Monday 16 November 2009

Mahabishwe Mahakashe


Amidst this vast cosmos

Through deep space and time

Alone I walk ever, in awe.

Amidst infinite mystery

Art Thou, Lord of All,

Alone in Thy glory, ever silent.


Across endless space,

From the stars beyond count

Thy gaze falls on me,

I gaze back at Thee.

Silence descends,

The world rests in peace.

Eternal One, amidst Thy Oneness

Alone I dwell, ever fearless.




Click the button to play the song.
Translation and song are both mine. The photo is not, but click on it for the full impact.

Sunday 18 October 2009

Prothomo Aadi Tobo Shakti


Thine is the power primordial,

Thy dazzling radiance fills the skies.

Thy ancient Word, bearing Thy eternal bliss,

Arises anew in endless forms.

In the heavens of Thy mind,

Shine the sun, moon and stars,

Life ebbs and flows with Thy breath.

Thou art the primal poet,

O guru of poets,

The cosmos resounds to thy chant.





Click the button to play the song.
Translation and song are both mine. The photo is not, but click on it for the full impact.

Akash Bhora Shurjo Taara


Amidst skies full of stars, a world full of life,

Have I found my abode.

My song awakes in wonder.

The vast surge of Endless Time

That ebbs and flows through all Creation

Ripples through the blood in my veins today.

My song awakes in wonder.


I have tread the soft grass on forest paths,

Delighting in the scent of woodland flowers,

I have seen the gifts of joy strewn all around.

My song awakes in wonder.

I have opened my eyes, aroused my senses,

Poured myself on the bosom of this world,

Ever amidst the known have I sought the Unknown.

My song awakes in wonder.





Click the button to play the song.
Translation and song are both mine. The photo is not, but click on it for the full impact.

Thursday 15 October 2009

The Bhagavad Gita In Brief


I am guessing many of you have never read the Gita, but at least some have felt they should have made an attempt. I’m in the category that tried, made some progress (making notes and all), then quit. Until recently, that is.

A late evening attempt to decipher the Sanskrit text with a friend resulted in a renewed surge of interest, and I decided to just go ahead and finish the project. It’s done now and what follows is my roadmap of the 18 chapters of the Gita – with some shlokas to highlight the path - for those wishing to delve in and explore further.


Chapter 1: Setting the stage. Surveying the armies at Kurukshetra, Arjuna is overcome by grief when he realizes what the war will entail. Good for him.

Standard interpretations speak of this as ‘weakness’ on Arjuna’s part. Au contraire, I find the very human anguish, the questioning of a war which entails the mass slaughter of kinsmen and loved ones for the sake of a kingdom, coming from a man who is expected to be a relentless killing machine, to be one of the brilliant character touches that makes the Mahabharat great. Krishna responds, and the main Gita begins.


Chapter 2: The soul stuff. “As a person casts off old garments and puts on new ones, so the soul leaves one body for another” and “Weapons do not cleave the soul, fire does not burn it, water does not wet it, nor wind make it dry” (Shlokas 22 and 23).

Get the point? Krishna is saying that Arjuna won’t really be killing his loved ones, just destroying their bodies. The soul is the real thing and that’s safe. Of course, if one doesn’t buy the soul stuff, this argument goes for a toss, along with much of the Gita.


Chapter 3: All work and no attachment makes Jack a Karmayogi. To be accurate, this starts off in chapter 2 with the famous “Karmanyevadhikaraste, ma phaleshu kadachana” (Chap 2, Sh 47). Acting without attachment – one of the central principles of the Gita.

To be honest, I find Karmayoga unconvincing. Why would one do anything if one has no interest in the results?

Furthermore, how is one supposed to act? The answer, as per Gita, is to follow ‘swadharma’ – nebulously interpreted as ‘one’s innate nature’ or ‘duty’, it’s never quite clear. “Better is swadharma, though carried out imperfectly, than the dharma of another carried out perfectly”(Sh 35).

Highly unsatisfactory. This suggests that people are born with some kind of innate duty (who dictates what that is?) and one should ‘just stick to it’. More problematically, if you interpret swadharma as ‘duty’, what if that duty conflicts with basic human values like compassion, love, loyalty and so on? This is really Arjuna’s question and Krishna never quite answers it, IMO.


Chapter 4: Krishna to the rescue !! “Yada yada hi dharmasya...” is right here ! (Sh 7 & 8)

The rest is largely a rehash of Karmayoga. Apparently, Arjuna is not convinced first time, and I don’t blame him. Apart from all the swadharma issues there’s the growing problem of “Who should take responsibility for one’s actions?” - very relevant when battle is about to commence. Well, over the past two chapters, there have been growing hints that humans are mere intermediaries and God is the ultimate source of all actions, so the answer is.....


Chapter 5: Blame it all on God!! Or at least, if you do, the responsibility won’t stick to you. “He who works, resigning his actions to God, is not touched by sin, even as a lotus leaf is untouched by water” (Sh 10).


Chapter 6: Introducing Mr. Detachee, aka, the Yogi, “to whom a lump of mud, a stone and a piece of gold are the same”, “who is equal minded among friends and foes” (Sh 8 & 9), “who does not rejoice on obtaining what is pleasant nor sorrow on obtaining what is unpleasant”. Personally speaking, I am more for rejoicing on getting the pleasant and staying calm in the face of the unpleasant, rather than zoning out equally on both. But this picture of the Yogi, devoid of worldly attachments, is a familiar presence in our culture.

The rest of the chapter is about what the Yogi should do – Dhyanayoga, meditation in the grand old style. “Holding the body erect and still, looking fixedly at the point of his nose, serene and fearless, firm in the vow of celibacy, let him sit, his mind turned to Me alone” (Sh 13 & 14). The ultimate goal of all this –“Thus making the self ever harmonized, the yogi experiences the infinite bliss of contact with the Eternal. He who sees Me everywhere and sees all in Me: I am never lost to him nor he lost to Me” (Sh 29 & 30).


The story so far: Act without attachment, remember that all actions are rooted in God, then focus, focus, focus on God. At this point, the reader may well ask, “So who is this God person anyway?” We’ll see.


Chapter 7: Ok, so let’s talk God. Here goes.

