degree of structure or pattern in that entity; and physical complexity, which interprets the shared Kolmogorov complexity of an ensemble of sequences as information stored in the genome about the environment. This last makes the interesting point that one cannot know anything about the meaning of a DNA sequence without considering the environment in which the corresponding organism is expected to live.

All of these capture some aspect of the way in which complexity might arise over time through an undirected evolutionary process and be stored in the genome of a species. However, in their physics-inspired search for minimal descriptions, they may be missing the fact that evolution does not produce optimal or minimal descriptions. That is, because biological organisms are the result of their evolutionary histories, they contain many remnants that are likely to be irrelevant to their current environmental niches, yet contribute to their complexity. Put differently, any given biological organism is almost certainly not optimized to perform the functions of which it is capable.

Another difficulty with many of these measures’ application to biology is that, regardless of their theoretical soundness, they will almost certainly be hard to determine empirically. More prosaically, they often involve a fair amount of mathematics or theoretical computational reasoning (e.g., to what level of the Chomskian hierarchy of formal languages does this sequence belong?) completely outside the experience of the majority of biologists. Regardless, this is an area of active research, and further integration with actual biological investigation is likely to produce further progress in identifying accurate and useful measures of complexity.

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