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A dumb introduction to z3
Exploring the world of constraint solvers with very simple examples.
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 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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Bijou64: A variable-length integer encoding
An accidentally fast variable-length integer encoding
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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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Tog's Paradox
Tog’s Paradox (also known as The Complexity Paradox or Tog’s ComplexityParadox) is an observation that products aiming to simplify a task for users tend toinspire new, more complex tasks. It’s one ...
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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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Gaussian Processes, not quite for dummies
Before diving inFor a long time, I recall having this vague impression about Gaussian Processes (GPs) being able to magically define probability distributions over sets of functions, yet I procrastinated reading up about them for many many moons. However, as always, I’d like to think that this is not just due to my…
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Why squared error? (2014)
its computational convenience • connections to the Gaussian distribution • differentiability and basis independence • why not squared error • absolute-error methods
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Using spaced repetition systems to see through a piece of mathematics
By Michael Nielsen, January 2019
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Why Aren't We Sieve-Ing?
Long-time readers of this blog will know that I have mixed feelings about caches. One on hand, caching is critical to the performance of systems at every layer, from CPUs to storage to whole distributed architectures. On the other hand, caching being this critical means that designers need to carefully consider what…
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Analysis of bank PIN numbers
Is your PIN number too predictable? Detailed analysis on PIN number databases.