Training a neural network to compress elementary functions into only two numbers (x,y) on an Archimedean spiral. From those two numbers, the original function can be recovered. Each family of functions is eventually beautifully clustered in the embedded space of the spiral.

Facebook in 2012 was 10x as popular as ChatGPT?

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

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

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.

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.

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

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.

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

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.

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

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

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 (@MagnusCarlsen) or the poker champion (choose one). What should you choose?

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).

In chess, they say when you find a good move, look for a better one. @nntaleb 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.

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.pdf