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The most popular blog posts about math & algorithms on Hacker News. 2,394 posts.
Noether's theorem is an amazing result which lets physicists get conserved quantities from symmetries of the laws of nature. Time translation symmetry gives conservation of energy; space translation symmetry gives conservation of momentum; rotation symmetry gives conservation of angular momentum, and so on.
The idea of "statistical significance" has been a basic concept in introductory statistics courses for decades. If you spend any time lookin...
You can construct the Rule 110 cellular automaton in JPEG XL.
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Today I'd like to share some math connecting ideas from information theory, algebra, and topology. It's all in a new paper I've recently uploaded to the arXiv (https://arxiv.org/abs/2107.09581), which describes a correspondence between Shannon entropy and functions on topological simplices that obey a version of the…
I recently attended the Matthias Felleisen Half-Time Show, a symposium held in Boston on 3rd November in celebration of Matthias’s 60th birthday. I was honoured to be able to give a talk ther…
The James-Stein Estimator with unequal variances
Recently I've been discussing the details of measuring the size of the Earth by watching a shadow descending a wall at sunrise, or ascending at sunset. The sums are easy enough if you do it at either Equinox, and at the Equator, and you can read about it here:
Mazes are typically constructed on regular grids: square, triangular, hexagonal, etc. But what if you generate a maze on top of a Penrose tiling, which is guaranteed to be irregular? (It is an aperiodic tiling .) The resulting mazes have a very characteristic appearance: they are filled with circles and stars, but the…
On the relationship between mixed-radix bases and array indexing
Intro Fuzzy search algorithms (also known as similarity search algorithms) are a basis of spell-checkers and full-fledged search engines lik...
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 was asked (again) today to explain why integer division in Python returns the floor of the result instead of truncating towards zero like...
Recently, somebody shared on Twitter a new proof of the irrationality of √2. Its claimed advantage is that “it requires no knowledge of mathematics above the definition of what it means for a number to be irrational, and can be written almost in one line.” These claims are dubious: the usual proof, which I’ve…
Reflections on a Wall Street legend.
Last Sunday the eminent British historian of the twentieth century, Richard Evans, tweeted the following: Let’s remember we use Arabic numerals – 1, 2, 3 etc. Try dividing MCMLXVI by XX…
I my previous blog post, I documented how one might proceed to compute the number of digits of an integer quickly. E.g., given the integer 999, you want 3 but given the integer 1000, you want 4. It is effectively the integer logarithm in base 10. On computers, you can quickly compute the integer logarithm … Continue…
An intuitive explanation of the James-Stein estimator.
A blog about computers, functional languages, Lisp, and Scheme.
An overview of my work on optimizing phone keyboard layouts for Swype and T9. There's some interesting history here as well as a novel simulation-based approach to keyboard optimization.
In almost every computation a great variety of arrangements for the succession of the processes is possible, and various considerations must influence the selection amongst them for the purposes of a Calculating Engine. One essential object is to choose that arrangement which shall tend to reduce to a minimum the time…
[By prior agreement, this post will be cross-posted on Microsoft’s Q# blog, even though it has nothing to do with the Q# programming language. It does, however, contain many examples th…
While reading through the fantastic book *[The Lost Art of Logarithms](https://www.lostartoflogarithms.com/)* by [Charles Petzold](https://www.charlespetzold.com/) I was nerd-sniped by a [simple method](https://www.lostartoflogarithms.com/chapter04/) of estimating the logarithm of any number base 10. According to the…
Building an intuition for the mathematics behind the "TLA" in "TLA+"
<img src="http://stevehanov.ca/blog/images/acer.jpg"/> If you have a web site with a search function, you will rapidly realize that most mortals are terrible typists. Many searches contain mispelled words, and users will expect these searches to magically work. This magic is often done using levenshtein distance. In…
This is our most recent work, started and led by Aleksey Charapko . (This is a joint post with him.) You can get the paper at arxiv.org . Th...
