Quantifying the Rise and Fall of Complexity in Closed Systems: The Coffee Automaton

See on Scoop.itIt Comes Undone-Think About It

In contrast to entropy, which increases monotonically, the “complexity” or “interestingness” of closed systems seems intuitively to increase at first and then decrease as equilibrium is approached. For example, our universe lacked complex structures at the Big Bang and will also lack them after black holes evaporate and particles are dispersed. This paper makes an initial attempt to quantify this pattern. As a model system, we use a simple, two-dimensional cellular automaton that simulates the mixing of two liquids (“coffee” and “cream”). A plausible complexity measure is then the Kolmogorov complexity of a coarse-grained approximation of the automaton’s state, which we dub the “apparent complexity.” We study this complexity measure, and show analytically that it never becomes large when the liquid particles are non-interacting. By contrast, when the particles do interact, we give numerical evidence that the complexity reaches a maximum comparable to the “coffee cup’s” horizontal dimension. We raise the problem of proving this behavior analytically.

Quantifying the Rise and Fall of Complexity in Closed Systems: The Coffee Automaton
Scott Aaronson, Sean M. Carroll, Lauren Ouellette


Eli Levine‘s insight:

Story of the universe.

An imperfect and potentially unstable homeostasis is reached and then dashed out of order.  It is then remade in a different, if sometimes similar matter, and the cycle repeats, as far as we can tell at present.

Think of a revolution in a society: the seeds of the old order’s collapse is rooted in the system and the psychologies it encourages and promotes.  Eventually, chaos sets in, and things are thrown out such that a “new” system emerges that, hopefully, is able and willing to learn from the mistakes of the past, in order to produce an anti-fragile social and political system.

The universe is going to end and everything is going to be dashed out, even if we do become otherwise perfectly capable of enduring, mitigating against and recovering from any disaster.  The question then is how quickly will the universe reset itself once its own imperfections come to light and another transition occurs?

Think about it.

See on arxiv.org


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