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.
Tachyooon · 1h ago
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?
hodgehog11 · 44m 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
Looking at the R code in this article, I'm having a hard time understanding the appeal of tidyverse.
gjf · 35s ago
Author here; I think I understand where you might be coming from. I find functional nature of R combined with pipes incredibly powerful and elegant to work with.
But what I find is that in a pipeline, you're mutating/summarising/joining a data frame, and it's really difficult to look at it and keep track of what state the data is in. I try my best to write in a way that you understand the state of the data (hence the tables I spread throughout the post), but I do acknowledge it can be inscrutable.
RA_Fisher · 55m 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 · 26m 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 · 51m 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?
But what I find is that in a pipeline, you're mutating/summarising/joining a data frame, and it's really difficult to look at it and keep track of what state the data is in. I try my best to write in a way that you understand the state of the data (hence the tables I spread throughout the post), but I do acknowledge it can be inscrutable.
https://www.youtube.com/watch?v=zeJD6dqJ5lo
(yes, that Galton who invented eugenetics)