Saturday, February 26, 2005


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"



  1. Makes perfect sense...

    Disturbing isn't it? Your piece on logic makes no sense to me and your piece on Chaos makes perfect sense...

    Do we see a pattern here?

    I need help...

  2. i do agree.. Nature is so..unpredictably 0rganized..
    ( does that make sense?..
    so why do we .. on earth , slave over organizing everything so we can tell exactly when we expect something to happen.. why do we break our backs over that?..
    what if we left everything to just "happen"

  3. My introduction to Chaos Theory came through Dr. Ian Malcolm, in Jurrassic Park (the book). That was awesome, the stuff that was propounded by Crichton in the book, was really great. One of my favorite segments is from the Lost World, where Malcolm, tries to explain Chaos, starting with the gamblers ruin, ends up with how there is no explaining (outside of chaos theory( how something as complex as human cellular structure was created - attibuting it to accidental evolution is like saying a hurricane sweeps through an junkyard and leaves behind a fully assembled 747.

    Next stop, the theory of intelligent design !

  4. intelligent design...
    * jumps up and down* yes please yes please!!!

  5. The pattern of Chaos is harder to comprehend than the pattern of logic.

    Till such time that the pattern 'make sense' or till we break the 'code', it remains chaotic, because its predictability is low.

    The interesting this is that Chaos is not a characteristic, but a perception. It is not a random event, but a series of events with a hidden permutation. And that either gives us a headache, or gives us hope that there are things yet to be understood.

    Chaos by itself has no relevance, unless the gaze is called to question. :)

  6. Neha: Its interesting that you think of the hidden permutations, as giving you hope that there are things to be understood. To me, it tells me that there are things that will never be understood. As a part of evolution, perfection is anti-ideal - any society that thinks itself perfect will become static and cease to evolve. Knowledge is part of this perfection. I think chaos embodies that which we can never truly perfect. On the side, its amazing how many things can actually be reduced to the uncertainty principle, starting from the movement of sub-atomic particles to what we are talking about here - "Chaos by itself has no relevance, unless the gaze is called to question".

  7. Perfection wasn't called into the thought process. I am not comfortable with the concept of perfection because I think it is self-contradictory.

    The chase for that which is hidden behind the permutation remains mostly hidden. And yet the chase is self-referencing. Knowledge is dynamic, and therefore the chase never really ends.

    And yeah, sometimes I do get the proverbial headache. :)

  8. :-| it was pseudo-scientific???and i fell for it.and i love blake, doncha?

  9. Ho about Mark Twain -
    'History doesn't repeat itself; it rhymes'

  10. @Morq - Chaos making perfect sense is perfectly sensible. Help... hmmm... maybe somebody who is less chaotic (than me) can help you out.

    @Grfx - Yep let it flow I say... let it flow and take the shape of your life. Don't ask me what's the "it" is here.

    @Vigs - Welcome. Super that you know abt Chaos Theory. Proves others too mess around with arcane sciences... atleast sometimes!

    @Neha - predictability is low and is not a random event .. contradictions?

    @Vigs and Neha - Interesting thoughts. Dynamics - change - random - patterns - predictable - remain still - Static. I forgot to put in the headache... that will figure somewhere right in the middle of all this, won't it?

    @Rap - Pseudo it was *looks around to see if the prof. is around reading any of this stuff* I hope you did not get a headache as well. Those two lines of Blake are absolutely fantastic. Do you not see a reflection of chaos in them... but then again I've been known to hallucinate earlier.

    @TP - Welcome. Shows Twain was really really clever - rhymes form patterns too *Any literature major around to second that motion?*. After all what can I say that hasn't already been said.

  11. Predictability refers to sequence and triggers. Hence, predictability is always with reference to context. Without the context, everything becomes random. However, predictability by itself can be inconsistent, due to the pattern of consistent inconsistency. (I hope this makes some sense outside my head. It's such an abstract thought!)


    My point. Chaos is not random by itself, but random only because we don't understand the sequence and triggers. Randomness is in the gaps that exist for us.


  12. Sorry for butting in again.

    But rhyme schemes can also refer to lack of rhyme. And so you are right, there is a pattern!

    For instance, Haikus don't rhyme, and that's their rhyme pattern. Pattern need not define compliance!

    (Thoroughly confuses herself!)

  13. Consistent inconsistency - now that takes the cake. You are trying to say that what we do not know is chaos and is random (because we do not know the pattern which exists there). That is a way to look at it.

    But sometimes - even after we know or understand the (gross level) pattern, there is sufficient randomness at micro levels to make any sort of prediction absolutely unpredictable. *Can't believe I just said that: unpredictable predictions*

    As for the rhymes - I know there are... meters in poetry...which form patterns. Does that dictate compliance or not is something I am not qualified to debate.

  14. LOL. As convoluted as that sounds. :)
    The relationship between 'expected' pattern and a rule would be interesting to explore.

    Your post prompted something, and I ended up posting something on mon blog as well.

    Perhaps in the end what I am 'really' trying to say that the circle is too vicious. Do you know how it is, you attempt to pick the top layer of a pyramid out, and then you can't stop, and before you know it.. you are digging away like a blood hound. (Something like a mirror facing a mirror... the infinity of images)

    Yes, that is a deep influence of Godel. :) Distorted (oooh!) perspective!

  15. I read your post and I see what you meant by a "deep influence of Godel" and infinite images in the mirror bit. I'll post something on possibilities of development of self-conscious machines someday. I have to resequence my ideas and research on the subject properly before I attempt that.

    PS: Your last-but-one post ends with "Thoughts?" Are you asking other people's thoughts here, for that is in contradiction with your blog design ... or does that mean something else. Also I absolutely absolutely agree with your thoughts about ICICI and that is putting it far too mildly!

  16. This goes back to what I was saying, that at some level, everything can be related to uncertainty. Chaos is random not because it really random, but because our frame of reference is random.

    Brings me to something my advisor used to say - at a high enough level of abstraction, everything is true. He was referring to levels of abstraction in software design, but I think that applies to everything in life.

  17. Oh and aren't we referring to Escher with that bit about self referencing imagery ?