mind draw the line on decent/indecent, good/bad and so on? these moral 'boundaries' we have in our head - how malleable are they? There was certainly a time in my life, when I thought using swear words was wrong. Then was a time with swear words in every sentence. But now I feel like I have reached the stage where it is ok to use them every once in a while, but not in front of strangers or people who you think might be offended. But today there are things in life which I think are loathsome (crazy sexual exchanges, murder, crazy sexual exchanges with a murderer, etc) but maybe there might come a day when these things are acceptable to me, or the people around me. maybe someday a very terry pratchett-like assassins' guild might form and instruct children on the correct approach to murder (ie. without being on the receiving end of such an instruction).

so the point is, is there a line which no man will ever cross? after watching TV shows today, my answer has to be a no.

next question: is man essentially bad, and wants to be good? or vice-versa?

by "man" here, i refer to the intuitive notion of the soul of the average person (you or me). now, as for me, i think i am essentially good. but how much of that is me convincing myself because I have such an endemic feeling that being a "good" person is important for my own happiness, therefore I will never think of myself as being a bad person. so, i guess it is impossible to answer that question about myself, simply because no amount of introspection is going to allow me a perfectly unbiased standpoint from which to judge myself.

hence, i choose a third person - the proverbial "One" in a conversation - now,

... story deleted because it was way too disturbing ....

Just to give an idea as to how bad it was, it ends with ...

And then Anna calls - she's pregnant. The child is his because she didn't fuck anyone else, you lying bastard. And I'm keeping it too! (Conscience: fucked)

This is the final straw. Neo is back in Paris ... this time with a loaded weapon ....


Reader: NO!
Author (ME): Obviously not, I wouldn't allow one of my charactes to kill a pregnant woman. How crazy do you think I am? One probably kills himself and there ends my tale of woe for our lonely survivor on the reality TV show called life. The question still remains? Was One essentially good? Did he just have a tough time and the lying, fighting, and killing was just a result of an essentially good person having a hard time of life? That's for you to decide, dear Reader, for I am sleepy now. And wish to ...

Global Village?

An interesting article by Douglas Adams back in the early 90's (from the looks of it) on the emergence of the internet, and the complete bewilderment with which people at the time greeted it. Cheers to the future!

DNA/How to Stop Worrying and Learn to Love the Internet

But the biggest problem is that we are still the first generation of users, and for all that we may have invented the net, we still don't really get it. In 'The Language Instinct', Stephen Pinker explains the generational difference between pidgin and creole languages. A pidgin language is what you get when you put together a bunch of people - typically slaves - who have already grown up with their own language but don't know each others'. They manage to cobble together a rough and ready lingo made up of bits of each. It lets them get on with things, but has almost no grammatical structure at all.

However, the first generation of children born to the community takes these fractured lumps of language and transforms them into something new, with a rich and organic grammar and vocabulary, which is what we call a Creole. Grammar is just a natural function of children's brains, and they apply it to whatever they find

Hoe Hoe Hoe

[Sung to the tune of Bitches Ain't Shit]

See, Brian Greene meets these bitches right?
And all dem hoes be really tight
He tells dem about his groovy string
But all they want is the bling bling

In case y'all niggaz wanna know where I get my groove thang : its this shit [muthafucka]

Hedgehogs

Had an excellent conversation just now about education, the future, stories, comics, literature, and the final consensus was ..

Roald Dahl is awesome!

and Pratchett, of course, but we didn't talk about it.

Neusis

Just discovered this wonderful website with Euclid's Elements. Have wanted to read this for a while now, and just read a few pages of it tonight. Discovered an interesting idea called "Neusis", or fitting a line into a diagram.

The operation is thus : You take a line segment of a fixed length (say the radius of a circle) and mark out it's length on a straight edge. You then move the straight edge and use the specific length to make another line segment of that same length. This is used in a very intuitive proof of trisection of a given angle (see link below) - ie. Given an angle, to find another angle whose measure is exactly one-third the measure of the original angle.

