The article presents a novel proof of the derivative relationship \\(\frac{d}{dx} \phi(x) = a\phi(x) \\iff \phi(x) = e^{ax}\\ in a discrete context. It introduces a basis approach that represents functions as vectors of polynomial...
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Ryan Tolsma is a problem solver with interests in math, physics, and AI, and enjoys poker, board games, and anime.
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6.4IVF Selection is Mid
2025-10-24 •
The blog post discusses the limitations of IVF embryo selection technology, particularly in optimizing traits like IQ and height. It explains that while companies like Orchid Health promote the potential for selecting desirable ph...
The blog post discusses the author's experience during a remote internship at Wealthfront, where they worked on developing an automated robo-advisor for wealth management. The author explains the complexities of wealth management,...
0Some Thoughts on Robotics
2024-07-10 •
The text discusses the author's research in the robotics space, sharing insights and frameworks after talking to various industry professionals. It covers the potential for VC scale business in robotics, high-level problems roboti...
0Topological Problems in Voting
2024-06-14 •
The text discusses the application of topological properties to voting systems, specifically Arrow's Theorem and Chichilnisky Theorem. It explains how these theorems apply to both discrete and continuous preference rankings, and t...
0Modelling Counterfactual Impact
2023-06-06 •
The text discusses the concept of counterfactual impact and how it can be maximized in altruistic fields. It presents mathematical models to show that seeking counterfactual impact implies prioritizing fields with heavy-tailed dis...
0Reflections on a Stanford Journey
2023-06-05 •
The text is a reflection on the author's time at Stanford, rating his social life, health, career, and academics each quarter. He discusses highlights and mistakes from each quarter, as well as his internship experiences and the i...
0Python: Autogenerated Dictionary
2023-05-27 •
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0Python: Single Forward Pass Gradients
2023-04-27 •
The text discusses a trick to compute gradients of a locally smooth function using complex numbers and a simple single f evaluation. It is not very numerically stable but can work without requiring any additional code changes.
0Physics: Special Relativity Speedrun
2021-04-06 •
The post explains the consequences of special relativity, starting with the invariance of physics in inertial frames and the constancy of the speed of light. It discusses symmetries, paradoxes, proper time, action, and energy, and...
0The Value of a Question
2021-03-21 •
The text discusses a prediction contest and the optimal strategy for participants. It presents a series of questions and scenarios to analyze the best approach to maximize rewards in the contest.
0Physics: Topological Fun Facts
2020-11-23 •
The text discusses two fun facts from the author's sophomore Stanford Quantum courses. The first fun fact is about the connection between Maxwell's equations and differential forms, and the second fun fact is about the rotational ...
0Productionizing Productivity
2020-06-14 •
The text discusses the inefficiencies in the hiring process and the lack of accurate measurements of value and productivity in skilled service corporations. It highlights the disproportionate risk tolerance and lack of equity upsi...