The (a) *Gaussian distribution* and (b) *Convexity (of sets)* are in some sense, similarly universal. How? (a) Summing non-gaussian r.v. often gives you approximately a gaussian rv. (b) Summing non-convex sets gives you approximately a convex set*. figure: arxiv.org/pdf/1712.08559…

In chess, they say when you find a good move, look for a better one. Nassim Nicholas Taleb mentions a related “contamination principle” in the value of financial contracts. This “contamination” often holds true in research too. Eg when you have a good algorithm, look for a better one.

What does Strong Duality really tell us: All these complicated constraints can be *summarized* by a single plane! It’s remarkable that such a reduction is possible (when it is / under mild conditions in convex programs).

Luck often narrows edges. Impact of your skill versus impact of randomness (the SNR ratio), should be a determining factor in taking bets. Suppose your life depends on beating either the chess champion (Magnus Carlsen) or the poker champion (choose one). What should you choose?

Markov Chain based sampling: sampling from various distributions using MCMC and Metropolis-Hastings. more: tsan.me/post/mcmc/

Sampling the US map with Markov Chains results in a pleasing animation when the step size is large enough.

Simulated Annealing on the Maximum Independent set Problem is very cool. The random solution at any time follows a random walk in the space of valid graphs. At the same time, its objective value itself is very Brownian-motion like.

I couldn't tell why I was getting new followers until this showed up on my home page. :-) Thanks!

Research is like a diffusion out of a labyrinth. Each researcher is a particle that faces obstacles in their effort to expand the frontier, yet they may bias their random walk around the challenges.

You can construct distributions with mean 30-50 and median 10.

How long before frontier AI labs start taking **some** business away from Hedge Funds and Prop shops? Edge tied to insanely hard-to-get data will likely remain for several years.

Here’s a trading game where you are betting on the fair value of barrier contracts on 2D brownian motions hitting bubbles. Go long if the market % is too low, short otherwise.

Becoming rich from working at a startup still requires beating the market while taking more individual risk than investors.

It's nearly 3 here, my favourite part of the night shift… locked in... 💪🚀

Made a little Soccer simulator with Gemini 3 in ~10 mins.