“I am the origin of the universe and its dissolution as well. There is nothing whatsoever higher than I. All that exists is strung on me like gems on a string.” (Sh 6 & 7).

Straight to the point and no mincing words either. That’s pretty much the message in this chapter. But some interesting asides exist.

Firstly, some glimmerings of the concept of Maya which hides the true form of God from the world. “Deluded by the three gunas, the world does not recognise Me who am above them. This divine Maya of mine is hard to overcome.” (Sh 13 & 14)

Secondly, an interesting piece about tolerance of worship for other gods, but emphasizing that they are inferior. This is clearly the period when the existing Vishnu and Shiva cults were taking over from the old Vedic deities.

“Those whose minds are distorted by desires resort to other gods, observing various rites. Whatever form a faithful devotee wishes to worship, I make his faith firm. But temporary are the results of their worship. Those who worship the gods go to them, but My devotees come to Me.” (Sh 20 to 23)


Chapter 8: Not too much going on here, frankly. The main point seems to be “He who utters Aum at the moment of death come to me” (Sh 13) and “having come to Me, they do not get back to rebirth” (Sh 15). The rest is a rehash of chapter 7.


Chapter 9: Panentheism. Distinct from pantheism (no ‘en’), which identifies God and the universe, panentheism is the belief that God pervades the universe, but also transcends it. Here it is, loud and clear.

“By Me is all the universe pervaded in My unmanifested form. All beings abide in Me, but I do not abide in them. My spirit which is the source all beings, sustains them, but does not abide in them. All beings pass into Me at the End, and I send them forth again at the Beginning” (Sh 4 to 7).

The superiority of bhakti to God over Vedic rituals is re-emphasized very explicitly.

“The knowers of the Vedas who drink the soma, pray for the way to heaven. They reach the holy world of Indra and enjoy the pleasures of the gods. Having enjoyed paradise, they return to the world of mortals again. But to those who worship Me alone, I bring attainment of what they have not.” (Sh 20 to 22).


Chapter 10: This is just God going ‘I am the Greatest”, over and over. “Of the Adityas I am Vishnu, of the heavenly lights I am the Sun, .....of the gods I am Indra....... of weapons I am the thunderbolt” and so on and on and on. Finally ends with, “I support this entire universe, pervading it with but a fraction of Myself”. Enuff said.


Chapter 11: Vishwarupa!! The grand climax of the Gita. Arjuna gets to see the Cosmic Form of God.

Imagine that! A mind-blowing, soul-searing, all-encompassing vision of Ultimate Reality, of All That Is or Was or Ever Will Be!!! What could ever be more awesome and humbling, more ecstatic and terrifying, more devastating and transformative than that?! What an absolutely brilliant concept.

Unfortunately, followed up by poor execution. It starts off well enough with, “If the radiance of a thousand suns were to blaze forth at once in the sky, that might resemble the splendour of the Exalted one” (Sh 12), but is followed by a huge overload of anthropomorphic imagery – eyes, hands, stomach, mouths, teeth, garlands and such. Just doesn’t do it for me.

IMO, contemplating the Hubble Ultra Deep Field or zooming into the Mandelbrot set can convey a far better picture of what Vishwarupa might have been like. :-)

(Deep field: http://www.spacetelescope.org/images/wallpaper3/opo0428b.jpg Every little speck in the image is a galaxy!

Mandelbrot set: http://www.youtube.com/watch?v=WAJE35wX1nQ )


Brief Interlude: So, now with the Cosmic Form shown and described, does the Gita end on a high note? Alas, no. Seven more chapters follow. Many of them are just remixes of the old ones, and give the impression of being added on to make the magic number, 18.


Chapter 12: Strong advertisement for bhakti. Devotion to a personal God (Ishwara) is declared at the outset to be superior to contemplation of the impersonal Brahman. And what is the ideal bhakta like ? “He who behaves alike to friend and foe, who is alike in heat and cold, pleasure and pain” (Sh 18)... sounds familiar? Yes ! Mr. Detachee from chapter 6 is back.


Chapter 13: Just Sankhya philosophy – Purush and Prakriti. Prakriti is dynamic and everchanging, ceaselessly bringing forth myriad different forms. Purush just sits around, observing and unobserved, unaffected by anything that happens. Yet, somehow, Purush is supposed to be the better of the two. Possibly because He is the Man.


Chapter 14: More on the three gunas – sattva, rajas, tamas – first seen in chapter 7. Sattva is goodness, rajas is passion, tamas is darkness/ignorance. Most of the chapter is an elaboration on what qualities are associated with each. But towards the end, Arjuna asks, “What are the qualities of one who has risen above the three gunas?” Turns out, this is someone who “regards pain and pleasure alike, treats alike a lump of mud, a stone and a piece of gold, who...” ok, ok, we got it, we got it. It’s Mr D. again.


Chapter 15: Remember the cosmic tree? It’s this very interesting image of the reality as an inverted tree, with its roots originating in Brahman, its leaves and branches constituting the world. Quite a unique picture, really. (Ok, there’s Yggdrasil of Norse myth, but it’s the right side up). I had no idea the image was in the Gita, so that was interesting.

But what are we told to do? “Cut off this firm rooted tree with the sword of non-attachment”. Uh-oh, it’s the D-word again. The rest of the chapter is about how the Lord dwells in all things and suchlike, but we’ve seen this all before in chapters 7 to 9.


Chapter 16: All about the daivic (divine) and asuric (demonic) natures intrinsic to human beings. The message: Daivic nature, very good, very good, Asuric nature, very bad, very bad.


Chapter 17: Rather artificial classification of diets, forms of worship, types of penance etc as sattvic, rajasic and tamasic. Don’t know why this wasn’t just attached to chapter 14. Sudden digression into the meaning and significance of “Aum Tat Sat” at the end.


Chapter 18: The finale, and a fairly eclectic mix of previous material. The three-way classification of the last chapter goes on for a bit. We have the three kinds of knowledge, three kinds of work, three kinds of understanding and so forth.