Apparently, this process of Neusis cannot be justified using Euclid's postulates and is thus outside the scope of the Elements. Seems reasonable as it is does intimately depend on the measurement of a length, but what's neater is that a mathematician named Whatzel actually proved that neusis would be unjustified under Euclid's axioms. This rabid quest for correctness in all respects is what makes this stuff so exciting!

Euclid's Elements, Introduction

I'm creating this version of Euclid's Elements for a couple of reasons. The main one is to rekindle an interest in the Elements, and the web is a great way to do that. Another reason is to show how Java applets can be used to illustrate geometry. That also helps to bring the Elements alive.

I Cthulhu

Crazy expedition to find life in extreme places of the world. Reminds me of H.P. Lovecraft's "At the Mountains of Madness" for some reason. The extreme biting cold, with the discovery of a terrifying form of life hitherto unknown to man :)

NASA - Extremophile Hunt Begins

Antarctica's Lake Untersee, fed by glaciers, always covered with ice, and very alkaline, is one of the most unusual lakes on Earth. The upper 70 meters of lakewater is so alkaline "its pH is like strong CloroxTM," says expedition leader Richard Hoover of NASA's Marshall Space Flight Center. "And to make it even more interesting, the lake's sediments produce more methane than any other natural body of water on our planet. If we find life here, it will have important implications."

Strange Fruit

It was Christmas Eve. Hassan walked out of the barn and was immediately struck by the biting cold. The cold reminded him of the time of year, and he grinned to himself looking forward to the warm meal his mother would have set out for him when he returned. This made him quicken his pace a notch, and he soon found himself out in the open fields whistling to himself. The last dregs of a red sunset were disappearing behind the clouds and an involuntary shudder ran through him. He had imagined a sound as he left the barn - a short, quick whisper maybe - but he quickly reprimanded himself for his silly daydreams. He was a dreamer - he made no bones about it - but to scare yourself half to death when alone on a winter's night, now that was foolishness!

But soon his thoughts turned towards home, and he felt warm inside. His mother would be happy when he gave her the money. She had been against his decision to work at the barn. "The white folk don't care for us", she said. "Slaves we were, and slaves we will be". That was her favourite saying these days. When father died, she couldn't get herself to accept that it was just fate that snatched him away from her - she suspected the villagers of foul play, and nothing Hassan said would change her mind. "You watch out for yourself, boy", she said "Never trust noone". Another of her mottoes.

But this would change her mind. Ten whole dollars! He could buy grain, and the blanket for little Tabitha, and still have some spare for a rainy day! Even mother could not say that the "white folk" had not been generous to Hassan. The old couple had been somewhat reluctant to accept him, mind you, but Hassan had pleaded his case well and the old lady had finally relented - letting him wash the animals and clear out the barn for a few dollars. Her husband was getting far too old to do it himself, she said, and who was going to find out? Although it was forbidden for black people to work in the village, she had smuggled him into the barn in the darkness and paid him well for his labours. Hassan was never one to forget a favour, and he thanked the old lady in his heart, and prayed for her happiness.

A stray cat ran across his path, and he thought he saw a silhouette in the distant trees. He crossed himself and muttered a prayer for his safety as he entered the patch of trees. The trees has been planted there by the villagers in order to keep the "vermin" outside of their wonderful village. "The government may want this filth to live, but I'll be damned if we allow it to steal our jobs and our land", the local Mayor had said, to raucous applause from the grinning mob. Hassan grimaced at the memory. He had been there when Mayor Stone had spoken to the village - hiding in the bushes in the hope of seeing Liz in the crowd. Liz! What a smile she had! He had seen her many times as she played with her friends on the borders of the forest. He had even left her a few flowers one day, and found a note in it's place the next day - she had thanked him! Of the joy! But then he had heard the Mayor's speech and was filled with disgust. It was no secret that the Mayor and most of his followers had been in the infamous KKK in their time. Even though the organisation was outlawed by the Federal government, people like Stone had continued to use their power to rally support for suppressing black freedom any way they could.

