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.
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Voice-over

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?

Catastrophe Theory

René defends his mathematical theory’s ability to predict history.

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Student: Can you give us a definition?

René: It’s the loss of stability in a dynamic system.

Student: And can you give us an example?

René: Well, a river flowing along suddenly drops into a catastrophic waterfall.

Student: Catastrophic for the river or the swimmer?

René: Both. But the maths can also predict why stockmarkets jump around. That’s its use in the financial markets.

Student: Have you used it to buy stocks?

René: I’m more interested in applying it to history. Here, this calculation shows that the French Revolution was the precipitating factor for France caving in so quickly when Germany last invaded us.

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Voiceover

Typical pattern of presenting an idea.

(1) Provide a definition.

(2) Give examples.

René Thom’s Catastrophe Theory got a lot of attention in the 1970s until it became difficult to apply it to scenarios involving more than five variables.

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