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How Useful Is Tufte for Making Maps? (2007)
Edward Tufte’s The Visual Display of Quantitative Information (1998, 2nd edition 2001) is a classic book, arguably his best, and certainly a key text in the field of information graphics (whi…
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
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What is static program analysis?
The halting problem asks whether the execution of a specific program for a given input will terminate.
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Who Expected That? Extreme close-ups create a Klein Bottle.
Suppose you go around taking extremely close-up black-and-white pictures of randomly chosen natural and unnatural objects (rocks, trees, streams, buildings, etc.). What do they look like? Well, eac…
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Solving a “Layton Puzzle” with Prolog
I have a lot in the works for the this month's Logic for Programmers release. Among other things, I'm completely rewriting the chapter on Logic Programming...
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Top mathematical achievements of the last 5ish years, maybe
I have recently been going through my book Maths 1001 making updates for a forthcoming foreign edition (of which more in future). So I have been looking over mathematical developments since approxi…
2437
Proof of the Singular Value Decomposition
The existence claim for the singular value decomposition (SVD) is quite strong: “Every matrix is diagonal, provided one uses the proper bases for the domain and range spaces” (Trefethen & Bau III, 1997) . MIT professor Gilbert Strang has a wonderful lecture on the SVD, and he includes an existence proof for the SVD…
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Conway's Game of Life for curved surfaces (2012)
Conway’s Game of Life is one of the most popular and iconic cellular automata. It is so famous that googling it loads up a working simulation right in your browser! The rules for the Game o…
2439
Break a dozen secret keys, get a million more for free
[An in-depth blog post by Daniel J. Bernstein, crossposted between the ECRYPT blog and the cr.yp.to blog .]
2440
Faster pathfinding using Jump Point Search
This is the final article in my three-part look at symmetry reduction algorithms for speeding up pathfinding on uniform-cost grid maps. Recapping the story so far: Part one introduces the notion of…
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Occluding Contour Breakthroughs, Part 1: A Surprisingly Hard Problem
Exact line rendering of smooth surfaces is harder than anyone would think
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Special Relativity and Middle-Earth
This post is an unofficial sequel to one of my first blog posts from 2007, which was entitled “Quantum mechanics and Tomb Raider”. One of the oldest and most famous allegories is Plato&…
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The Discovery of Statistical Regression
We explore the hotly contested history of the crowning jewel of statistics.
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Mathematics Distillation Challenge – Equational Theories
Mathematical research traditionally involves a small number of professional mathematicians working closely on difficult problems. However, I have long believed that there is a complementary way to …
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Tag Systems
I've tried to write a blog post on tag systems for years now. Literally years, I think I first started drafting it out in 2018 or so? The problem is that...
2450
Cracking random number generators (xoroshiro128+)
In software, we generate random numbers by calling a function called a "random number generator". Such functions have hidden states, so that repeated calls to the function generate new numbers that appear random. If you know this state, you can predict all future outcomes of the random number generators. O'Neill, a…
2451
Bell inequality violation finally done right
A few weeks ago, Hensen et al., of the Delft University of Technology and Barcelona, Spain, put out a paper reporting the first experiment that violates the Bell inequality in a way that closes off…
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Making all your integers positive with zigzag encoding
You sometimes feel the need to make all of your integers positive, without losing any information. That is, you want to map all of your integers from 'signed' integers (e.g., -1, 1, 3, -3) to 'unsigned integers' (e.g., 3,2,6,7). This could be useful if you have a fast function to compress integers that fails to ……
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Knuth-Morris-Pratt string-searching algorithm: DFA-less version
You see, there are two memory accesses per one character of the input string (at average). Hence, the total number of all memory accesses can be len*2 at worst.
2455
TLA+ Action Properties
There’s not a whole lot on TLA+ technique out there: all the resources are either introductions or case studies. Good for people starting out, bad for people past that. I think we need to write more intermediate-level stuff, what Ben Kuhn calls Blub studies. Here’s an attempt at that. Most TLA+ properties are…
2456
Iterated Log Coding
I've created a new format for encoding real numbers on computers. I'm proud of it! Let's dive in.
2457
Categories for Programmers: The Yoneda Lemma
This is part 15 of Categories for Programmers. Previously: Representable Functors. See the Table of Contents. Most constructions in category theory are generalizations of results from other more sp…
2458
Algorithm efficiency comes from problem information
This is a high level post about algorithms (especially mathematical, scientific, and data analysis algorithms) which I hope can help people who are not researchers or numerical software developers better understand how to choose and evaluate algorithms. When scientists and programmers think about efficiency of…
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