331
PHP 5.3.3 hangs on numeric value 2.2250738585072011e-308
I stumbled upon a very strange bug in PHP; this statement sends it into an infinite loop:
Most cited
Posts that commenters keep linking to, ranked by how many different people have cited them in Hacker News comments. 494 posts.
332
333
The secret life of NaN
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 ...
334
A mathematical formalization of dimensional analysis (2012)
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…
335
Calculus on Computational Graphs: Backpropagation (2015)
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…
336
337
Impossible Escape?
Can you use math to escape from, what seems like, an impossible prison escape problem based on coins and a chessboard?
338
Logical Induction
MIRI is releasing a paper introducing a new model of deductively limited reasoning: “Logical induction,” authored by Scott Garrabrant, Tsvi Benson-Tilsen,
339
340
Nicholas Polson has authored 258 academic papers in 2026 so far
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.
341
Combinatorial Music Theory (1991)
graph theory, music theory
342
343
Speech to Birdsong Conversion
A blog about signals, programming, music, and other stuff.
344
345
Projective Geometric Algebra Done Right
[This is part one of a two-part series. The second part can be found here: Symmetries in Projective Geometric Algebra .]
346
347
Singular Value Decomposition Part 2: Theorem, Proof, Algorithm
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…
348
The Amazing Power of Word Vectors (2016)
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…
349
Succinct Data Structures: Cramming 80,000 words into a Javascript file
<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.
350
Same Stats, Different Graphs: Datasets with Varied Appearance and Identical Stats
Why graphical representation and visualization are so important to...
351
The two cultures of mathematics and biology
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…
352
The Scientific Case for P≠NP
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…
353
354
355
What is the roundest country?
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…
356
Alpha Compositing
Interactive article explaining alpha compositing concepts.
357
The Dome: A simple violation of determinism in Newtonian mechanics (2005)
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
358
Traveling Salesman: the most misunderstood problem
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...
359
The largest number representable in 64 bits
A rewrite of this blog post with many new insights and updates appeared in Jan 2026
360
Modelling a Basic Income with Python and Monte Carlo Simulation
Basic Income is a popular policy floating around the internet lately. The idea consists of declaring that the government will pay each living adult a fixed amount of money every month - an amount comparable to a minimum wage job. This policy would then replace all current welfare programs - welfare, unemployment …