Karmayoga and swadharma re-appear, but this time, the dharma is laid out by caste in shlokas 42 – 44. (I really don’t buy that stuff.) A bit of Dhyanayoga pops in. Then, a particularly strong form of ‘God is responsible for all action’ – “The Lord abides in all hearts, driving them as machines” (Sh 61). The implication is that if Arjuna refuses to fight, the will of God will compel him.

And finally, “Fix thy mind on Me, be devoted to Me, prostrate thyself before Me. Abandoning all duties, come to Me alone for shelter. I shall deliver thee from all evils” (Sh 65 & 66).


In conclusion: Thus, ultimately, it is ‘Surrender to Me and do My will’.

How disappointing! So much better would have been, “Use your new knowledge, think carefully and make up your own mind.” Don’t you think so?


Thursday 10 September 2009

Large Numbers


L
et’s talk about large numbers. Not your humdrum, everyday sort of large number, like the number of stars in the galaxy (about 10^11 or 100,000,000,000) or drops of water in the ocean (about 10^25 or 10,000,000,000,000,000,000,000,000). Not even the somewhat larger numbers like atoms in the visible universe (10^80, I won’t bother to write it out) or the Googol (10^100, not to be confused with Google).

No, today I want to talk about seriously large numbers. A good first try is the Googolplex, or 10^(10^100), that is 1 followed by a googol zeroes. While a googol vastly exceeds the number of atoms in the known universe, a googolplex can’t even be written out in full within the universe, even assuming you could write each zero using only one atom!

Ok, now we’re talking, but this is just the beginning. To represent the sort of numbers I have in mind, we need a new type of notation, called Arrow Notation. Here goes.

Arrow Notation:

If a and b are positive integers, a^b is just defined as ab.

The general definition is recursive:

a^...n arrows...^b = a^..(n-1) arrows..^a^..(n-1) arrows..^a^.......^a

where the (n-1) arrows operation is executed (b-1) times. The arrow operations are executed from right to left.

Let’s illustrate by example. It’s easy to check that a^^..n arrows ..^^ 2 is just a^2 for any n and any a. The smallest value of b which gives us something interesting is 3.

So, to start off:

3^3 = 33 = 27

3^^3 = 3^3^3 = 327 = 7,625,597, 484, 987

Ok, so that’s one of our garden variety large numbers. The ^^ operation, known as the ‘tower’ operation quickly gives us much bigger numbers.

For example, 3^^4 = 3^3^3^3 = 3^7,625,597,484,987, which is a number with about 3.5 trillion digits. 3^^5 would be 3^(3^7,625,597,484,987), which means if you wrote it out in base 3, the number of digits would be 3^7,625,597,484,987 !! And so on...

But now let’s get serious. How about adding yet another arrow?

3^^^3 = 3^^(3^^3) = 3^^7,625,597, 484, 987

How big is this? Well, when we look at 3^^3, 3^^4 and 3^^5, we see the incredible impact of increasing the number to the right of the ^^ by 1. Well, we’ve just increased it by about 7.6 trillion, so it’s impossible to imagine not only the number itself, but even the number of digits in the number, or even the number of digits of the number of digits of the number , or even....hmmm, running into some serious linguistic limitations here, but you get the idea.

But ok, let’s quit trying to imagine and just add one more arrow.
Let’s look at 3^^^^3

3^^^^3 = 3^^^3^^^3 = 3^^3^^......3^^3

where the ^^ operation is done 3^^^3 times.

Take another quick read through the part where I describe 3^^^3. Now take a very deep breath.

Imagine you are doing the evaluation of the right hand side in the expression above. Remember it’s done from right to left.

So, at step 1, you get 3^^3 which is kid-stuff.

But at step 2, you already have 3^^(3^^3) which is our mind-cracking 3^^^3 !!! Now, you just have to continue for another (3^^^3 – 3) steps....

If you’re really feeling masochistic, you can try working out 3^^^^^3, but by now I hope you’ve realized the effect of adding just one extra arrow. So, I’ll go ahead instead and mention the biggest number ever used in a mathematical proof.

Graham’s Number

First brought to attention in 1977, the number was used by the mathematician Ronald Graham working in a field called Ramsey theory. Ramsey theory deals with problems of the form, “How many elements must a set have for a certain property to occur.”

So, for example, suppose you have a gathering where any two people either know each other or don’t. How many people must there be, so that you always have either three people who all know each other or three people who all don’t know each other ? The answer in this case is 6. (Prove it!).

If you make the property more complex, the size of the set increases correspondingly. Graham showed that for his problem, the desired property is always satisfied if the set has at least Graham’s number of elements.

So, what is this number? Let’s define a sequence as follows.

G1 = 3^^^^3, our humongous old friend.

Now let G2 = 3^^...^^3

where - and read this bit very carefully – the number of arrows is G1 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! (What I really feel like doing is adding at least a googol exclamation marks here, or maybe a googolplex.)

G3 = 3^^...^^3 where the number of arrows is G2.

Still hanging on? Ok then, so we define G3, G4, G5 etc in the same style.
Graham’s number is G64.


Infinity

So, finally, we come to the biggest of them all. “Nonsense!”, interjects the mathematician, “Infinity is not a number at all. It’s an abstract concept and a pretty tricky one at that.”

Of course, of course. But when we mere mortals think of Infinity, we do tend to think of something very, very big which goes on and on and on and on.

How big? Well, the ancients used to mention things like “stars in the heavens”, “drops of water in the ocean”, “grains of sand in the desert” etc to convey a sense of infinity. But as we saw right at the start, these concepts are easily tamed with standard mathematical notation, and turn out to be all too finite and very manageable.

If we go beyond and introduce arrow notation, we can quickly write down numbers which completely drown the imagination all the way up to Graham’s number (and way beyond of course.)

However, compared to Infinity, there is no difference between Graham’s number and zero.

In fact, think about the sequence G1, G2, etc, where Graham’s number if G64. If we take the “Graham’s number”-th number in this sequence (!!!) and subtract it from Infinity, it makes, not a small difference, not a tiny, puny, minute difference, but absolutely no difference whatsoever.

That’s what Infinity is. Treat it with respect.

