The Biggest and Weirdest Commits in Linux Kernel Git History
Clauset Shalizi Newman 2007 has not-nice things to say about the classic physicist's idiot trick of fitting power law distributions by drawing a straight line on a log-log graph: it's got huge bias. <a href="https://arxiv.org/abs/0706.1062" rel="nofollow">https://arxiv.org/abs/0706.1062</a><p>However, the other difficult thing about power law distributions is that the dataset size requirements for proper determination of the fact that it's a power law distribution are occasionally incredibly difficult. So their critique is very strong, given the comparative lack of data. It is often the case that computer systems, with the overflowing reams of data, are still not enough. Note that the paper I cited up there suggests MLE and then a Kolmogorov-Smirnoff test, so it'll say a lot of things aren't power laws that could well be.<p>Another way to look at it is from a more geometric point of view. The metric entropy of any generic system of variables is defined as the sum of the positive Lyapunov exponents: and as an "entropy" that quantity does have a lot of commonalities with the other entropies. But to have positive Lyapunov exponents is often to have a chaotic dynamics, so it could just be conjectured that the time series of commits and merge octopus sizes in kernel git history is chaotic, so the evolution of the time series will be fractal in nature.<p>But it's also really fucking hard to confirm or deny that one, because there are varied and strange definitions of chaos itself and the methods that have been suggested to measure Lyapunov exponent in real systems are arcane and difficult. You could try some synchronization methods, but they remain arcane and crap. Fractal measurement methods are also shitty and full of dark magic.<p>One neat little trick might be to discretize the series, symbolic dynamics-style (it's already discretized but discretize further, into like percentiles or something) and run it through one of the dynamical machine learning dealies to see if there's patterns. Not too much literature on that but it's a thing that some randoes in like 2004 or something did