The most canonical example of a "natural ontology" comes from gasses in stat mech. In the simplest version, we model the gas as a bunch of little billiard balls bouncing around in a box.

The dynamics are chaotic. The system is continuous, so the initial conditions are real numbers with arbitrarily many bits of precision - e.g. maybe one ball starts out centered at x = 0.8776134000327846875..., y = 0.0013617356590430716..., z=132983270923481... . As balls bounce around, digits further and further back in those decimal representations become relevant to the large-scale behavior of the system. (Or, if we use binary, bits further and further back in the binary representations become relevant to the large-scale behavior of the system.) But in practice, measurement has finite precision, so we have approximately-zero information about the digits/bits far back in the expansion. Over time, then, we become maximally-uncertain about the large-scale behavior of the system.

... except for predictions about quantities which are conserved - e.g. energy.

Conversely, our initial information about the large-scale system behavior still tells us a lot about the future state, but most of what it tells us is about bits far back in the binary expansion of the future [...]

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Outline:

(03:31) Emphasizing Insensitivity

(06:56) Characterization of Insensitive Functions/Predictions?

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Narrated by TYPE III AUDIO.