Posts that commenters keep linking to, ranked by how many different people have cited them in Hacker News comments. 494 posts.
Last Thursday night at Oredev, after the sessions, was "Birds of a Feather" - a sort of mini-unconference. Anyone could write up a topic on the whiteboard; interested individuals added their names, and each group got allocated a room to chat about the topic. I joined the "Spatial Indexing" group, and we spent a…
There is hardly ever a good reason to invert a matrix. What do you do if you need to solve Ax = b where A is an n x n matrix? Isn't the solution A−1 b? Yes, theoretically. But that doesn't mean you need to actually find A−1. Solving the equation Ax = b is
The Christian doctrine of trinitarianism states that there is one God that is manifest in three persons, the Father, the Son, and the Holy Spirit, who together form the Holy Trinity. The doctrine…
In terms of unreasonable effectiveness, the transformation to continuation-passing style (CPS) ranks with the Y combinator .
This article attempts to outline, in informal terms, a new theory of combinators, related to the theory of Combinatory Logic pioneered by Moses Schonfinkel, Haskell Curry, and others in the 1930s. Although not essential, an understanding of the classical theory of combinators may be helpful (see the links at the…
I had to get there eventually. I had a blog post called “I Wrote a Fast Hashtable” and another blog post called “I Wrote a Faster Hashtable.” Now I finally wrote the fastest…
By Jonas Kristoffer Lindeløv ( blog , profile ). Last updated: 28 June, 2019 (See changelog ). Check out the Python version and the Twitter summary .
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A Bloom filter is a data structure designed to tell you, rapidly and memory-efficiently, whether an element is present in a set.
Almost all mathematical questions one could have about Wordle are settled by now. I summarize here what is known so far.
Stephen Wolfram explores minimal models and their visualizations, aiming to explain the underneath functionality of neural nets and ultimately machine learning.
When I posted about decals last week, a number of readers commented that they would be interested in posts about linear algebra as it…
The following table shows diagrams of identity, the booleans, some standard combinators, some Church numerals, the predecessor function on Church numerals, and Omega. term definition diagram alternative I/1 λx.x K/true λx.λy.x false/0 λx.λy.y S λx.λy.λz.(x z)(y z) Y λf.(λx.x x)(λx.f(x x)) 2 λf.λx.f(f x) 3 λf.λx.f(f(f…
Note: the following is a record of some whimsical mathematical thoughts and computations I had after doing some grading. It is likely that the sort of problems discussed here are in fact well studi…
Posted by Matt Braithwaite, Software Engineer Quantum computers are a fundamentally different sort of computer that take advantage of aspec...
I recently came up with what I think is an intuitive way to explain Bayes’ Theorem. I searched in google for a while and could not find any article that explains it in this particular way.
Blog of Raph Levien.
The following pictures show $n$ unit squares packed inside the smallest known square (of side length $s$). If a pictured packing has multiple numbers in its label above, the picture represents the largest; each smaller is represented by removing any square. For the $n ≤ 324$ not pictured, the trivial packing (with no…
The Riemann zeta function $latex {\zeta(s)}&fg=000000$ is defined in the region $latex {\hbox{Re}(s)>1}&fg=000000$ by the absolutely convergent series $latex \displaystyle \zeta(s) = \su…
Algorithms, circle mazes, hex grids, masking, weaving, braiding, 3D and 4D grids, spheres, and more!
Continuing the theme of alternative approaches to teaching calculus, I take the liberty of posting a letter sent by Donald Knuth to to the Notices of the American Mathematical Society in March, 199…
For over six years now, I've been studying mathematics on my own in my spare time - working my way through books, exercises, and online courses. In this post I'll share what books and resources I've worked through and recommend and also tips for anyone who wants to go on a similar adventure.
Markov chains, named after Andrey Markov , are mathematical systems that hop from one "state" (a situation or set of values) to another. For example, if you made a Markov chain model of a baby's behavior, you might include "playing," "eating", "sleeping," and "crying" as states, which together with other behaviors…
We are all having to keep revising upwards our assessments of the mathematical capabilities of large language models. I have just made a fairly large revision as a result of ChatGPT 5.5 Pro, to whi…
