https://gptzero.me/ Says that at large portions of it are 100% human

Interesting comment. Why is it common decency to call out how much ai was used for generating an artifact?

Is there a threshold? I assume spell checkers, linters and formatters are fair game. The other extreme is full-on ai slop. Where do we as a society should start to feel the need to police this (better)?

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?

Yes, came here to say the same thing. Not telling people that the CLT makes strong assumptions is important.

Otherwise, they might end up underestimating rare events, with potentially catastrophic consequences. There are also CLTs for product and max operators, aside from the sum.

The Fundamentals of Heavy Tails: Properties, Emergence, and Estimation discusses these topics in a rigorous way, but without excessive mathematics. See: https://adamwierman.com/book

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

> find out

Finite?

It is correct in the article. As the sample size approaches infinity, the distribution of the sample means approaches normal.

https://en.wikipedia.org/wiki/Central_limit_theorem

Yes indeed, if the sample size approached infinity (and not the number of samples), you would essentially just be calculating the mean of the original distribution.

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.

OTOH 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.

    set.seed(10)
    n <- 10000; samp_size <- 60
    df <- data.frame(
        uniform = runif(n, min = -20, max = 20),
        normal = rnorm(n, mean = 0, sd = 4),
        binomial = rbinom(n, size = 1, prob = .5),
        beta = rbeta(n, shape1 = .9, shape2 = .5),
        exponential = rexp(n, .4),
        chisquare = rchisq(n, df = 2)
    )
    
    sf <- function(df,samp_size){
        sdf <- df[sample.int(nrow(df),samp_size),]
        colMeans(sdf)
    }
    
    sim <- t(replicate(20000,sf(df,samp_size)))

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).

the equivalent in any other language would be an ugly, unreadable, inconsistent mess.

and the Galton Board https://en.m.wikipedia.org/wiki/Galton_board

(yes, that Galton who invented eugenetics)

Very much an inspiration and resource when composing the post.