Rule 6 of Akin's Laws of Spacecraft Design:

6. Everything is linear if plotted log-log with a fat magic marker.

http://spacecraft.ssl.umd.edu/akins_laws.html

Back in my academia years, I was really frustrated with that group of researchers, "cult of power law" I called them - mainly centered around Santa Fe Institute.

In all their talks, the pattern was always the same: 1) take a dataset from some random system, and strip it from all its domain context ("interdisciplinary" research) 2) brag about being a "physicist" thus applying a "physicist's" approach to new areas of research 3) plot data on log-log scale - kind of looks like a power law 4) make a toy model and use it to "simulate the system" 5) plot simulation vs real data on log-log scale -- kinda look the same 6) promise that your trivial little model will reveal whole new horizons for that field you know nothing about - because others are stupid and you're a "physicist" 7) write a grant proposal

Power laws and scale-free networks are discussed in https://arxiv.org/abs/1801.03400 with HN comments at https://news.ycombinator.com/item?id=16144867. Both this and the cited paper are worthwhile reads for power law users.

You can't use a goodness of fit test to claim that your data follows a power law (or any distribution). You can only use a GoF test (such as Kolmogorov-Smirnov) to collect evidence that your data don't follow some hypothesized distribution. And if you collect enough data, your GoF test will reject every hypothesized distribution.

Note that paper appeared in SIAM, not "Reviews of Modern Physics" or some place where physicists might read it.

(Speaking as someone who wrote a probably invalid paper about power laws and who had Mark Newman working just across the hall in the 1990s)

Can anybody say which kind of function on these graphics?

Distribution of atoms in Solar systems looks like cos(m): https://upload.wikimedia.org/wikipedia/commons/e/e6/SolarSys...

Star clusters, looks like sin(s): http://cdn.iopscience.com/images/0004-637X/725/2/1717/Full/a...

Exoplanets, looks like sin(m): http://exoplanets.co/img/exoplanets-mass-distribution.jpg (more at http://exoplanetsdigest.com/author/yaqoob/ )

Any similar articles or advice about power law relationships in general (not distributions)? I've fit a lot of data to power law relationships in the past but don't know if there are any non-obvious pitfalls. I can recognize when a power law obviously won't work, but as has been said, a lot of data can look like a power law relationship. So for each obvious failure of a power law relationship, there are a certain number of false positives.

Why do you guess that their paper from June 2007 mentioned in the blog was only released February 2009? Seems like a long revision period.

Nothing important, just threw me a bit off guard seeing the date of the blog post and the authors own prediction "forthcoming (2009)". But maybe he edited the blog once he knew when the paper finally came out.

Title should have: (2007).

IMHO this feels like quibbling as the author doesn't make clear when this would actually make a difference.

This a fascinating article that provides lots of worthwhile information for anyone planning in fitting a power law to their data.

I will probably never read another of the author's writings due to the pervasive negativity.

I used a power series to approximate the radius of a planet to its mass for a webgl space game I'm making [0] where solar systems are randomly generated. I needed something to roughly approximate the size of a planet or star based solely on mass. Using the 8 planets + (sedna & pluto) and our star to generate the curve function I got a r^2 value of 0.989. [1]

I'm not about to make some scientific claim based on it but for my purpose (a neat game) using a power series to approximate mass was an extremely efficient and simple solution to my problem.

[0] http://thedagda.co:9000/

edit: if you have an xbox controller you can use this: http://thedagda.co:9000/?gamepad=true

[1] https://docs.google.com/spreadsheets/d/1GKPNNMJrZMaf8aQqgGD-...