Thursday, March 14, 2019

SFI on fractals and scaling

Continuing this post, Santa Fe Institute (SFI) has a recent, several part online course on fractals and scaling, summarized in the video below. Some real world objects indeed display fractal-like scaling but are limited within real world constraints, unlike abstract, mathematical fractals ad infinitum (2:00). Other real world applications do not exhibit fractal scaling, so other models are better suited to measure them (10:00). Here Clauset et al's earlier work was cited, Clauset's later empirical work (cited previously) on about 1000 networks confirming that scale-free networks are indeed rare so thus different models are needed to evaluate them. Hence questions arise if one wants to make a model of everything based on fractal scaling as first principles (11:25). Summing up the themes, the video notes that objects can be more or less fractal like (as Clauset's recent study attests) and are not in an either/or category. And that fractal scaling, where it is seen in objects, "does not necessarily reveal its essence" (17:40). I'd add that it in no way reveals its essence, as that is a topic well investigated in postmetaphysics.

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