Occam’s razor and the ubiquity of power-law distribution
張欽德1, 張景皓1, 洪在明1*
1物理系, 清華大學, 新竹市, Taiwan
* presenting author:洪在明, email:ming@phys.nthu.edu.tw
Preference for simplicity partly contributes to the wide variety of phenomena that claim to exhibit simple power law distribution, y=a*x^b. Examples include the sizes of earthquakes, craters on the moon and of solar flares, frequencies of words in most languages, the species richness in clades of organisms. By mixing the crackling noises from two separately crumpled materials that exhibit distinct power-law exponents b, we show that the combined data can still be fit to power law with ironically even smaller error bar for b. This delusion prompts us to adopt the more rigorous Akaike’s information criterion from statistics, which mimics the Helmholtz free energy of thermodynamics, to reexamine the legitimacy of famous applications of power law in the literature. Examples are found that power law not only cannot be regarded as a beauty in the eyes of beholder, but may turn out to be bad fitting function.

Keywords: Occam's razor, power law, crackling noise, Akaike's information criterion