Zusammenfassung für den Vortrag am 26.02.2009 (14:00 Uhr)

David Wolpert (NASA Ames Research Center, USA)

Self-dissimilarity as a high dimensional complexity measure

For many systems characterized as ``complex'' the patterns exhibited on different scales differ markedly from one another. For example the biomass distribution in a human body ``looks very different'' depending on the scale at which one examines it. Conversely, the patterns at different scales in ``simple'' systems (e.g., gases, mountains, crystals) vary little from one scale to another. Accordingly, the degrees of self-dissimilarity between the patterns of a system at various scales constitute a complexity ``signature'' of that system. Here I present a novel quantification of self-dissimilarity. This quantification can be measured for many kinds of real-world data. This allows comparisons of 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.). Moreover, in contrast to many other suggested complexity measures, evaluating the self-dissimilarity of a system does not require one to already have a model of the system. These facts may allow self-dissimilarity signatures to be used as the underlying observational variables of an eventual overarching theory relating all complex systems. To illustrate self-dissimilarity I present several numerical experiments. In particular, I show that underlying structure of the logistic map is picked out by the self-dissimilarity signature of time series' produced by that map.