math

I got a set of non-transitive Grime dice from UK enterprise Maths Gear.

What To Do When Nothing Has Happened?
Raymond “Randy” Freeman
Process Safety Progress September 2011 (Vol. 30 No. 5)

How should you estimate the probability of some catastrophic event that hasn’t happened yet?

Wikipedia has this entry for Benford’s Law, which deals with the distribution of leading digits of a collection of samples.

I read a blog post titled The golden ratio as a number base. It had an interesting statement:

According to Zeckendorf’s Theorem, every positive integer can be represented in a unique way as a sum of distinct, non-consecutive Fibonacci numbers.

Edit 2026-10-01: Numberphile on YouTube did a video on Base Fibonacci, but I scooped them by almost 2 months! The mathematician explaining Zeckendorf’s theorem to Brady Haran, Tony Padilla, does a great job of motivating, almost proving, the theorem.

I read a paper by Aidan Lyon, Why are Normal Distribution Normal?, which is apparently properly cited as Brit. J. Phil. Sci. 65 (2014), 621-649

From Statistics Libre Text:

For samples of size 30 or more, the sample mean is approximately normally distributed, with mean μ_X = μ and standard deviation σ_X = σ/√n where n is the sample size. The larger the sample size, the better the approximation.

The above is a pretty typical assertion in statistics texts. The derivation must be a doozy, it’s never shown, and there’s rarely a discussion of the Central Limit Theory itself.

It is said that the Fibonacci Sequence appears all over the place in nature.

In 2020, when one particular political faction created a controversy by claiming that national elections might be rigged, I decided to check into how my state, Colorado, audited the results of elections.

From the Wikipedia article on Cauchy distributions:

When U and V are two independent normally distributed random variables with expected value 0 and variance 1, then the ratio U / V has the standard Cauchy distribution.

Since I’m limbered up by making linear combinations of Cauchy distributions, I feel like this one is easy.

Edit 2025-07-20: Dr Drang mentioned this post! He did an analytical solution and found my curve fit wanting! That’s cool, I violated the assumptions, so it should be wrong!

Wikipedia says, about stable distributions:

a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters.