Chaos

After the response to my last pseudo-scientific post, Incomplete, I've decided to try my hand at another one. This one though, covers not a theorem, but a whole science in itself. Again I'd ask anyone reading this to hold on and read through the whole thing. You'll never think the same way about the world again...

The story begins in the year 1961 at MIT, Massachusetts, USA. Meteorologist Edward Lorentz was simulating global weather on his primitive computer. He had boiled weather down to the barest skeleton, to a set of few equations. The output was in the form of a string of numbers, merrily spewing out from a printer. If you knew how to read the printouts you could see westerly winds changing course, cyclones erupting and dying down, temperatures and pressures playing see-saw in
the atmosphere. One day Lorentz, wanting to examine a particular sequence in greater detail, decided to start his simulation midway through. He bootstrapped his simulation using numbers from one of his earlier printouts. He had expected the simulation to start and proceed from the point, from where he had taken the numbers he input and take the already pre-determined course. But on returning from his coffee break he found what was to be the birth of a new science.

His current simulation did not resemble the older one in any way. It had diverged at some point, and gone on diverging more and more after that. Even though he had initialized it with the same input values. Soon he realized that while his program maintained numbers up to six places of decimal (for e.g., 1.264067), the printout showed them rounded off to three place (i.e., 1.264). The only difference had been that he had used that rounded off value to initialize his toy weather. The result - where it was snowing earlier, it was now a scorching summer.

This came to be known as the Butterfly Effect which implies something like "If a butterfly flaps its wings in New York, the air currents change such that it will rain next Tuesday in Beijing."

And from this emerged the fascinating science of Chaos.

Risking a little bit scientific imprecision, let me try explain what is it all about. Determinism is the philosophical belief that every event or action is the inevitable result of preceding events and actions. Thus, in principle at least, every event or action can be completely predicted in advance, or in retrospect. Translated into laws governing the physical world it means, that given accurate measurements of the world around us, we can predict the state of the world at any point in the future. Now let us throw the monkey wrench into the machinery - No real measurement can be infinitely precise. All physical systems need measurements to start with. And hence long-term predictions about the state of these systems are nothing but mere guesses. This science of the unpredictable is called Chaos Theory.

So what? Why should you care with some arcane set of physical laws not doing something they were supposed to do? Chaos permeates our universe. Some examples: It has been found in systems describing wildlife and human population patterns, stock prices, shapes of clouds, paths of lightning bolts, intertwining of blood vessels, physiological models of the human heart, galactic clustering of stars, evolution. And it means you will never get an accurate weather prediction beyond 3 or 4 days.

But Nature is not chaotic - everywhere in Nature we see order and patterns. Where does this order come from, when there is chaos everywhere? But Chaos does not rule out patterns: Since our world is classified as a dynamical, complex system, our lives, our weather, and our experiences will never repeat; however, they should form patterns. They do and in precise terms it is called the concept of self similartiy and self similar patterns are called fractals. It is like this: never in history have two events been exactly the same, but as everyone knows history repeats itself.

For a most wonderful introduction to this subject I would suggest: "Chaos: The Amazing Science of the Unpredictable" by James Gleick.

I have an uncanny feeling that it has some metaphysical implications as well, like understanding the human mind and thought. Just think in terms of the assumptions we make daily about ourselves and others and our world, and the actions we take, and consequently the future we build for ourselves and others. But I'll not venture there. I'll leave you with this quote from William Blake:


"To see a world in a grain of sand and heaven in a wild flower
Hold infinity in the palms of your hand and eternity in an hour"



References:

• Chaos: The Amazing Science of the Unpredictable by James Gleick.
• An Introduction to Chaos Theory and Fractal Geometry
• What is Chaos?

Encounters of the Bovine Kind

I step down the staircase, hurried in my time warp,
And behold in the stairwell, Her majesty,
Ruminating the secrets of the universe,
Looks up at me with eyes overflowing with kindness.

With not a inch of free space to pass,
I pole-vault my way over her towering presence,
And almost faint on top of her,
Her perfumed aura overwhelming my olfactory senses.

I somehow get out, into my car, and drive away,
Only to find in the middle of the road,
His majesty taking a stroll, absolutely nonchalant,
To the blaring horns and ruckus he's left behind.

As I screech to a halt, and crane my neck out of the window,
He turns his head back, to gaze upon his insolent subjects,
While some puny bikers slip by,
Just avoiding a trip and a fall over his tail.

When he reaches his breakfast patch,
He parts the flow with his divine horns, and moves aside,
I drive on, into the humdrum of my daily life,
Wondering, how sacrilegious is it, to be considered sacred?

Reasons for Being

Romantic reason	:	I love therefore I am
Philosophical reason	:	I think therefore I am
Culinary reason	:	I eat therefore I am
Artistic reason	:	I draw therefore I am
Nerdy reason	:	I program therefore I am
Sleepy reason	:	I dream therefore I am
Literary reason	:	I write therefore I am
Working reason	:	I animate therefore I am
Surfing reason	:	I blog - hop therefore I am
Prosaic reason	:	I exist therefore I am
Poetic reason	:	I am alive therefore I am
Narcissistic reason	:	I am therefore I am

What am I?

Err ... that is not a valid question.

How can I prove anything ?

A little child of three or four
With a freckled face and curly locks
Looked up at me with a toothy grin
She seemed like a brook tripping on the rocks

Barely standing, she asked of me
"Are you sure the sky is blue ?"
"Ofcourse! What a question!" I said
I will just now prove it to you

"Just look up and see", and I saw at twilight hour
The sky turning golden, red and pink all at once
"Which of these is blue ?," she asked
I stood there, mute, feeling like a dunce

She stared at me, with a innocent look
"Tell me no ... Is it that hue ?"
I saw the world, mirrored in her eyes
"You know it all already, how can I prove anything to you ?"

The Paper and the Wind

Standing on the simmering tar,
Baking in the heat reflected of dreary concrete,
I looked up and saw,
A white paper page descending from the heavens.

It floated, rising and falling, billowing in the wind,
I turned my head away, away from the relentless gleam of the noon sun,
The paper fluttered, playing with the currents of air,
Flirting with the rising passions of the ardent draft.

Then a fierce gust rose,
Swatting the paper with all its might,
The paper merely bent, and mocked, and laughed,
Rolling away, always on top, always falling in delight.

The dusty waft gave in, defeated,
Ever so lightly, it touched the brick,
Caressing the mud crusted sidewalk,
And then lay stagnant.

When I bent and tried to touch the page,
It eloped with the newborn wind,
Leaving me with a fistful of heat,
Staring at the frolicking lovers' dare.

Swades Hangover

I saw Swades. It was a good movie. I've been restless since. I do not know why? I remembered something I had read in Vivekananda's works once. I found it in an essay titled "Modern India." He says:


Thou brave one, be bold, take courage, be proud that thou art an Indian, and proudly proclaim, "I am an Indian, every Indian is my brother." Say, "The ignorant Indian, the poor and destitute Indian, the Brahmin Indian, the Pariah Indian, is my brother." Thou, too, clad with but a rag round thy loins proudly proclaim at the top of thy voice: "The Indian is my brother, the Indian is my life, India's gods and goddesses are my God. India's society is the cradle of my infancy, the pleasure - garden of my youth, the sacred heaven, the Varanasi of my old age." Say, brother; "The soil of India is my highest heaven, the good of India is my good," and repeat and pray day and night, "O Thou Lord of Gauri, O Thou Mother of the Universe, vouchsafe manliness unto me! O Thou Mother of Strength, take away my weakness, take away my unmanliness, and make me a Man!"^*


I do not know my land. I do not know myself.

How can I hope to know the world, and her people?

I am still restless ...


^*  If you have not read his works, I am requesting that you think before you comment on his sayings. However, no such requests before you comment on the post per se.

Incomplete

I've been pondering for some time as to whether I should write about "this" or not. Today concluded I should do it anyway.

If you are reading this post, I'd like to suggest that though it might get a tad confusing for a moment, but read it fully ... If you understand this one, then ...; you'll see ... Just read on.