Sunday 23 August 2009

Project Mahabharata


I
am planning to read the Mahabharat. All of it. You can, too. A complete and unabridged translation of the Sanskrit original is available at http://www.sacred-texts.com/hin/maha/index.htm

In addition, I have a copy of Kaliprasanna Singha’s translation in Bengali. I remember seeing it first in my grandfather’s house when I was about 9. It seemed inconceivable that anybody could finish reading even a chapter of that humongous tome, let alone the entirety. My grandfather, it seemed, had done this, proving once again that he was the smartest man in the world, ever.

Now, over two decades later I have a copy of my own. I estimate that if it was written out in the same style as, say, the US hardbound edition of the Harry Potter series, it would be about 5000 pages. Now that’s big, but nowhere near infinite. The HP series itself is a total of about 2500 pages, and children routinely read it all. So, it’s eminently possible to read the entire Mahabharat from start to finish! How cool is that?

So, I’m reading the Mahabharat and I must admit it’s a lot tougher going than Rowling’s work or Tolkien’s, because, boy, this book needed an editor!!!

To begin with there’s an incredible amount of fluff, and descriptions tend to be overly detailed and highly formulaic. If I have to read yet another description of warriors fighting ‘like passionate bull elephants during mating season’, I swear I’m going to throw the book at somebody’s head (and severely sprain a muscle in the process). Every time a deity or rishi or even a minor dignitary enters the scene, be prepared for a mile-long stava (‘oratory of praise’) elevating him all the way to Param-Brahma. And if anybody starts lamenting, especially Draupadi, you might as well head for the hills, or at least skip the next several pages.

Secondly, the narrative is highly nonlinear. There’s no “Once upon a time there were five brothers.....”. The Mahabharata is more like the Arabian nights. People start telling a story, and the characters in the story start telling each other another story, and on it goes. Then, all of a sudden, somebody gets beheaded or something and you're like, "Wait, wait, wait, what?? Which level of the loop was I on???"

Then there’s the whole blasted habit of giving away the ending. Happens all the time in the war chapters. For example, right at the outset of Karnaparva, Sanjay goes, "And so after two days of valiant fighting, the mighty Karna was slain by Arjuna..." . Dhritarashtra promptly faints away in shock, and I'm going, "Damn you, that was supposed to come at the END." Then they revive the old King, and Sanjay goes, "So, as I was saying, after Drona died, Duryodhana made Karna the new senapati...." and so on.
Honestly, those ancients had NO concept of slowly building up the tension to a big climax!!

It makes more sense if you remember that the epic was designed for listening in real time. So, during an endless stava or lamentation sequence, you could let your mind wander or run a small errand. Whereas maybe an ending-giveaway was a way of saying, “Hey, don’t go to the bathroom now. Big action scene coming up!” But for a modern reader, it can be rather frustrating.

So, then why bother, you may ask? Why not just read one of the dozens of abridged versions available in the market?

Well, I already have. In fact, if you can read Bengali, I will highly, highly recommend Upendrakishore Raychaudhuri’s (he was Satyajit Ray’s grandfather) version for children. I knew it as ‘CCheleder Mahabharat’ (Mahabharat for Boys), but apparently its been PC-ly renamed ‘CChotoder Mahabharat” (Mahabharat for Youngsters). The book is a gem – very entertainingly written and very faithful to the original as I am finding.

Part of my motivation is a reality check – one constantly hears that something or the other is ‘written in the Mahabharat’, I want to see if that’s really so.

But what really drives me is the sheer feel of reading the massive old epic. It’s not like reading a novel at all. Apart from the main plotline, the Mahabharat contains tons of other stories. Virtually every ancient Indian story you’ve heard of is present somewhere or the other – ‘Shakuntala-Dushyanta’, ‘Nala-Damayanti’, ‘Kacha-Devayani’, a condensed version of the Ramayan and much, much more. And often in the most unexpected of places – for example, the story of Shiva, Parvati and the birth of Kartika suddenly shows up before the final battle between Bhima and Duryodhana. Add to all this a huge dollop of philosophical discourse, political advice, social directives and whimsical folk tales thrown in almost at random and you have the big, bewildering mishmash that is the Mahabharat. Reading the great epic is a lot like walking the ways of an ancient city – you wander around pondering the well-known sights, and all of a sudden you are in a dingy little alleyway which leads to an exquisite garden, tucked away where you least expect it. It’s an experience you shouldn’t miss.

P.S: If you want to try the Mahabharat project yourself and want some company, some of us have set up a discussion blog at http://groups.google.com/group/mahabharata-discussion
All are welcome.

Saturday 8 August 2009

BANG!!!


Ten to twenty billion years ago, something happened. The Big Bang, the event that started our Universe. Why it happened is the biggest mystery we know. That it happened is reasonably clear”. Thus wrote Carl Sagan in 1980.

Now nearly three decades later, we know that it happened not “ten to twenty billion years ago”, but more like 13.7 billion years give or take 200 million. And we’re beginning to home in on why it happened.

For the cosmologically uninitiated, the Big Bang is the colossal explosion which started our Universe. It’s not really your garden variety explosion - it happened everywhere at the same time and space itself began to expand and has been expanding ever since. (Expanding into what ? Wrong question! Space just expands. There need not be anything outside for it to expand into.). As a bonus, all the matter and energy in the Universe came into existence at the Big Bang. Must have been really something to see (for the picosecond before your retina evaporated.)


Ok then, so what caused the Big Bang? Answer: Gravity.


“Now hang on”, you say, “gravity is an attractive force. It makes everything collapse and clump together. The Big Bang was an explosion. Am I missing something here?”

We-e-ell, you see, there’s gravity and gravity. Our usual type of gravity, the type that foils your attempts at spontaneous levitation, is caused by our everyday type of matter. But make that matter sufficiently weird, and gravity can push things apart with enough OOOMPH to satisfy the most ardent anti-gravity aficionado.

Let me elaborate. Our best model of gravity today is Einstein’s General Theory of Relativity. What GTR says is that the gravitational force generated by an object is proportional to its mass/energy. This is pretty much what we know, the heavier the body, the more the gravity. But there’s also something else – the pressure of the system also contributes.

