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What I've learned about flow fields so far
Noise functions and the tiniest bit of trigonometry can take you a long way towards making art.
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,391 posts.
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Quantum computing bombshells that are not April Fools
For those of you who haven’t seen, there were actually two “bombshell” QC announcements this week. One, from Caltech, including friend-of-the-blog John Preskill, showed how to do quantum faul…
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Statistics, Fast and Slow
Written for and first published in the Financial Times on 13 April 2018. One way to understand China is to look at the statistics. Real income per person has increased nearly tenfold since 1990. Si…
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Implementing Cosine in C from Scratch (2020)
How does the math library's trigonometric function work?
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Everything is correlated (2014–23)
Anthology of sociology, statistical, or psychological papers discussing the observation that all real-world variables have non-zero correlations and the implications for statistical theory such as ‘null hypothesis testing’.
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Pathfinding for Tower Defense
In a Tower Defense game, there are many enemies that are all headed to the same place. In many Tower Defense games, there is a predetermined path, or a small number of paths. In some, such as the classic Desktop Tower Defense [1] , you can place towers anywhere, and they act as obstacles that affect the paths taken by…
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How traffic actually works
Every so often this article makes the rounds and it annoys me. That isn’t how traffic works and the proposed solutions won’t fix anything. Maybe you can eliminate the annoying stop-and-go, but no one gets home any faster. In fact you can prove that you and everyone behind you get home strictly later than if you had…
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The rectangularness of countries
What is the most rectangular country?
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Neural Networks, Manifolds, and Topology
Recently, there’s been a great deal of excitement and interest in deep neural networks because they’ve achieved breakthrough results in areas such as computer vision. 1
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A dumb introduction to z3
Exploring the world of constraint solvers with very simple examples.
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What is an eigenvalue?
An eigenvalue of a square matrix $LATEX A$ is a scalar $latex \lambda$ such that $latex Ax = \lambda x$ for some nonzero vector $latex x$. The vector $latex x$ is an eigenvector of $LATEX A$ and it…
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Linear Algebra: What matrices are
Most high school students in the United States learn about matrices and matrix multiplication, but they often are not taught why matrix multiplication works the way it does. Adding matrices is easy…
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Math for seven-year-olds
As a guest today in my daughter’s second-grade classroom, full of math-enthusiastic seven-and-eight-year-old girls, I led a mathematical investigation of graph coloring, chromatic numbers, ma…
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What sort of maths are LLMs good at?
For the sake of anyone who might read this blog post in the distant future (a month from now, say), let me mention that I am writing it a few days after OpenAI announced that it had solved ten majo…
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The Fastest FizzBuzz Implementation
Benchmarks & Tips for Big Data, Hadoop, AWS, Google Cloud, PostgreSQL, Spark, Python & More...
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A Universe in One Line of Code with 10 PRINT
Generating a Universe with One Line of Code
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GPS and Relativity
People often ask me "What good is Relativity?" It is a commonplace to think of Relativity as an abstract and highly arcane mathematical theory that has no consequences for everyday life. This is in fact far from the truth.
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Finding all regex matches has always been O(n²)
every regex engine that promises linear time breaks that promise the moment you ask for all matches. the problem has been there since the 70s, hiding in the iteration loop.
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Explaining Sex Rate Changes
According to the Post, polls say 28% of US men age 18-30 report not having sex in the last year, almost 3 times as many as a decade ago.
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Breaking RSA with a quantum computer?
A group of Chinese researchers have just published a paper claiming that they can—although they have not yet done so—break 2048-bit RSA. This is something to take seriously. It might not be correct, but it’s not obviously wrong. We have long known from Shor’s algorithm that factoring with a quantum computer is easy…
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An RNG that runs in your brain
Humans are notoriously bad at coming up with random numbers. I wanted to be able to quickly generate “random enough” numbers. I’m not looking for anything that great, I just want to be able to come up with the random digits in half a minute. Some looking around brought me to an old usenet post by George Marsaglia…
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