The "this" I was referring to is something called the incompleteness theorem.

Kurt Gödel, in his famous paper "On Formally Undecidable Propositions" proved this celebrated and oft misunderstood theorem.

Consider this:

1. Someone introduces Gödel to a UTM, a machine that is supposed to be a Universal Truth Machine, capable of correctly answering any question at all.
   
   
2. Gödel asks for the program and the circuit design of the UTM. The program may be complicated, but it can only be finitely long. Call the program P(UTM) for Program of the Universal Truth Machine.
   (If the concept of a computer program or a circuit seem alien terms just think of P(UTM) as a (formal) description of the UTM and its workings in words or symbols)
   
   
3. Smiling a little, Gödel writes out the following sentence: "The machine constructed on the basis of the program P(UTM) will never say that this sentence is true." Call this sentence G for Gödel. Note that G is equivalent to: "UTM will never say G is true."
   
   
4. Now Gödel laughs his high laugh and asks UTM whether G is true or not.
   
   
5. If UTM says G is true, then "UTM will never say G is true" is false. If "UTM will never say G is true" is false, then G is false (since G = "UTM will never say G is true"). So if UTM says G is true, then G is in fact false, and UTM has made a false statement. So UTM will never say that G is true, since UTM makes only true statements.
   
   
6. We have established that UTM will never say G is true. So "UTM will never say G is true" is in fact a true statement. So G is true (since G = "UTM will never say G is true").
   
   
7. "I know a truth that UTM can never utter," Gödel says. "I know that G is true. UTM is not truly universal."
   

The logic in the embodied in the above lines is simple. But the more you think about it, the more it grows on you. Stated very very loosely the theorem implies (The prof. who taught me the formal logic course would probably flip if he saw this one):


All logical systems of any complexity are, by definition, incomplete; each of them contains, at any given time, more true statements than it can possibly prove according to its own defining set of rules.



Although this theorem can be stated and proved in a rigorously mathematical way, what it seems to say is that rational thought can never penetrate to the final ultimate truth. But, paradoxically, to understand Gödel's proof is to find a sort of liberation.

The metaphorical analogue to Gödel's Theorem suggests that ultimately, we cannot understand our own mind/brains ... Just as we cannot see our faces with our own eyes, is it not inconceivable to expect that we cannot mirror our complete mental structures in the symbols which
carry them out?

Gödel's Theorem has been used to argue that a computer can never be as smart as a human being because the extent of its knowledge is limited by a fixed set of axioms, whereas people can discover unexpected truths.

Fantastic, is it not ? I stumbled across this theorem about a year back when doing a course called the Theory of Computation. It is a masterpiece of formal logic. Imagine the fields of study and thought it cuts across.

For those whose curiosity I piqued by this post I suggest you read this fascinating, Pulitzer prize-winning book by Douglas Hofstadter "Gödel, Escher, Bach: an Eternal Golden Braid". You'll find that mathematics, art and music are not so different from each other. They are all reflections of the most beautiful of nature's creation: the human mind. Hofstadter explains the book is about "the word I. Consciousness. It was about how thinking emerges from well-hidden mechanisms, way down, that we hardly understand."


Sources I used to research this article:

• Gödel's Incompleteness Theorem
  
• Wikipedia Entry on the Incompleteness Theorem
  

"We regret to inform you that ...."

Ah ... those words ... those hateful words! They typically adorn the
first line of the many rejection letters I've seen so far.

What is it about a rejection that makes it feel that the people
rejecting you, are doing it on purpose. It feels they have this very
personal dislike of me. "Why me ?" - its that unanswered question
which pops up like the jack in the box every time I read one of those.

And I got another one today morning (BIG SIGH !!). Did that feel bad -
you bet it did. It also made me think back to few days in the past,
when a dinner offer I made to a dear friend got rejected too. How was
that rejection different from this one? Did that one make me feel
... ummm .. more rejected? I can't believe I wrote this !

Damn, damn, ... damn, damn! (You always gotta say ``damn'' four times,
twice quickly, pause, and then twice again. Unless ofcourse you want
to say it only once.)


``We put our hands over our eyes and weep that it is dark."