To illustrate, if you have a spring, then its mass will create a gravitational attraction. If you squeeze the spring, its pressure increases and so does the pull of its gravity. Now here’s the crux – if you stretch the spring, the pressure term becomes negative and the gravitational pull decreases. And if you stretch it enough, the negative pressure term can totally overwhelm the effect of the spring’s mass, and the gravitational field will repel rather than attract. A sufficiently stretched spring is an anti-gravity machine!

Unfortunately, any real spring will rip into pieces long before anti-gravity sets in. But there does exist a substance which can act like our hyper-stretched theoretical spring. What is it? Nothingness.

No, I haven’t suddenly gone Zen on you. If you remove all our usual matter and energy, the empty space that remains (which would qualify as nothing for most people) might still have an ‘energy’. The details are technical, but the gist is, this weird ‘vacuum energy’ generates a ferocious burst of antigravity, the Bang of the Big Bang. In the space of 10^(-35) seconds the nascent universe expands by a factor of at least 10^30, and the rest is history.

But wait, first let’s give a sense of those numbers. 10^30 is one followed by thirty zeroes. That’s like blowing up a virus to the size of our galaxy! And how fast did this happen? Well, if a blink of an eye was scaled down to 10^(-35) seconds, then the lifetime of our universe would be one hundred millionth of a nanosecond. Unimaginable doesn’t even begin to describe it.

As if this wasn’t enough, we have every reason to believe that the expansion went on way beyond this. A consequence is, our observable universe is miniscule compared to the actual universe. To picture this, imagine the entire Universe to be the surface of a giant balloon studded with galaxies. The observable universe, which is what we can see, from the Earth to the most distant galaxies spotted by our telescopes, would be like a patch drawn on the balloon. The diameter of that patch would be about 90 billion light years, which is about 10^27 metres. Now the question is, “What is the circumference of the entire balloon?” A possible estimate is, 10^(10^12) metres. Yes, you read that right. One followed by a trillion zeroes!!!

Usually astronomers like to convey the scale of things with analogies like, “Suppose the earth was the size of an orange, then the Sun would be...” etc. So, let me try to convey the size of the whole Universe. Shrink the Universe by a factor of 10^40. The observable universe, with all its hundreds of billions of galaxies is now the size of an atomic nucleus. Now repeat the procedure 25 billion times. At this point, the Universe has the same size as our observable universe... or an atomic nucleus if we’ve scaled down one too many times by accident! Does it really matter?

Now let’s go back to the beginning, before that miniscule speck of vacuum energy expanded to incomprehensible size. On the smallest of scales, quantum physics rules, which implies roughly that “nothing ever sits still”. So, even on the tiniest scales, the vacuum energy cannot be uniform- it is perpetually roiled by quantum fluctuations which ensure that its values are never quite the same everywhere. What do these elusive quantum fluctuations look like? Take a look below.


What you saw was a map of our universe on the largest scales we can see. The reddish foam-like structure represents clusters of galaxies strewn across space with vast voids in between. The gigantic cosmic expansion stretches the quantum fluctuations out from submicroscopic scales to cosmic ones - resulting in a froth-like clustering of galaxies as far as we can see. The largest structures we see in the visible universe are quantum fluctuations stretched across the heavens.


And finally the grand slam. The universe contains an enormous amount of matter and energy. At least a hundred billion galaxies with a hundred billion stars each. Where did all this come from? The traditional answer is, “From the Infinite and Eternal Mind of God”.

But we’ll try for something much humbler – by starting with a glass falling from your hand. The glass gains kinetic energy from the earth’s gravitational field, which then gets converted to sound, heat and a mess on the floor. A rather more spectacular example is a supernova. A giant star at the end of its life collapses under its own gravity. The energy gained from the gravitational field converts into a cataclysmic explosion which blows the star apart and temporarily outshines an entire galaxy. This is all with our familiar matter and energy.

A speck of vacuum will also gain a gigantic amount of energy from its own gravitational field. But instead of collapsing while doing so, it blows apart in a Big Bang. At the end of this blast of expansion, the energy gained at gravity’s expense is let loose in a flood of radiation and matter that makes up everything you see and much more. So, there we go - you don’t need a hundred billion galaxies worth of material to start off the universe. Just a tiny seed of vacuum energy and the rest will follow.

At this point, it’s a case of ‘almost, but not quite’. After all, where did that seed come from? Nobody knows, but here’s a possibility. Start off with truly empty space – so empty, it’s even devoid of vacuum energy. Now, remember those pesky quantum fluctuations? They’re always around, wriggling, wiggling, flickering and jittering. So, even if you assume that the vacuum energy of empty space is zero, it’s never quite so. The value keeps fluctuating up and down, here and there. Given enough time, somewhere, on some miniscule, submicroscopic domain, a fleeting fluctuation will exceed a critical threshold, and.... BANG!!!

So, at the end of things (or is it the beginning?), think of Space. From the endless voids between the galaxies and the yawning gulfs separating the stars therein to the emptiness within an atom, space pervades everything. Think of the fact that every bit of that space, every minute, infinitesimal bit – so small that an atom looks is a galaxy in comparison – has the potential to blossom into an entire Universe of stars and galaxies, life and mind. Maybe it is happening somewhere right now. Maybe, even as you read this sentence, a billion, trillion, zillion Universes are exploding into existence....

Sunday 26 July 2009

The Western Experience


If you’ve read the ‘About Me’ part of the blog, you already know I’m not a galaxy. Good start. To be a bit more explicit, I’m human, male, grew up in Kolkata till end of college, went off to the US, lived in the West (USA and UK) for about 12 years, and came back to India for good (Yes ! Really !!).

It seems de riguer for an NRI, or ex-NRI, to write an angsty piece about their life in the West and make grand extrapolations to the experience of ‘all Indians’. (It’s generally considered totally uncool to just say, “Ya, life was/is very chilled out t/here”). So, here it comes.
Ok, to begin with, I didn’t feel I was abandoning my parents and cultural roots, I wasn’t appalled by the ‘lack of family/spiritual values’, I wasn’t in the least bothered by women in tank-tops or couples snogging in public. For all that, there’s Jhumpa Lahiri.

But here’s what did bother me.

