| As a followup to an on-line discussion, the face-to-face FRIAM group last week spoke some more about kinds of complexity. I mentioned a paper of Seth Lloyd's, which is called "Measures of Complexity: A non-exhaustive list." I have a hard copy, undated, and retrieved from Joe Traub's files,. I have no idea if this brief note has been published elsewhere. (Joe remembers its first appearance as "31 Flavors of Complexity" with a jokey little nod to Baskin-Robbins.) Anyway, it begins: "Recently, measures of complexity have multiplied rapidly. Some take this proliferation as a sign that no one knows what complexity really is. In fact, asking for the true mathematical definition of complexity today is like asking for the true mathematical definition of electricity in 1800: to understand electricity, it turned out to be much more productive to define several quantities, such as charge, current, voltage, inductance, etc., that could be related by simple formulas, than to define a single mathematical definition of electricity. In addition, like H and B , a number of quantities that originally were thought to describe different effects, later were discovered to be closely related, and in many circumstances, identical. The many definitions of complexity stand in similarly close relations to each other. This list groups measures that are in some situations closely related to each other, or identical." He then lists 5 groupings of kinds of complexity which seem related to each other, along with subgroups. The large groupings are information, mutual and conditional information, computational complexity, distinguishability, and definitions without precise mathematical _expression_. In short, the field is in its infancy. We force it into premature adulthood at our own cost. Pamela I sit in one of the dives On Fifty-second Street Uncertain and afraid As the clever hopes expire Of a low dishonest decade W. H. Auden |
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