Of Eeyore and Donkey

Here is an authentic chronicle of the words that got exchanged, between
Eeyore (from Winnie the Pooh) and Donkey (from Shrek), when
they met recently.

Donkey on the return from the Kingdom of Far Far Away decided to
take a detour and visit his friend of yesteryears Eeyore in the 100
Aker Woods. He finds Eeyore at his gloomy best ...

D: Hey Eeeyoreee ... how ya doing buddy, and how is your tail doing ?
I've been having the most smashing adventures with Shrek .... you
remember Shrek - you remember Shrek? That big fat ugly ogre who is
like an onion. That's the layered intellectual interpretation. He
really is like a cupcake, I just looove cupcakes ! And then ....

Eeyore looks at Donkey, his wide droopy eyes trying to make sense of
all he sees.

E: Adventure? Oh I see ... an Expotition ... Have you seen my tail?

D: Lost it again, did you? Let me tell you a secret ... there are
these guys at a place called HP labs ... I gave them a proper piece
of my mind when my mane suddenly disappeared one day. And they grew
it back! Maybe you could ask them to fix it. Fix it with gum this
time.

E: Oh, well. Someone must have taken it. How Like Them.

D: (Thoughtfully) That's deep Eeyore ... that's really deep ...

Eeyore was thinking "Why?", and then "Wherefore" and sometime later he
thought, "Inasmuch as which?" and then he didn't quite know what he
was thinking about. He stood by the side of the stream and looked at
himself in the water.

E: Pathetic, That's what it is. Pathetic.

He turned and walked slowly down the stream for twenty yards, splashed
across it, and walked slowly back on the other side. Then he looked at
himself in the water again.

E: As I thought, No better from this side.

D: Chin up - Noble steed! We will find it, after all if one can find a
princess and a puss in boots and a dragon (Oh I miss her), one can
find a tail ! I am the official sidekick .. guy .. here .. I say we
will find it! You got that I don't care what nobody thinks of me
thing ... I like that .. I respect that and so I'll help you.

I know .. it will be in the highest room, in the tallest tower.

You hang on Eeyore ... I'll handle the tail ... Oh I'll find that
tail .. I'll whip its butt too .. It won't know which way to go !

E: Good night, Donkey. If it is a good night. Which I doubt.

And as Eeyore turned to get into his house at Pooh Corner, there was
his tail ... hanging from his back. Its was curled up in a tight bun
.. so that Eeyore could not see it. Donkey sees the tail ...

D: You know what I think ... I think this whole tail thing is to keep
somebody out. Are you hiding something? Aaaw its not another of
those onion things. Why dont you want to talk about it? Why are you
blocking? Who are you tryin to keep out Eeyore, just tell me, who?

E: Oh, well, Thanks for noticin' it.

D: You cant do this to me Eeyore .. I am too young to be sad, ..and worried (sniff) !

E: We can't all, and some of us don't. That's all there is to it.

D: Can't all what?

E: Gaiety. Song-and-dance. Here we go round the mulberry bush.

D: I think I need a hug.

E: Don't blame me if it starts raining now.



Apologies to A. A. Milne, Disney, William Steig and DreamWorks SKG.
All copyrights rest with their legal owners.

Finding Doubt

I thought I had always been and will be a rational thinker. I was open to suggestions and ideas and that elusive other point of view, always eager to get the other perspective as well. I thought I was a sensistive guy, with a taste for the subtle and the sublime. I used to think I understood something of colour, space, light and composition - be it in writing, arts, cinema or in physics, mathematics, biology. I was the king of my castle, safely tucked away in the fortress of my imagination well cordoned off by a moat of calmness and satisfaction.

But then came a movie called Black, and I saw the movie. As with everything I had my opinion about it. Only this time it was different from a vast majority of other people. I tried to voice it, and I did not even get a patient hearing most of the time. What I got was this:

"You're crazy", "You're insensitive", "You've no sense, no understanding of art or of acting", "Its such a great movie, out of this world - you are just being cynical about the whole thing", "Look around you, Hindi movies these days are such a pile of junk - this on is a diamond in the rocks", "Who are you to judge Amitabh and Rani, and Sanjay Leela Bhansali - you are an idiot", "You are wrong", "You are dead."