I grew up on a pretty rich diet of English books and movies. Tintin and Asterix comics, Famous Five, Hardy Boys, Sherlock Holmes, Agatha Christie, you name it. Then there was Star Trek, Mickey Mouse and Spiderman on TV, and the big surge of Hollywood films during Christmas was always eagerly anticipated. Being a bit of a geek (just a bit?), I was heavily into science fiction and fantasy, which are genres of literature almost completely dominated by North American and British authors. Then there were all the great popular science authors, once again, mostly American or British.

So, to cut it short, I grew up absorbing, enjoying and admiring many of the products of western culture, and I believe my experience of quite typical of urban, middle-class Indian children (extrapolations have begun!).

It was a shock, therefore, to go to the West, and find that this feeling is absolutely not reciprocated.

To the average urban, middle-class westerner, India is invisible. Some people may have heard of Gandy (“what was that? Oh, Gandhi”), some New Age types have some curiosity about Indian religion (“chakra, chakra, not shakra”) and you get asked whether you like ‘curry’ (“curry is not a dish, idiots! Its like asking, Do you like soup?”). But apart from that, there’s just a very vague awareness of India as a land of starving people and cows, and nowadays, telemarketers and IT nerds. And there it ends.

Once, this sank in I re-read my beloved science and SF authors and realised with great disappointment that this was true of them as well. People like me were never part of their intended audience, and in fact, probably outside their mental horizon altogether. A very notable exception was Arthur C. Clarke, who often introduces Hindu and Buddhist names and themes into his novels. Carl Sagan dwells at some length on Indian cosmological speculations in Cosmos. But that’s about it.

And then I started seeing it in all the English books and movies I grew up with. Here I’d been thinking, like any eager reader, that the authors were ‘talking to me’, so to speak. But no, they weren’t. In fact, they had no idea that people like me might even read their work, just like all the ignoramuses I kept meeting in everyday life!

Now I’ll make a grand extrapolation and say that my experience is quite typical of Indians arriving in the West. And this is a problem. Most of us grow up with an awareness that our country has a vibrant culture with deep roots and this is a source of pride. To suddenly end up in a place where all of that is completely ignored or peripheralized, feels like, well, Arthur Dent looking up the Hitchhiker’s Guide and finding that the only entry under ‘Earth’ is ‘mostly harmless’! (If you didn’t get that reference, er..., let’s just have a chat sometime, ok?)

People react to this in different ways. Some decide that the best way to regain importance is by trying to act as ‘western’ as much as possible. Nowadays, their numbers are dropping and good riddance. Others embark on private crusades to raise India-awareness. As a result any unfortunate westerner in the vicinity is subject to long lectures on ‘glorious Indian culture and traditions’ (and subsequently avoids any Indian event like the plague.) Many get into an angry defensive crouch – “If they can’t be bothered about us, screw them! We can’t be bothered about them either”. Kind of difficult if you are living in their country, so what happens is a gradual tendency to segregate into rather claustrophobic all-Indian communities.

Of course, the circus really begins when the next generation comes along, but that’s a can of worms to be opened elsewhere.

Thursday 23 July 2009

Why Science Will Never Accept God


Amidst all the clamour of the science/religion debates, one persistently hears the accusation from the religious camp that scientists do not want to believe in God.

Scientists, claim the believers, are being obdurate – they have decided to shut their minds to God’s existence and would stretch their theories to any length to avoid the possibility of divine involvement. Is there any truth to this ?

On casual inspection, the claim is patently false. There are any number of scientists who have produced excellent work while being devoutly religious. And to my knowledge, there is no stricture against scientists holding religious and/or supernatural beliefs. Humans hold all kinds of personal beliefs and scientists are no exception.

However, the accusation begs a deeper question. Namely, is the scientific method itself incompatible with God? Or, in other words, can God ever be a valid scientific hypothesis?
I think the answer to the latter is No.

To begin my argument, science works by making careful observation
s of nature and framing hypotheses to explain those observations. The hypotheses are then used to make further predictions which are then tested by observation and experiment.

This is admittedly a gross simplification of the scientific method, and in reality, the scientific enterprise does not proceed in a linear fashion. Guesses, prejudices and misunderstandings abound. Theories are ignored on first publication or dismissed by prominent scientists, only to resurface decades later and gain prominence. However, for the purposes of our argument, the observation- hypothesis-testing model of the scientific method suffices.

Now to begin with, there is no observational evidence for God, of course, or this whole debate would be moot. So we need to ask if God can be a good scientific hypothesis. Indeed most theist-atheist arguments traditionally start with, “What made the universe?”

So: Observation: Universe, Hypothesis: God, Test: ????

This is the point where the problem arises. An unwritten rule in science is Occam’s razor – We choose the simplest possible hypothesis to explain a given fact. In accordance with this, the basic ingredients in scientific models are as elementary as possible.

For example in physics, the typical entities in models are particles and fields, - mathematical constructs whose behaviour is completely described by a handful of numbers. For all the intimidating math in theoretical physics, the models contain nothing remotely as complex as even a virus!

Now let’s take a look at God.

God is the Supreme Being, “omnipotent, omnipresent and omniscient” according to the Abrahamic religions, “ the infinite, immanent and transcendent reality which is the Divine Ground of all matter, energy, time, space, being, and everything beyond” according to Hinduism.

Very impressive indeed, but from a scientific viewpoint, extremely problematic!
Such a being is the polar opposite of simple and elementary. In fact, almost by definition, this is the most complex entity that can ever be hypothesized in a model. Thus, by Occam’s razor, every possible alternative should be considered before suggesting God as an explanation. On an infinitely long list of conceivable explanations for a phenomenon, God would be right at the bottom !

So much for Occam’s razor. How about predictive power?

If God is your hypothesis, what’s the prediction? Well, everything - after all, there’s nothing an all-powerful being can’t do. And nothing - because His Omnipotence is certainly not obliged to do anything! Thus, the God hypothesis produces no testable predictions.

Awe inspiring and humbling though the idea of God may be, as a scientific hypothesis it is useless.

So if God is no good as a hypothesis, how about a proof by observation? Once again, trickier than it seems.

