Posts that commenters keep linking to, ranked by how many different people have cited them in Hacker News comments. 417 posts.
Most commodity processors support single-precision IEEE 754 floating-point numbers. Though they are ubiquitous, they are often misunderstood. One of my readers left a comment suggesting that picking an integer in [0,232) at random and dividing it by 232, was equivalent to picking a number at random in [0,1). I am not…
How do QR codes work? How much is it possible to distort one and still have it readable?
(Updated 2020-09-06 with pointers to related work and a bit more explanation)
A space efficient UTF-8 binary-to-text encoding
How Stephen Wolfram helped with the theory of interstellar travel, communication with aliens and questions from the actors in “Arrival”, the movie.
I stumbled upon a very strange bug in PHP; this statement sends it into an infinite loop:
The floating point standard defines a special value called Not-a-Number (NaN) which is used to represent, well, values that aren’t numbers. Double precision ...
Mathematicians study a variety of different mathematical structures, but perhaps the structures that are most commonly associated with mathematics are the number systems, such as the integers $late…
Backpropagation is the key algorithm that makes training deep models computationally tractable. For modern neural networks, it can make training with gradient descent as much as ten million times faster, relative to a naive implementation. That’s the difference between a model taking a week to train and taking 200,000…
Can you use math to escape from, what seems like, an impossible prison escape problem based on coins and a chessboard?
Nicholas Polson has, by my count using his SSRN page, already written 258 working papers in 2026 alone. He’s already written (or at least published to SSRN), six papers today, August 26, 2026.
graph theory, music theory
A blog about signals, programming, music, and other stuff.
[This is part one of a two-part series. The second part can be found here: Symmetries in Projective Geometric Algebra .]
I’m just going to jump right into the definitions and rigor, so if you haven’t read the previous post motivating the singular value decomposition, go back and do that first. This post will be theorem, proof, algorithm, data. The data set we test on is a thousand-story CNN news data set. All of the data, code, and…
For today’s post, I’ve drawn material not just from one paper, but from five! The subject matter is ‘word2vec’ – the work of Mikolov et al. at Google on efficient vect…
<img src="http://zwibbler.com/shared/1024.png"/> jQuery creator John Resig needs a little help storing lists of words in his side project. Let's go overkill and explore a little known branch of computer science called Succinct Data Structures.
I’m a (50%) professor of mathematics and (50%) professor of molecular & cell biology at UC Berkeley. There have been plenty of days when I have spent the working hours with biologists and…
Out there in the wider world—OK, OK, among Luboš Motl, and a few others who comment on this blog—there appears to be a widespread opinion that P≠NP is just “a fashionable dogma of…
We can define roundness in many ways. For example, as you may know, the circle is the shape that given a fixed perimeter maximizes the area. This definition has many problems. One of the problems is that countries generally have chaotic perimeters (also known as borders), so they tend to be much longer than they seem…
Interactive article explaining alpha compositing concepts.
John D. Norton Department of History and Philosophy of Science, University of Pittsburgh Pittsburgh PA 15260. Homepage: www.pitt.edu/~jdnorton This page is available at www.pitt.edu/~jdnorton/goodies
Whenever people start talking about NP-Complete problems, or even NP problems, one of the first examples they reach for is the classic Traveling Salesperson Problem. TSP makes sense because it int...
