Chaos with Legos and Shapes

It’s not that easy to make a chaos model. A system where a slight tweak in the initial conditions creates major change down the road and even makes it impossible to make predictions. Many important systems that we would love to model work that way, including, for example, the weather, financial markets and, possibly, even human history. Our current bed-time read, How To by the creator of xkcd Randall Munroe (did you know he used to build robots for NASA and has an asteroid named after him?) says that while over extremely long term, the chaotic variations average out, predicting the weather medium term (like a year from now) “may to some extent be fundamentally unknowable”.

“Is history chaotic like the Game of Life – simple on a small scale yet unpredictable on a large one? Or is its unpredictability like the weather’s – with wild swings on the small day-to-day scale yet averaging out in the long run to a stable climate? Or is it perhaps like the Koch snowflake – with chaos on every level, complexity at every scale?” Ben Orlin asks at the end of his epic Math with Bad Drawings that we have just finished (yes, we only read books with stick figures in them).

Personally, I prefer thinking of human development in terms of minimizing uncertainty, bounding entropy, aka active inference as described by revered intelligence researcher Karl Friston. In other words, human development (a nested processes that unfolds over many timescales from milliseconds to decades) needs a degree of disorder, but not total chaos.

Friston places attention in very close relation to the experience of prediction errors and writes that a completely unpredictable world, where there is no opportunity to answer “what would happen if I did that” and all uncertainty is irreducible, is a joyless world. Because it’s the process of reducing disorder that brings us joy: “In a world full of novelty and opportunity, we know immediately there is an opportunity to resolve reducible uncertainty and will immediately embark on joyful exploration”, he writes, adding that it a world freed of uncertainty, where everything is predictable and all exploration is done defines boredom.  “Boredom is simply the product of explorative behaviour; emptying a world of its epistemic value—a barren world in which all epistemic affordance has been exhausted through information seeking, free energy minimising action.” This is exactly why we have celebrated the historic moment in our family when we hopped off the assembly line crawling towards boring predetermined results and chose joyful, self-directed and self-paced discovery instead. I guess the same is true for human history: a society in complete chaos is joyless and a society with rigid predetermined set of goals comes is bored to death.

Simon tried modeling chaos many times, both in code and crafting it from various materials. The easiest model that comes to mind is a double pendulum. Whereas a single pendulum symbolizes exact prediction (think of clocks), double pendulum is so sensitive to the initial conditions, that “a tiny perturbation at the start can yield a dramatic transformation later. To make sound predictions, you’d need to measure its initial state with virtually infinite precision”, Ben Orlin writes, warning us that in mathematics, an “aperiodic” system may repeat itself, but it does so without consistency.

Simon’s double pendulum made of legos. He had also tried making double pendulums using other materials.
Simon’s collab with his friend Abhay Kashyap
Simulation of multiple particles connected mutually with springs.
2 particles:
Four particles:

We are all just shapes in space-time (ensemble densities or the relative probabilities of states of affairs) and can be thought of in terms of density dynamics, Friston says:  “Interesting shapes (i.e., those characteristic of self-organizing systems like you and me) have a low entropy. Crucially, in the absence of any movement, a low entropy “shaped” probability distribution would simply not exist”. (Karl Friston, “Of woodlice and men: A Bayesian account of cognition, life and consciousness. An interview with Karl Friston (by Martin Fortier & Daniel Friedman)”, published in ALIUS Bulletin)

Read more about chaos in the context of children’s learning in my essay Joyfully Sorting Out the Disorder.

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