Certainly, it is possible that we may observe supernatural phenomena, though none have been documented to date with any credibility. Water turning into wine, or people walking on water, or statues drinking milk for instance. These would be completely contrary to our current understanding of the world, and scientists would be forced to admit that ‘something else’ was at work. But even so, how would we know this was God, the Supreme Being, in action and not some more mundane creature, such as a genie or an asura?
Similarly, even if we had incontrovertible evidence that our universe was intelligently designed, how would we know it is the Mind of God that designed it? Maybe it’s just an alien schoolboy in a metaverse which was itself sneezed out by the great green Arklesnoozer in a meta-metaverse and so on.

In some ways, this is akin to the problem of figuring out if the universe is infinite or just really large. We can keep going and always finding more, but it can still be that the end is just beyond our horizon....

So, where does all this leave us? Not, I think, with the conclusion that science has disproved God, as some may claim. In fact, from what I just said, science cannot prove or disprove the existence of God, because the God hypothesis makes no testable predictions. But since science is the best way we know of producing reliable, objective knowledge, it is unclear how we can ever resolve the issue.

For this same reason, God will never be part of an attempted scientific explanation of anything, though people may, and will, of course continue to believe in Her for other reasons.

All I can say is that, to date, we have succeeded in explaining all observed phenomena within the framework of elementary entities behaving according to elegant mathematical laws. It is possible that these laws were designed by a transcendent intelligence beyond the universe. But this is by no means inevitable, or the only possibility.

Furthermore, there is no way to scientifically test claims about beings beyond the universe, since all our observations and experiments are necessarily confined within it.

So, this may be a good time to invoke the eminently sensible proverb, “Whereof we cannot speak, thereof we should remain silent.


Tuesday 21 July 2009

Harry Potter and the Half-Baked Flick


SPOILERS GALORE !!! READ AT YOUR OWN RISK !!!

Right off the bat, let me admit that Harry Potter and the Half Blood Prince is a cut above the previous five movies. But only because the others are so lame.

The movie starts off at a brisk walk with storm clouds gathering above London and Death Eaters streaking out like sooty comets to wreak havoc in the city. By half-time it looks like it might even run. Then it shoots itself firmly in both feet to collapse in an anticlimactic heap. In what follows I will assume, that you like myself, have read and loved the book (and preferably, all the books.) So, I’ll abandon the usual refrains of “Harry Potter and friends are back in a deeper, darker, scarier, more adult, more mature, ...... yakkety yak yak”.

In a bizarre inversion of quality, the film shines precisely where the book fails and vice versa. Anybody who has read the series (or is it just the old and cynical ones like me ?) tends to agree that Rowling’s depictions of teenage romance and angst are by far the most annoying aspects of Book 4 onwards, and a general lowering of overall standards. However, the romance bits of the movie are genuinely entertaining and often very amusing. Jessica Cave delivers a hilariously over-the-top performance as the lovestruck Lavender Brown. Rupert Grint’s idiotic grin as Ron under the effects of love potion has to be seen to be believed. Also very amusing are Harry and Ginny’s awkward attempts at romance, continually interrupted by the bumbling Ron.

Unfortunately that’s where the good news ends. Now for the bad.

The central thread of the Half-Blood Prince book is a series of revelations about Voldemort’s life, seen in Dumbledore’s pensieve. Dumbledore is demystifying Voldemort – showing Harry that the Dark Lord is not an invincible superbeing as he wants all to believe. He is just a man, who was once a child, and then a teenager. In a fascinating series of snippets, we read about his ancestors, obsessed with heritage and wizard pride. We see him as a boy already inclined towards cruelty and domination, a teenager ever adept at flattering teachers to get the information he needs. We find out about his obsession with objects of antiquity and value. Then the final revelation and the key to bringing down the Dark Lord – the multiple Horcruxes, each created by murder, which bind him to the world.

All this is replaced by two hasty scenes totalling not much more than 5 minutes!!
Then the chilling scene of locating the Horcrux locket – the huge underground lake, the deadly potion in the basin, Dumbledore screaming in terror and agony, then lying in a faint begging for water... Once again,very clumsily done. To begin with the sets look so obviously fake,that disbelief is hard to suspend. The lake looks tiny. Dumbledore flails about a bit all right, but in half a minute, looks quite fine. When he asks Harry for water, it seems he’s just being lazy.

And now the finale.

I remember how it felt when reading the book. The Dark Mark hovers above Hogwarts. Harry suddenly finds himself petrified beneath his invisibility cloak. He watches, helpless, as a visibly weakening Dumbledore faces Malfoy, who has come to kill him. But the old wizard is completely unfazed. He is sure Draco’s heart is not in it. In fact, yes, Malfoy is losing his nerve and lowering his wand. All’s well after all...

Then four Death Eaters burst in. Tension once again. Dumbledore remains composed but now the outcome is far from certain. Then Snape enters. At this point I know all will be fine. Dumbledore trusts Snape. Snape will surprise the Death Eaters and rescue him, he’s the ace in the old man’s sleeve.... Snape kills Dumbledore !!! What the ****** ???!!! While this is yet to sink in, we find Hogwarts in chaos. Death Eaters are battling the students and the Order of the Phoenix. Spells fly everywhere and pandemonium reigns, while the Death Eaters make their exit. And as a last, shocking revelation, Snape is the Half Blood Prince, whose potions book has helped Harry all year round !

That’s the book. Now for the film.

They come back to Hogwarts all right. Then Dumbledore tells Harry to stay out of sight. No petrifying spell, no cloak. Enter Malfoy, enter Death Eaters, enter Snape. No build up, no tension, nothing. Snape does the Avada Kedavra almost as an afterthought. And all the while Harry just watches with the moronic, vacant expression that seems to be Daniel Radcliffe’s trademark. Then the Death Eaters sort of saunter out with Harry obligingly following behind, with no attempt to attack them, raise the alarm, or create any resistance. And I’m thinking, “Is everyone finding this as stupid as I am?”

Bellatrix Black trashes the great hall and sets fire to a couple of buildings. Nobody wakes up, nobody notices. Is everybody in Hogwarts on drugs or what? Only when the Death Eaters are well out of the building, does Harry challenge them and get his butt thoroughly kicked. Serves him right for being such a retard!

