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 We can think of the compression from physics to (say) chemistry, then, as resulting in a new configuration space for the same old system—one where points represent regions of the old space, and where every point represents a significant difference from this new (goal-relative) perspective, with the significance stemming from both the discovery of interesting new macrostates and interesting new dynamics. This operation can be iterated for some systems: biology can define a new configuration space that will consist of points representing regions of the original configuration space. Since biology is more “lossy” than chemistry (in the sense of discarding more state-specific information in favor of dynamical shortcuts), the space defining a system considered from a biological perspective will be of a still lower dimensionality that the space considering the same system from a chemical perspective. The most dynamically complex systems will be those that admit of the most recompressions—the ones for whom this creation of a predictively-useful new configuration space can be iterated the most. After each coarse-graining, we’ll be left with a new, lower-dimensional space wherein each point represents an importantly different state, and wherein different dynamical patterns describe the transition from state to state. That is, repeated applications of this procedure will produce increasingly compressed bitmaps, with each compression also including a novel set of rules for evolving the bitmap forward in time.

We can think of this operation as akin to changing magnification scale with physical objects that display fractal-like statistical self-similarity: the self-similarity here, though, is not in shape but in the structure and behavior of different abstract configuration spaces: there’s interesting

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