Math

The Veritasium chap made a video about Markov Chains. Veritasium outlines Markov’s original text-based experiment. The experiment seems like something that could be educational to duplicate.

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

I have verified Grime dice with a monte carlo simulation, but it’s not that hard to calculate the actual probabilities.

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.