“On a log-log plot, my grandmother fits on a straight line.” -Physicist Fritz Houtermans There's a lot of truth to this. log-log plots are often abused and can be very misleading 1/5 - ThreadSky

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docmilanfar.bsky.social • 123 days ago

“On a log-log plot, my grandmother fits on a straight line.”
-Physicist Fritz Houtermans

There's a lot of truth to this. log-log plots are often abused and can be very misleading

1/5

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docmilanfar.bsky.social•123 days ago

A plot of empirical data can reveal hidden phenomena or scaling. An important and common model is to look for power laws like

p(x) ≃ L(x) xᵃ

where L(x) is slowly varying, so that xᵃ is dominant

Power laws appear all over physics, biology, math, econ. etc., however...

2/5

docmilanfar.bsky.social•123 days ago

...just because on a log-log plot your data looks like a line, you can't conclude that you're looking at a power law

In fact, a roughly straight behavior on a log-log scale is like a necessary condition, but it is not sufficient for power-law behavior. Take this example:

3/5

docmilanfar.bsky.social•123 days ago

To establish power law behavior we need statistical tests. This paper is a nice overview of statistical methods for testing power laws

"Power-Law Distributions in Empirical Data"
by A Clauset, CR Shalizi, & MEJ Newman
SIAM Review, 51(4), 661–703

https://arxiv.org/abs/0706.1062

4/5

docmilanfar.bsky.social•123 days ago

One of the only cases where a power law is strongly true is the distribution of frequencies of occurrence of words.
word frequency ∝ 1/word rank

This is an instance of Zipf's law: sort a list in decreasing order & the value of n-th entry is inversely proportional to n 

5/5

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