Symmetry Representations and Fourier Transforms
There are many ways to motivate Fourier analysis, and recently I discovered a new one: fourier transforms are what happens when you diagonalize translation symmetry.
Ryan Tolsma
Latest posts
Fun Discrete Calculus Tricks
I’m not sure why, but high school calculus traditionally jumps straight into the continuous setting completely ignoring the fact that most of the computational methods have clear discrete analogues.
The Optimal Amount of Illiquidity is Non-Zero
Prediction markets have been taking off. Unsurprisingly, the casino-ification of everything with sports betting, election betting, etc. often gets framed as an information access democratization project with all of the fuzzy happy social good vibes that verbiage bestows. The usual framing is that markets are the best information aggregator we’ve ever built, so making them bigger, more liquid, and…
IVF Selection is Mid
IVF embryo selection is having a moment. Companies like Orchid Health are pitching parents on the promise of optimizing their future kids for IQ, height, disease resistance, and other desirable phenotypes with celebs and politicians (quietly) leaning in. The tech is real and improving, but the actual upside and long-term vision is limited by some pretty basic math.
Fun Derivative Eigenfunctions
I came across this article today on top of Hackernews which reminded me of some quant interview questions requiring some clever discrete derivative matrix tricks. I realized after reading the article, that you can construct a new clever proof that \(\frac{d}{dx} \phi(x) = a\phi(x) \iff \phi(x) = e^{ax}\) in the discrete perspective.
Some Thoughts on Robotics
Last fall, I spent a couple of months actively researching the robotics space for problems to solve or good companies to join. My background from working on RL research with Dorsa and Chelsea’s labs during undergrad, and the rapid capability improvements we’ve witnessed in the last three years had me pretty excited. A lot has changed, but I thought it would be useful to share with others a draft…
Topological Problems in Voting
Back in college, I developed an interest in unexpected impossibility proofs applied to real world systems. The fact that certain abstract mathematical structures inherently have limitations which profoundly impact actual applications is both captivating and sobering. Here’s a cute instance of topological properties applied to voting systems a friend shared with me through this video (we’ll take a…
Modelling Counterfactual Impact
You’re a bright young kid striving to change the world. As a pure bred rationalist, you of course seek to maximize your counterfactual altruistic impact, but in practice, what does that mean?
Reflections on a Stanford Journey
It’s now been almost two years since graduating from Stanford, and I wanted to carve out a post to reflect deeply on how well I spent my time there, now with the benefit of hindsight, and with the additional goal of informing my future self to bias towards activities that matter longer term. There a variety of ways to measure quality of time, but the core aspects that I’ve grown to appreciate can…
Autogenerated Dictionary
Autogenerated Dictionary