We, God and the Chaos
Thursday, September 06, 2007
"Tell me how microprocessors and micro controllers work", thats how the discussion got started by Rahul at 10:17pm in our room; the discussion that would obey the chaos theory in the topics being discussed and keep us awake till 4:50am.The talk started with the controller architecture, the paradox of data bus and memory addresses and graduated to the processing power. When Pankaj got up to fetch a bottle of water from kitchen it was already 1:40am, and meanwhile I arrogantly pronounced that the weather data crunching supercomputers deals with terabytes of data and actually measure fluctuations at every point in a about 1 sq km of area. Suddenly the team was energized to argue that it was just not possible and voila! thanks to Chaitanya we landed up in Chaos theory and butterfly effect, the brilliant yet mind boggling theory.
Butterfly effect phrase refers to the idea that a butterfly's wings in Brazil might create tiny changes in the atmosphere that ultimately cause a tornado to appear (or prevent a tornado from appearing) in Texas. The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale phenomena.
The Chaos theory on other hand describes the behavior of certain nonlinear dynamical systems that under specific conditions exhibit dynamics that are sensitive to initial conditions (butterfly effect). As a result of this sensitivity, the behavior of chaotic systems appears to be random, because of an exponential growth of errors in the initial conditions.
No I am not going to discuss about how the movie by same name described the effect and repercussions of changing something in past, what I want to discuss is that even after a system being totally chaotic, it still may be deterministic. In the essence that even though the essence of God is still a mystery, it may not be some day when we get enough variable to discuss the origin and expanse of the universe.
Let us have a look at the long term behavior of a chaotic motion. The Lorentz Attractor would show a graphical representation of the time variation of three variables X(t),Y(t) and Z(t), coupled by non-linear evolution equations. For single solution evolving from an initial condition (X0,Y0,Z0) will be very different from another solution running simultaneously from initial conditions separated by (dX0,dY0,dZ0) by setting any of dX0, dY0, dZ0 to nonzero values (e.g. 0.01). This tiny difference in the initial conditions becomes amplified by the evolution, until the two trajectories evolve quite separately. The amplification is exponential, the difference grows very rapidly and after a surprisingly short time the two solutions behave quite differently, even though they may be having a similar trajectory. This is an illustration of the butterfly effect - the idea in meteorology that the long term behavior becomes impossible to forecast. Hence Rahul said we can't predict the weather to escape the price of acquiring the knowledge!
But this raises the question about our existence. How many times have you got boggled down thinking if all started from big bang, what was around that big concentrated ball of mass, how did it come there, whats the end of the universe? I personally believe that like the discovery of earth being round body answered infinite questions, there is yet some truth to be found which will suddenly make many disconnected theories and questions fall in place. The motion of almost every natural thing is chaotic, but then given a long duration it can be expressed in significantly complex mathematically equation. The challenge is the expression and not the chaos!
Let us have a look at the long term behavior of a chaotic motion. The Lorentz Attractor would show a graphical representation of the time variation of three variables X(t),Y(t) and Z(t), coupled by non-linear evolution equations. For single solution evolving from an initial condition (X0,Y0,Z0) will be very different from another solution running simultaneously from initial conditions separated by (dX0,dY0,dZ0) by setting any of dX0, dY0, dZ0 to nonzero values (e.g. 0.01). This tiny difference in the initial conditions becomes amplified by the evolution, until the two trajectories evolve quite separately. The amplification is exponential, the difference grows very rapidly and after a surprisingly short time the two solutions behave quite differently, even though they may be having a similar trajectory. This is an illustration of the butterfly effect - the idea in meteorology that the long term behavior becomes impossible to forecast. Hence Rahul said we can't predict the weather to escape the price of acquiring the knowledge!But this raises the question about our existence. How many times have you got boggled down thinking if all started from big bang, what was around that big concentrated ball of mass, how did it come there, whats the end of the universe? I personally believe that like the discovery of earth being round body answered infinite questions, there is yet some truth to be found which will suddenly make many disconnected theories and questions fall in place. The motion of almost every natural thing is chaotic, but then given a long duration it can be expressed in significantly complex mathematically equation. The challenge is the expression and not the chaos!
Labels: Philosophy, Physics
posted by Jas @ 2:19 PM,
