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Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,851 posts.
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What is ergodicity? (2016)
Why are election polls often inaccurate? Why is racism wrong? Why are your assumptions often mistaken? The answers to all these questions and to many others have a lot to do with the non-ergodicity…
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How to Conquer Tensorphobia
A professor at Stanford once said, If you really want to impress your friends and confound your enemies, you can invoke tensor products… People run in terror from the $ \otimes$ symbol. He was explaining some aspects of multidimensional Fourier transforms, but this comment is only half in jest; people get confused by…
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TreeMaker: Origami Design Software
In 1989, I wrote an article for the magazine Engineering & Science about the state of technical folding, which, even then, seemed to be progressing by leaps and bounds due to an infusion of scientific and mathematical principles. In recounting some of the connections between origami, math, and technology, I wrote:
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Game Theory Patterns at Work
Foundations: Games, Rationality, and Traps In organizations, strategies and execution are interdependent. Outcomes depend not just on what you do, but on what others do, and what they expect you to…
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Failing to Understand the Exponential, Again
Posts and writings by Julian Schrittwieser
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Complex numbers have never been so intuitive to me
Imaginary numbers always confused me. Like understanding e, most explanations fell into one of two categories: Gee, what a great way to encourage math in…
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Floats Are Weird
Compute this limit more accurately with one weird trick!
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Chess engines do weird stuff
Since AlphaZero, lc0-style chess engines have been trained with RL. Specifically, you have the engine (search + model) play itself a bunch of times, and train the model to predict the outcome of the game.
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Double Descent in Human Learning
The uncanny resemblance between double descent and a 50 year old theory from psychology
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Topics in Core Mathematics at Graterford Prison
Topics in Core Mathematics sounds like the blandest possible math class. The course title is meant to convey the one important aspect of the class for many students: this class fulfills the core math requirement for the College of Liberal Arts and Sciences. Box checked. However, the advantage of blandness is that it…
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Learn you Galois fields for great good (2023)
This is the introduction to a series on Abstract Algebra. In particular, our focus will be on Galois Fields (also known as Finite Fields) and their applications in Computer Science. This is a project I've been excited about for many years now, but have been too busy to dedicate the adequate effort to meet my…
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The Essence of Datalog (2018)
Mistral Contrastin's thought bubble, blog, and personal revelations.
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Beautiful Abelian Sandpiles
I can't remember where I first saw them, but ever since, I have been unable to forget them: abelian sandpiles. I'm far from the only one . They're remarkably simple, yet produce lovely symmetric patterns. I loved them so much that I adorned the title banner of this blog with an animation of an abelian sandpile. But…
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Quantum Computing for the Curious
Presented in an experimental mnemonic medium that makes it almost effortless to remember what you read
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Google Earth Fractals
The following is a "photographic" gallery of fractal patterns found while exploring the planet with Google Earth. Each is provided with a KMZ file so the reader can explore the region for themselves. Readers are encouraged to submit their own discoveries for inclusion, credits will be included. Besides being examples…
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Modern SAT solvers: fast, neat and underused – part 2
The previous post in this series was a quick introduction to the world of SAT and SAT solvers. In this post, we will convert a harder real-world problem, namely _master-key system_, into SAT and explore some of the more advanced techniques used to efficiently convert problems to SAT.
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10-year-old problem in theoretical computer science falls
Interactive proofs — mathematical games that underlie much modern cryptography — work even if players try to use quantum information to cheat.
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Optimizing things in the USSR (2016)
A review of Red Plenty, by Francis Spufford
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All Horses Are the Same Color
Problem: Show that all horses are of the same color. “Solution”: We will show, by induction, that for any set of $ n$ horses, every horse in that set has the same color. Suppose $ n=1$, this is obviously true. Now suppose for all sets of $ n$ horses, every horse in the set has the same color. Consider any set $ H$ of…
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P = NP Proofs: Advice to claimers
Advice to claimers The Claimers The Claimers are a gang on the hit AMC television series The Walking Dead. They are the main antagonists in the second half of the zombie-apocalypse show’s Sea…
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Why does F = ma?
By Michael Nielsen, November 23, 2019
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Sunset Geometry (2016)
Robert Vanderbei has written a beautiful series of articles and talks about a method for finding the radius of the earth based on a single photograph of a sunset over a large, calm lake.
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Reconciliation is a knapsack problem
Yesterday, we announced adding AI to our recon engine. Today, we're underscoring how reconciliation is a pain point by delving into the math.