Model of Life

The thermodynamic entropy of a system will always increase. This is the second law (SLOT). By contrast, the complexity of the system in disequilibrium will initially increase and then decrease again Figure 1.

A simple example is pouring milk into coffee. Initially complexity is low and entropy is low (relatively) when liquids are separate. As the milk is poured in, the complexity increases as the milky frontier swirls in choatic complexity and dilutes down. The entropy increases, aka the liquids merge and molecular order decreases. Eventually there is no frontier, and the solution becomes simple again (complexity has decreased), and entropy is maximal with liquids completely mixed.

While a trivial example, there is something profound about the system in choatic disequilibrium as it approaches equilibrium. The earth is a disequilibrium system. One side of the planet accepts photons with a peak energy density in the range of visible light, and loses photons with a energy density in the range of infrared (thermal) energy. While the energy in and energy out is the same, the magic of planet earth is what happens during this conversion. In some sense, the persistent disequilibrium of high energy photons being converted to low energy photons and re-emitted is the 'chaotic frontier' of planet earth. So life is born from the turbulent chaos of a photon conversion machine.

Ok, so where is life in all of this? I don't see intelligence emerging in my mug every morning.

Chaos can be modelled by dynamical systems, often defined by Differential Equations. These systems can produced attractors (sometime strange attractors if there is a fractal strcture). Physical systems on earth tend to revolve around attractors (such as hurricanes - for which the modelling inspired the Lorenz attractor). In a much more difficult modelling scenario, the paths of molecules and ions that form a 'simple' biological cell could be interpreted as forming around an attractor - the 'cell' attractor. Cells then follow paths that nest around a higher order attractor (eg a mouse attractor, or human attractor). For humans, these even higher order attractors then follow a path around a social network or group (societal attractor).

Care must be taken to make sure this interpretation isn't a glib handwaving repurposing of the word attractor. While it's not exactly clear how attractors could form like this, there is work happening in this space. For example, these guys uncovered methods to construct chaotic systems with multiple co-existing attractors. This was followed by these guys who found a way to construct infinitely many attractors in a no-equilibrium chaotic system (sound familiar). While it's not exactly easy to show you could make a no-equilibrium chaotic system with attractors that have independent paths around bigger attractors… it's at least conceivable.

A very interesting study also found self-reproducing attractors, which opens up that possibility to evolutionary systems.

This whole area is something I'm still learning a lot about, but I am enjoying playing with these ideas that are (seemingly) fundamental.

Another way of viewing the problem is through the lens of cellular automata. These are discrete systems that can produce similar behaviours to their continuous brethren from dynamical systems. These tricky little computational systems seem like a perfect analogy for life. Starting with simple rule set and space of cells, you iterate across time and observe what happens. In it's most extreme you can perform any computation with such a system and even simulate a CA in a CA, such as the game of life in the game of life.

CA also can exibit attractor-like behaviours, and even the word cell smacks of biology.

What are the perfect conditions that can foster life? Based on my thoughts above, you need at least the following:

1. A non-equilibrium system (this doesn't mean the system could never reach equilibrium but at the very least is being kept out of equilibrium)
2. Some luck in landing the right calibration of the constants that dictate the behaviour of the potential chaos in that non-equilibrium system.