Highly entertaining, here a little fun fact: there exist a generalisation of the central limit theorem for distributions without find out variance.
For some reasons this is much less known, also the implications are vast. Via the detour of stable distributions and limiting distributions, this generalised central limit theorem plays an important role in the rise of power laws in physics.
hodgehog11 · 42m ago
I thought the rise of power laws in physics is predominantly attributed to Kesten's law concerning multiplicative processes, e.g. https://arxiv.org/pdf/cond-mat/9708231
3blue1brown has a great series of videos on the central limit theorem, and it makes me wish there were something similar covering the generalised form in a similar format. I have a textbook on my reading list that covers it, unfortunately I'm I can't seem to find it or the title right now. (edit: it's "The Fundamentals of Heavy Tails" by Nair, Wierman, and Zwart from 2022)
Do you have any good sources for the physics angle?
kgwgk · 35m ago
> find out
Finite?
lottin · 1h ago
Looking at the R code in this article, I'm having a hard time understanding the appeal of tidyverse.
RA_Fisher · 53m ago
Why? The tidyverse is so readable, elegant, compositional, functional and declarative. It allows me to produce a lot more and higher quality than I could without it. ggplot2 is the best visualization software hands down, and dplyr leverages Unix’s famous point free programming style (that reduces the surface area for errors).
lottin · 24m ago
I disagree. In this example tidyverse looks convoluted compared to just using an array and apply. ggplot2 is okay but we already had lattice. Lattice does everything ggplot2 does and produces much better-looking plots IMO.
ekianjo · 49m ago
the equivalent in any other language would be an ugly, unreadable, inconsistent mess.
For some reasons this is much less known, also the implications are vast. Via the detour of stable distributions and limiting distributions, this generalised central limit theorem plays an important role in the rise of power laws in physics.
Do you have any good sources for the physics angle?
Finite?
https://www.youtube.com/watch?v=zeJD6dqJ5lo
(yes, that Galton who invented eugenetics)