Tuesday, March 27, 2012

Butterfly Effect, Chaos and Catastrophe Theories

Lorenzo Monarch and Tiger Moth discuss theories
Lorenzo: You’ve heard of the butterfly effect?
Tiger Moth: You’re telling me that Monarchs rule the world? That one flap of your wings here in Mexico and you set off a maelstrom in Mauritius?
Lorenzo: Chain of events sets off a crisis far away. Chaos theory.
Tiger Moth: And you’ll be aware of catastrophe theory?
Lorenzo: A steady state that suddenly experiences change? It’s a branch of chaos theory.
Tiger Moth: Have you thought about how these apply to us? Today we choose to sip nectar from this bush, the bird misses us and we live. Tomorrow, we sip nectar from the next bush, the bird sees us and we’re dead. Catastrophe.
Lorenzo Monarch is good at giving definitions. An abstract ability. Tiger Moth excels at giving examples. And makes it personal. But can either of them solve non-linear equations?


Anonymous said...

How do you measure “chaos”? In my maths class I learned about the Lyapunov exponent, a quantity that expresses the rate of separation of very close trajectories. But it seems difficult to link a butterfly trying to survive in its life to complex algebra.

I saw Hunger Games recently – a story of survival. Could a butterfly communicate with a bird, to make peace in the jungle?

Barry Natusch said...

Measuring chaos? Well, you can measure the force of such events as typhoons (1 to 10). Perhaps some measure of intensity of chaos is also possible, although this would be applying a linear measure to a non-linear event!
Lyapunov? That must have been an ADVANCED Maths class! Impressive!
Algebra and butterflies? There's an algebraic butterfly curve expressed as x^6 + y^6 = x^2. Pretty!
Could a butterfly enter peace negotiations with birds, ask them to stop being predators? I suspect such negotiations, being against instinctive behavior, might take a l o n g t i m e! ;-)