Mysterious Statistical Law May Finally Have an Explanation – WIRED

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10 points·kumarshantanu··3 comments

I don't pretend to be a statistician, but I don't think the distribution is nearly as mysterious as the article is trying to make it sound. At least it's not any more mysterious than the normal distribution that we're all familiar with. When you have similar assumptions and inputs (even if those inputs are random) in a statistical model, you'll usually get similar distributions.

Yes, but interactive systems are quite complicated to describe mathematically. There is very little known still. A while ago there was an article on HN in which a connection was made between renormalization group theory and deep learning: https://www.quantamagazine.org/20141204-a-common-logic-to-se.... The thing is, a lot of systems, are called "critical", or with Kauffman's words "edge of chaos", or "poised at criticality".

Another example, even more recent there was a discovery about correlated novelties and both Heap's and Zipf's law: http://www.nature.com/srep/2014/140731/srep05890/full/srep05.... Different from the normal distribution which indeed just comes from the law of large numbers (central limit theorem), these come from much more interesting processes.

You can have all kind of distributions and all kind of power-law like behaviour around complex systems. It is henceforth extremely important to weed out all the nonsense. To be able to deduct what kind of microscopic relations bring about Tracy-Widom distributions especially in the context of other mathematical objects than random matrix brings lots of disciplines forwards. From physics to machine learning.

https://news.ycombinator.com/item?id=8459264

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