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I've started working on the mathematics behind optimal pool play, which is quite challenging. It's one of the best examples of both applied extreme value distributions and the optimality of seemingly suboptimal wagers because of prize splitting.

And with any difficult problem, attitude is always important. I always assume I will be able to solve a problem, until proven otherwise.

Another top 10 finish?

Complexity theory and theory of computation were two of the most interesting topics I've studied in computer science. They always reminded me of how cardinal numbers are studied in set theory and logic.

The Motion of Point Particles in Curved Spacetime Eric Poisson “The reader is also assumed to have unlimited stamina, for the road to the equations of motion is a long one.” Scary but honest.

When a probability-generating function for a random variable X is referenced, it's assumed X takes non-negative integer values. That's an interesting restriction. Are PGFs not useful for other discrete random variables? As one example, we wouldn't necessarily have convexity.

My question on PGFs came up because I was struggling to solve a Math Monthly problem for 20 minutes when I realized X was implicitly restricted to nonnegative integers, making the problem simple. A real dumb-dumb maneuver.

Inigo Montoya: You keep using that word. I do not think it means what you think it means.

I'm begging you people to do the math. It's literally a single derivative.

Monsky's theorem!

I actually had to use Cantelli's inequality today. It seems particularly helpful for bounds on Pr(X=0) with discrete random variables.

Since nothing of interest is happening today, it's as good a time as any to announce I'll be writing on Substack, covering topics in sports analytics and sports betting. I don't think there'll be much overlap with anything else that's out there.

We'd have a functional government?

I had an insightful childhood friend who would exclaim, when anyone would argue that professional wrestling was real, that if it were real "everyone would be dead".

National security is an area that needed more hallucinations.

One of the primary issues I'm having with AI engines is that they're continuing to hallucinate references for theorems that don't exist.

Seems apropos given today.

Look at this adorable little guy.

The idea that there are "official" Great Books, and if you read them you'll be literate and well-educated, is lazy and comforting. It's also less challenging than reading good contemporary fiction, which tends to confront a broad range of modern issues and concerns.