Hassan shook the snow from his head to clear away these dreadful thoughts. He was an optimist, he laughed to himself, and he hoped that someday he would be able to go upto Liz's parents and ask her hand in marriage. He was hard working, and a good person, so why not? But he knew in his heart of hearts that there was a fine line between optimism and daydreaming - and he was walking it.

As these thoughts ran through his head, he suddenly walked into a clearing. Strange, he thought to himself, I don't remember seeing this before - I must've taken a wrong turn somewhere. He turned to retrace his steps - and immediately knew something was amiss. The bushes around the clearing were alive with people .. and hunting dogs. Up ahead he saw a torch and a hood beside it. "Who's there?", he cried, knowing that he did not want to hear the answer. "It talks", someone said, and the rest sniggered. There were at least ten of them, Hassan figured. "Please let me go my way, I mean no harm!", he said, as his heartbeat quickened. "No harm?" said the person under the white hood as he walked out into the open. "Did it say, `NO harm?' Why you lying, stealing piece of shit!", he said, slapping Hassan across the face. Mother was right to warn me about the job, he said to himself. "I didn't steal nothin'", he said, "I was paid for my work is all". But he knew this was futile. "Since when are rats like you allowed to work in our fair town?", the man in the hood said, as a murmur ran through the crowd. "You steal from hard working folk and then lie about it!", the man said, as he grabbed the money from Hassan's pockets. How did he know it was there? I must've been followed from the barn, Hassan thought, remembering the quiet whispers.
The man continued to talk, as Hassan let his gaze roam over the crowd. What he first thought was ten people, was in reality, closer to twenty. Strong lad though he was, and an eternal optimist, he knew he was not going to be able to brave his way out of this one. They had him cornered, and he knew it. The others saw the fear and resignation in his eyes, and they knew they had their prey. ".. and working in our homes, feeding our cattle?!", the white hood was talking now. Hassan looked back at him, in the vain hope that he wasn't being asked a question. He had taken off the hood now - it was Stone. He should've known. ".. and I've seen him stare at my daughter, the lecherous pig!". Liz's father was in the crowd too, apparently. Hassan's head was reeling. He thought he was going to faint from the fear, but as he thought of his mother waiting for him at home, his little sister, his dead father, and all the good and bad things in his life - he felt a cold, calm anger well up inside him. He had to stop this madness. He looked around for a weapon, and saw a pitchfork in the hands of a drunken man to his left. As swift as he could, he lunged at it with all his might, grabbing thin air. The bastard had moved just in time, and Hassan fell to the ground.

Stone walked upto him, and placed his foot on Hassan's neck, pressing down slowly but surely. Bending down low, he said, "I hope your mama sees you tomorrow". Standing up, he signaled to the dogs, saying "He's all yours boys - make sure you eat your fill". And then the beasts converged on him. Looking up, all he could see was the mad look on their faces. And all he could think of was Tabitha in a new blue blanket.

Broken

He sat hunch-backed on the rocks watching the waves wash over the shore, the evening sun refracted through the shards of his broken life. His eyes rested on the gun that lay between his feet. Emotions washed over him - guilt, anger, and even a mild sense of satisfaction at the look in her face when it happened. It almost made it worth it. Almost ..

The gun was cool now, having had its day in the sun. He cradled it in his palm, letting its deadly weight play on his nerves. It mocked him - all his life he had been the golden boy - the straight-A student, phd, great job, beautiful wife - yes, life had made a mockery of him, and the gun was the only thing that had the nerve to say it to his face. It was as though his entire life had been one big charade leading up to this very day - to find her naked, writhing body in bed ...

He had done the right thing. He knew it. The gun knew it.

It felt cold against his temple. And then he heard the sirens ringing ...

Untitled

Man going quietly mad in the privacy of his own mind. Oh the horror!

Ghost in the Brain

I am stoned right now, and just finished watching the 'Ghost in the Shell' (GITS) anime, and thought I should write down some of my current thoughts on the different forms of artistic expression (for the moment, I will call these 'media' for want of a better word) that I am most familiar with - Books (by that i mean the written word) , Manga, Movies, Music and Anime.

