InterJournal Complex Systems, 117
Status: Accepted
Manuscript Number: [117]
Submission Date: 971014
Revised On: 981118
Self Dissimilarity: An Empirically Observable Complexity Measure
Author(s): William Macready

Subject(s): CX.07, CX.08, CX.12

Category: Brief Article

Abstract:

In this paper we propose several candidates for empirically measurable attributes of interest that are common to most complex systems. These attributes arise from the observation that for systems usually characterized as complex/living/intelligent, the spatio-temporal patterns exhibited on different scales differ markedly from one another. (E.g., 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 non-living/simple systems(e.g., gases, mountains, crystals) do not vary significantly from one another. Such self-dissimilarity can be empirically measured on almost any real-world data set involving spatio-temporal densities, be they mass densities, species densities, or symbol densities. Accordingly, taking a system's (empirically measurable) self-dissimilarity over various scales as a complexity ``signature" of the system, we can compare the complexity signatures of wholly different kinds of systems (e.g., systems involving information density in a digital computer vs. systems involving species densities in a rainforest, vs. capital density in an economy etc.). Signatures can also be clustered, to provide an empirically determined taxonomy of kinds of systems that share organizational traits. Many of our candidate self-dissimilarity measures can also be calculated (or at least approximated) for physical models. The measure of dissimilarity between two scales that we finally promote is the amount of extra information on one of the scales beyond that which exists on the other scale. It is natural to determine this ``added information" using a maximum entropy inference of the pattern at the second scale, based on the provided pattern at the first scale. We briefly discuss using our measure with other inference mechanisms (e.g., Kolmogorov complexity-based inference).

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