The latest blog posts to take off on Hacker News. 2,393 posts.
For those who aren’t regular readers: as a followup to this post, there are four posts detailing the basic four methods of proof, with intentions to detail some more advanced proof techniques in the future. You can find them on this blog’s primers page. Do you really want to get better at mathematics? Remember when…
This article is a short guide to implementing an algorithm from a scientific paper. I have implemented many complex algorithms from books and scientific publications, and this article sums up what I have learned while searching, reading, coding and debugging. This is obviously limited to publications in domains…
A tale of numbers that like to turn: a different look at complex numbers and the strange things they do.
It is a wonder that we have yet to officially write about probability theory on this blog. Probability theory underlies a huge portion of artificial intelligence, machine learning, and statistics, and a number of our future posts will rely on the ideas and terminology we lay out in this post. Our first formal theory…
Here's what we can do with today's computing power (using publicly available data and the processing power of my own personal computer; I'm not relying on access to corporate computing power):
This article was originally published in the Russian functional programming journal http://fprog.ru/ and this translation was intended to be published in Peter Seibel’s http://codequarterly.com/ journal, but as Peter eventually decided not to proceed with the journal, I am publishing it on my personal space.
On 13 June 1944, a week after the allied invasion of Normandy, a loud buzzing sound rattled through the skies of battle-worn London. The source of the sound was a newly developed German instrument …
It’s often said that the Age of Information began on August 17, 1964 with the publication of Cooley and Tukey’s paper, “An Algorithm for the Machine Calculation of Complex Fourier…
The programming profession is blessed with a number of gifted essayists. Today I will pick on three of my favorites — Eric Raymond, Paul Graham, and Steve Yegge — because they all seem to disagree about why (and whether) mathematics is relevant to the practicing programmer. Their attitudes might be summarized as:
This weekend I decided to play around a bit with genetic programming and put evolution to the test, the test of fine art 🙂
Presentation-quality math with Three.js and WebGL.
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...
You may feel like you've seen this before. If you have, skip to the end where I talk about a formula, and discuss the relevance to parameters in computer hashing algorithms. In particular, I'm going to talk about how large hash spaces should be to avoid collisions with a given level of probability. If there are just…
Mathematics, applications of mathematics to life in general, and my life as a mathematician.
The MIT Challenge My friend Scott Young recently finished an astounding feat: he completed all 33 courses in MIT’s fabled computer science curriculum, from Linear ... Read more
Experimenting with the "divisibility" of complex numbers, I stumbled across this thingy. It looks like a fractal. Although the formula does not do any iterations. It reminds me of something. But I dont know what. Doing a Google image search brings up a couple of galaxies :) This image shows the region from (-1/-1) to…
The following is a "photographic" gallery of fractal patterns found while exploring the planet with Google Earth. Each is provided with a KMZ file so the reader can explore the region for themselves. Readers are encouraged to submit their own discoveries for inclusion, credits will be included. Besides being examples…
Conway's Game of Life, emulated in Conway's Game of Life: The life simulator used is Golly which has a built-in script to generate these metapixel grids (select a pattern, and choose "metafier.py" from the scripts list). Outer Totalistic Cellular Automata Meta-Pixel: The metacell uses a period 184 tractor beam, which…
A continuous version of Conway's Life, using floating point values instead of integers: supports many interesting phenomena such as gliders that can travel in any direction, rotating pairs of gliders, wickstretchers and the appearance of elastic tension in the 'cords' that join the blobs. Slides showing how the rule…