I thought damn them - they just do not want to listen to what I have to say. I went back and researched my material, trying to find a basis for how I felt, trying to materialize my intuition. I even decided at one point I'll write it in a blog entry. And unknown to me, amidst all these fervent discussions and searches - it crept back into some recess of my being. Doubt - doubt that perhaps I was wrong, perhaps I was mistaken, perhaps I was being irrational about it all, perhaps I did not understand anything at all.

And that frightened me, it did. Suddenly my castle was a house of cards which blew over with a gust of strong wind.


I was reading my old art (as in painting) notes today. I wrote them when I was in class 8th or 9th. And I found in those old pages something which I had forgotten - an innocent curiosity to explore and understand. And that nagging doubt which appeared dark and devilish, became bright and haloed. I remembered it is ok to not know, to not understand, to not sense, to say as I feel, to ask why, to be confused and chaotic. Doubt and chaos are a way of nature, a way of growth, a way of life.

I am smiling now, and the second law of thermodynamics flashes through my mind, "All (physical and chemical) processes involve an increase in entropy in the system and its surroundings" - so there; I do know my high school physics.

Thank you Black. Thank you for finding my doubt for me.

Hoshwalon ko khabar kya

A Jagjit Singh ghazal ...


Hoshwalon ko khabar kya bekhudi kya cheez hai,
Ishq keejiye phir samajhiye zindagi kya cheez hai.

Unse nazre kyaa mili roshan fizaye ho gayi,
Aaj jaana pyar ki jadoogari kya cheez hai,
Ishq keejiye phir samajhiye zindagi kya cheez hai.

Khulti zulfon ne sikhayee mausamo ko shayari,
Jhukti aankhon ne bataya maikashi kya cheez hai,
Ishq keejiye phir samajhiye zindagi kya cheez hai.

Ham labon se keh na paye unse haale dil kabhi,
Aur woh samjhe nahi ye khamoshi kya cheez hai.
Ishq keejiye phir samajhiye, zindagi kya cheez hai.

Hoshwalon ko khabar kya bekhudi kya cheez hai,
Ishq keejiye phir samajhiye zindagi kya cheez hai.

Alive today

Feeling happy, sad, idiotic, logical, flummoxed, focused, satisfied, restless, scared, valiant, poetic, morose, spiritual, mundane, mortal, divine .....

Manifestations of a mortal life

Shrouded in lovelorn nights,
Hearts set aflutter with desire,
As moths drawn to the burning lights,
Rekindled embers of a forgotten ire.

Glasses of scorned amour,
Show the stony soul of an angelic form,
Laughther effusing from the bewitched lure,
Mocking despondent passions bygone.

Black velvet skies part for golden hues,
Phantom dreams melt into earthen moulds,
Perhaps rejuvenated by a virginal muse,
Manifestations of a mortal life, behold.

Strange meetings

I have had this thought buzzing in my head since morning. What is it
like to meet (as in for a coffee) a complete stranger? What does one
do, how does one act when confronted with the rendezvous?

When I meet a person known to me already I have an opinion about the
opinion the person has of me. Do I try to mould myself to conform or
force myself to deviate? How many people I really know with whom I am
myself? Do I actually know how to be myself? Now I am definitely
feeling befuddled and bemused ...

Any strangers volunteering to help alleviate my doubts?

Page 3 blues

I saw Page 3 yesterday night. After having fallen instantly in love
with Konkona Sen, I realized midway that it was a very depressing
movie. I was definitely down in the dumps when I felt my cellphone
vibrating in my pocket. Curious as to who would message me at this
hour, I took it out instantly and saw it was a message from a very
dear friend. Her parents are trying to fix up her marriage and she is
plain scared of the whole proposition. I'd been asking her how would
she know who was her prince charming ...

The message made me smile ... made me bounce back to my world, with my
friends and my insecurities. And voila! On the screen I saw Konkona
was smiling as well.

Kitne ajeeb rishte hain yahan par ....