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Formally Modeling Dreidel, the Sequel
2 model 2 dreidel
New
The latest blog posts to take off on Hacker News. 2,851 posts.
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Maximum likelihood estimation and loss functions
When I started learning about loss functions, I could always understand the intuition behind them. For example, the mean squared error (MSE) for regression seemed logical—penalizing large deviations from the ground-truth makes sense. But one thing always bothered me: I could never come up with those loss functions on…
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A visual proof that a^2 – b^2 = (a + b)(a – b)
A visual proof that a2 – b2 = (a + b)(a – b). Sophie Germain wrote, “It has been said that algebra is but written geometry and geometry is but diagrammatic algebra.”
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Hacking physics from the back of a napkin (2020)
February 24, 2020. The computational power of a humble napkin is awesome. I discuss three napkin algorithms — dimensional analysis, Fermi estimates, and random walks — and use them to figure out why rain falls, the length of the E. coli genome, and the mass of a proton, among other things. These examples suggest a…
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Fermat's Last Theorem – how it’s going
So I’m two months into trying to teach a proof of Fermat’s Last Theorem to a computer. We already have one interesting story, which I felt was worth sharing.
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Make a "Magic Eye" image using Excel
I’ve been on a weird kick lately making images using Excel. [Here’s one post. I hope to post more soon.] If you add a background color to each cell in a spreadsheet and resize the cell …
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Derivative at a Discontinuity
Alok Singh's Blog
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Square roots and maxima
A brief numerical and graphical check on a 3Blue1Brown video.
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Accidentally writing a SAT solver
where my words occasionally escape /dev/null
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Fine, I'll Play With Skiplists
Follow me on Bluesky! A Log-Structured Merge tree, or LSM, is a popular data structure for storage engines. It’s what is used by RocksDB, which is sort of...
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The Art and Mathematics of Genji-Ko
You might think it’s unlikely for any interesting mathematics to arise from incense appreciation, but that’s only because you’re unfamiliar with the peculiar character of Muromachi (室町) era Japanese nobles. There has never been a group of people, in any time or place, who were so driven to display their sophistication…
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The Deceptively Asymmetric Unit Sphere
The deficiencies of the Unit Sphere and an exploration of Lie groups.
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SQL, Homomorphisms and Constraint Satisfaction Problems
Database queries are a pretty surprisingly powerful tool that can solve seemingly intractable problems.
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AlphaProof's Greatest Hits
Here I’ll try to explain the coolest ideas in each of AlphaProof’s IMO 2024 solutions. AlphaProof produces proofs in Lean, and each Lean proof is composed of a series of tactics. So I’ll pick out the tactics that correspond to these ideas in the proofs for problems 1, 2 and 6 (the three problems that AlphaProof…
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Nash equilibria in Ballmer's binary-search interview game
Yesterday John Graham-Cumming posted about “Steve Ballmer’s incorrect binary search interview question,” and in the Hacker News discussion, among the predictable “interview culture is flawed!!” complaints, there was some discussion of whether binary search was even the right way to solve Ballmer’s puzzle. Here’s a…
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An alternative construction of Shannon entropy
The underpinning of information theory is Shannon’s formula for the entropy H of a discrete probability distribution P. Derived in 1948 in the paper “A mathematical theory of communication”, this is given by \[ H[P] = -\sum_{i=1}^N p_i \log p_i \] where \( p_i = p(x_i) \) is the probability of sampling \( x_i \) from…
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How Chordcat works – a chord naming algorithm
chordcat is a chord-naming application and a pet project of mine. It is written in C++ and SFML.
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Diffusion models are evolutionary algorithms
Authors: Yanbo Zhang, Benedikt Hartl, Hananel Hazan, Michael Levin
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My Notes on Apple Math Notes
Apple's effort to improve the UX of math.
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Perceptually lossless (talking head) video compression at 22kbit/s
Achieving extreme video compression rates using the LivePortrait model for talking head videos.
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Alonzo Church: Architect of computer intelligence
The man who gave us the solution to the Entscheidungsproblem
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Adventures in Probability
I hope everyone had a good weekend. I went on a hike. It was great. Statistics One of my great school regrets, next to “taking three years of business...
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A Hamiltonian Circuit for Rubik's Cube
At last, the Hamiltonian circuit problem for Rubik's Cube has a solution! To be a little more mathematically precise, a Hamiltonian circuit of the quarter-turn metric Cayley graph for the Rubik's Cube group has been found.