ABSTRACT
For many systems characterized as “complex/living/intelligent” the spatio-temporal patterns exhibited on different scales differ markedly from one another. For example the biomass distribution of a human body “looks very different” depending on the spatial scale at which one examines that biomass. Conversely, the density patterns at different scales in “dead/simple” systems (e.g., gases, mountains, crystals) do not vary significantly from one another. Accordingly, we argue that the degrees of self-dissimilarity between the various scales with which a system is examined constitute a complexity “signature” of that system. Such signatures can be empirically measured for many real-world data sets concerning spatio-temporal densities, be they mass densities, species densities, or symbol densities. This allows one to compare the complexity signatures of wholly different kinds of systems (e.g., systems involving information density in a digital computer, vs. species densities in a rain-forest, vs. capital density in an economy, etc.). Such signatures can also be clustered, to provide an empirically determined taxonomy of “kinds of systems” that share organizational traits. The precise measure of dissimilarity between scales that we propose is the amount of extra information on one scale beyond that which exists on a different scale. This “added information” is perhaps most naturally determined using a maximum entropy inference 626of the distribution of patterns at the second scale, based on the provided distribution at the first scale. We briefly discuss using our measure with other inference mechanisms (e.g., Kolmogorov complexity-based inference).
