I have read the book Scale by Geoffrey West and I find many of the charts tautological and suffer from the part whole fallacy. I wonder how many of the scaling relations are predictive and not related to the physical dimensions of weight and height of the many species he approximates with algorithmic charts that are consistent with random numbers.

Leandro Toriano writes: 

West's stuff is poorly regarded among technical people–it pops, but power laws can be made to look like they fit too many things. (There are a few critiques on arXiv, iirc.)

Recently I came across Indra's Pearls by David Mumford, Caroline Series, and David Wright. They do hat-tip Mandelbrot's Hausdorff (fractal) dimension, but don't fall into trendy theory. Easily makes my top 100 of all time, and probably top 3 mathematics books for non-mathematicians. In it you'll find more reasonable discussions of this stuff than elsewhere.

Koebe 1/4 on youtube has a good video of Curt MacMullen speaking on Renormalisation.





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1 Comment so far

  1. chris davis on June 13, 2018 4:26 pm

    seems like this article from Quanta magazine would be consistent with what you were saying.


    regarding sample sizes;
    “it is possible for small values of n that the empirical distribution will follow a power law closely, and hence that the p-value will be large, even when the power law is the wrong model for the data. This is not a deficiency of the method; it reflects the fact that it is genuinely harder to rule out the power law if we have very little data. For this reason, high p-values should be treated with caution when n is small.” (https://arxiv.org/pdf/0706.1062.pdf)


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