Ok, that’s it. The film ends shortly in a total anticlimax. I don’t know if this is a deliberate ploy in order to get a PG rating, but every previous Harry Potter movie shows the same tendency to downplay and rush through the darker, chilling parts that make Rowling’s books such a pleasure to read. It is unfortunate that the Half-Blood Prince movie makes the same, tired mistake and leaves you with the same insipid taste in your mouth.

The Credit Crisis -----Continued


Penetrating all the jargon in finance articles has been tough, but I

think I've done it.
So I'm going to write it up here.


The subprime mortgages and defaults are the easiest part to understand, but wasn't clear to me what exactly the investment banks had done and why everyone is panicked.

Now I think I do.
It’s all due to the invention of new financial
technology (yes, we quants are called financial engineers officially).

Its an instrument called the Credit Default Swap (CDS) and its heavyweight cousin, the CDO.

I've been working in this area doing models and all the last few years, but the big picture was never made clear to us all this time. Turns out, the models were window dressing, it was mainly a lot of fraud.

Here goes...

Credit Default Swap - Part I

The CDS is a very simple instrument.

The idea is, suppose you have XYZ company which is BBB rated (very bad shape). Now you own $1m worth of XYZ bonds and you are getting interest. But problem is, XYZ can go bust any day and you'll lose $1m.

So, big investment bank, let us refer to it as Evil I-Bank, offers you a credit default swap on XYZ.

The CDS on XYZ specifies that you will pay a quarterly premium to Evil I-Bank, (usually specified as a percentage on the underlying, in this case, $1m). In return, if XYZ goes bust, Evil I-Bank, pays you $1m.

Typical insurance scheme.
So how can that cause a crisis ?

Because, rather than just insurance, CDS can also be used for speculation.


Credit Default Swaps – Speculation

So, now suppose you are a speculator. You know that XYZ is BBB rated, so could go bust any day.

How do you take advantage of that ?

Well, the standard way is to short XYZ stocks. You can even short XYZ bonds (though more complicated).

But there's a problem with that. You need someone to lend you the XYZ stock to short it, and there's only a limited number around.

Maybe $10m max, since XYZ is a small company. Ditto with bonds.

But now you have a new means. Simply get into a $10m CDS with Evil I-Bank on XYZ company. You see, one doesn't need to actually own any XYZ bonds to set up a CDS on XYZ !

Its as though, I can buy car insurance which will pay me if my neighbour has an accident.
And so can all of you.

Thus, previously if XYZ went bust, the max total loss to anybody is $10m.

Now it can be $1 billion, $10 billion, who knows ? Because everyone can set up a CDS to bet against a company and many people did.

This is the leveraging everyone's talking about.

But on the other hand, why were the I-banks so eager to set up CDS's with whoever wanted them.

Weren't they liable to lose a lot ?

Enter the CDO.


CDOs

Collateralized Debt Obligations (CDOs), the hot product of the last few years, engineered by all us math/physics PhDs.

The idea is suppose you are Evil I-Bank.
You have 100 BBB rated companies like XYZ. You've just sold $10m worth of CDS on each. So, now if they all go bust, you can lose $1billion. What do you do ?

Answer: Slice it up !

So, you create a "0 to 3%" slice. (technically, tranche)

Which means you go to a client and say, Look, I have an asset based on 100 underlying companies. Now I'm going to pay you a quarterly premium. In return every time a company in this pool goes bust, you pay me $10m, but *only up to the first 30m dollars* (so that's 3% of 1bn). Of course, the client will want a high premium for bearing this risk.
But lets go on.

Then you have a "3 to 7%" slice. So, you pay another client a somewhat
smaller premium. The idea is in return he will start paying you back when the total loss
to the underlying portfolio exceeds 30m (i.e., from when he 4th company goes bust), but stops at 70m (so from 8th company onwards, not his problem).

And so it goes, till you usually have a 15 - 100% slice.

This total scheme of slices is a CDO.

So, now here's the deal.

Note that every time one of the 100 XYZ companies defaults, you have just passed the loss onto one of the clients of the CDO.

And in return you can pay them a part of the quarterly premiums you were getting from the people who had CDS on the XYZ companies !

So, the more CDS's you sell on one end, the more CDO's you can sell on
the other.
Perfect !


But is it really so great. Who wants to take these slices ??


CDOs and the ratings debacle

Its all in the ratings.
If you have a basket of BBB rated companies, not many people will want to buy into those.

But now what if you've sliced and diced it the way I described ? How much are those slices worth ? What's theirs rating ?

Underneath all the high math, here's the heart of the business.

The I-banks managed to convince the ratings agencies hat the 15 - 100 % slices were AAA !! You'd get interest on those, but it was extremely unlikely that more than 15 of the 100 companies would default, so as good as having a bond of a blue-chip corp !

And this is the crux of the crisis. Any type of long term investor, like a pension fund, wants to invest in AAA securities. But these are generally hard to find, expensive, etc.

Now I-banks had a way to (spuriously) manufacture them out of thin air. Simply, sell tons of CDS on crap companies to speculators and charge them high premium (because these are BBB rated).

Join them together into CDO's. Sell the 15 - 100% slices to long term investors. Since, these are AAA rated, you pay them a low premium and they are happy. Voila ! Money for nothing !

And long term investors were snapping these up, so big bonuses and party time.

What about the 3-7% slice etc. These are bought by hedge funds as a way of getting easy cash in the short term. Hedge funds always need quick, short term cash


All fall down

So, that's the big picture.

Once things started going south and companies went bankrupt, losses were magnified gigantically by the proliferation of CDSs.

The AAA rated CDO slices built on the CDS turned out not to be AAA after all, so the long term investors are collapsing.

Hedge funds are dying by the thousands as the earlier slices get hit.

I-banks are hit hard. After all you think you are well hedged. But what happens when the pension funds you duped go down and *can't* pay the losses you passed on ?

Plus they have to mark to market, which means the books start showing big losses long before companies actually collapse.

All because of the CDS, which allows you to 'take out insurance on your neighbours life'.

There's still an estimated 45 to 60 *trillion* worth of CDS liability which can be called in as recession deepens and more companies fall.
No one knows how corresponding CDO slices are placed...