4 ms·
Agreed. The old saying is "anything looks linear when plotted on a log-log graph." However, the OP was giving a rough approximation in the first place, in sayi
by dalke 10y ago
Agreed. The old saying is "anything looks linear when plotted on a log-log graph."
However, the OP was giving a rough approximation in the first place, in saying that all natural distributions follow a Gaussian curve. But Gaussian curves go from -∞ to +∞. Many of the real-world distributions must only have positive values, like heights and weights. Although for real-world purposes, they can usually be approximated as Gaussian.
With that roughness in mind, I think it's okay to say that the Stefan–Boltzmann law, the inverse-square laws of Newtonian gravity and electrostatics, or Kleiber's law, which are all listed in the Wikipedia link are close to a power law to be acceptable counter-examples.
(Stefan–Boltzmann assumes a perfect black body, the inverse-square laws ignore relativity, and Kleiber's law is a rule-of-thumb in the first place.)
- mattkrause 10y agoOh sure. When there's a plausible reason for thinking something is scale-free, I'm all for it. For a while though, it was en vogue to find power law distributions in all sorts of weird places (email response times, numbers of friends), and that's what I was attempting to object to!