[rndn]

Here are the slides of a talk on universality that Terry Tao gave some time ago: https://terrytao.files.wordpress.com/2011/01/universality.pd...

It's basically the observation that large systems converge to exhibit rather simple behaviors. It generalizes other reoccurring patterns such as power laws, Euler's number, the normal distribution and the fibonacci sequence. For some reason nature is surprisingly frugal regarding the forms and behaviors that she allows. I think the simpest explanation for that comes from the anthropic principle and the multiverse hypothesis which state that all possible physical laws are realized in different universes and we happen to be in the one that has the necessary conditions to bring us into existence (universality being perhaps one of them).

[squidfood]

Well, sure. I say "oh look, when animals breed, it has this curve" and then I say "oh look, when money is invested it grows with this curve." The insight is that "multiplication works".

This helps, because I don't need to re-invent logarithms and e to study animal population growth. And of course, different rules lead to different math (be it power laws, the Normal distribution, universiality, Phi, whatever).

This is interesting philosophically. HOWEVER, these models are still simplifications of reality. What happens with slight departures in animal population trajectories can be very different than perturbations in interest rates, so it would be a mistake to say "these things are truly connected" beyond the practicality of using similar math.

[rndn]

I'm not too familiar with all of this (perhaps I'm even misinterpreting it), but I think they do realize that it would be problematic to throw population trajectories and interest rates into the same pot. I think the motivation is rather to find reasons why things do not behave completely unpredictable at larger scales and I cannot think of good reasons against efforts to find more and more general descriptions of that.

[squidfood]

I agree with the motivation and interest! The issue comes when people try too hard to find patterns to fit a preconceived hypothesis.

I maintain a large (publicly available) ecological dataset, and my data have been drawn into several meta-analyses of this type. Often the idea is to simply see if my data empirically fit the "right" distribution. And they fit it and say "wow, it's all connected".

But then I look at the Bus data in this example (the +'s that represent actual data). I'm guessing I could fit a lognormal distribution, a Gamma distribution, or the Dyson distribution that they actuall use, and the data wouldn't be enough to distinguish between them.

Now, all of these distributions result from "simple" rules, but they are three very different sets of simple rules. For the Bus data, the "repelling" by little slips of paper makes sense as the mechanism, so it's a good hypothesis.

But then to flip that around, and say "since this distribution fits the ecological data, the underlying mechanism must be Bus Repelling" is wholly unjustified (as there are other possible fits). And there's a lot of junk science that does that.