Books are the most suited to rereading passages, ie. a way of revisiting complex ideas without fundamentally breaking the continuity. The same is not true for movies or music, because if you feel like you missed something in a movie or missed a crucial beat in a song, there is no way of going back, watching/listening to that piece, and returning immediately to where you originally were without hampering the message. Although this is made somewhat easier today with DVD/CDs instead of the old VHS tapes, it still involves considerable physical effort for you to go back and forth in a movie all the time.

Now Manga offers this, but where it lacks is in making complex ideas flow into each other seamlessly. The panel-to-panel reading makes it an inherently 'discrete' medium, thus losing the important aesthetic appeal of music or movies. While reading 'words' is also discrete, in my case (and this may not be so with people who have been reading comics all their lives) the words flow into each other much more easily than still panelled pictures. The advantage, though is in exactly that - the medium allows you to just stop and stare at a particular panel feeling the beauty and artistry of it. This is not true for words - noone would catch themselves staring at a sentence entranced in its beauty (you'd have to be pretty far gone for that to start happening). Although I must say that the art work of things like Ronin/Sandman, and the writings of Oscar Wilde/Wodehouse make me wonder how much of that is in the hands of the artist.

Now Music is a totally different kettle of fish - it is the only form I've listed which does not require sight. That in itself makes it pretty special in my opinion - you can literally feel it in your veins, whereas all the other mediums are essentially external (ie. you are only observing the beauty but you are not a creative part of the process). Music, therefore, is exciting because it makes you feel strangely productive and at the same time relaxed. Unfortunately, such a personal process as listening to music is also /impossible/ to share with people. This isn't strictly true, but one has to admit that it is hard to define in words what you feel for a tune although that is probably a limitation of one's vocabulary and of spoken language. Also music, like movies, are linear and so .. (read the para on books).

Movies have the fundamental draw back of being on TV - the boob tube. As many eminent film-makers have proved - one can have a really big hit in the box-office for something that is completely devoid of any artistic brilliance (an idea parodied in the South Park movie). However, it can also have a very immediate impact on the viewer. Music and books can move you, but it typically takes longer for the message to filter to the brain simply because only one sense organ is in play. Movies tap into both sight and hearing, and so it is much easier to crack a joke, for instance, an act which may involve physical actions, words and a facial expression for the message to go across completely (think Monty Python). And how many times have you walked out of a movie-theatre in a daze because of the recent information overload?

The last one I tackle is Anime. Having just watched GITS, I feel like I am in a good position to evaluate what I think. Anime has all the benefits of both Manga and Movies. A well-made anime movie typically stands still on important and artistic scenes, thus achieving (to some extent) what ordinary Manga achieves and at the same time allows the dialog to deliver a 'situational'* message to the viewer (Again, this might be typical of me, but whenever I watch Anime, I am much more prone to look out for the subtle images and sounds than in ordinary movies) (See how I used ordinary for both Manga and Movies but not for Anime? Aren't I exceptionally clever? :) Unfortunately, I do also frequently feel overwhelmed by Anime. I feel like I am trying to 'read' the comic and watch the movie at the same time - which is very hard to do, and I often find myself straying from the conversation looking at all the beautiful scenery. Although this is not necessarily a bad thing, I do have to go back re-watch GITS now!

PS : There is another medium I thought of - that of Plays or Live Theatre, but although I have seen and done the odd play, I still feel somewhat out of my depth describing the expressive power of the medium because I don't think I have seen or done a single /great/ play. So do forgive my reticence on this matter.

PS2: While I realise I am breaking down these media rather haphazardly and making a mash of things, I hope that it will at least have a shred of sense in it when I read it tomorrow. That would be nice.

* The word 'situational' here is meant to describe a message telling the viewer where in the storyline he/she is, whereas the pictures/music give the more subliminal 'situational' messages ( ... must break out of self-referential loop).