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If 1+x is 1, how much is 1-x?
► Versión en Español (The title should be "if (= (+ 1 x) 1), how much is (- 1 x)?", but ...) Toy floating point Mathematically, if we...
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Is there such a thing as half a derivative?
The original question was: Another one of those questions of the type “does this make sense”. You have first derivatives and second derivatives. f'(x), f”(x) or sometimes dy/dx …
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A regular expression to check for prime numbers
Regular expressions are extremely powerful. This is something I read at least once or twice every day while reading articles and blogs on the Web.
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MathBox 2: PowerPoint Must Die
PowerPoint must die.
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Gravity's Oldest Puzzles
Every now and then the orbital motion of a body doesn’t match our prediction. And that might lead to interesting discoveries.
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How to implement a spreadsheet
My friend Lindsey Kuper recently remarked on Twitter that spreadsheets were commonly understood to be the most widely used dataflow program...
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12-minute Mandelbrot: fractals on a 50 year old IBM 1401 mainframe
When I found out that the Computer History Museum has a working IBM 1401 computer [1] , I wondered if it could generate the Mandelbrot frac...
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Introduction to Monte Carlo Tree Search
The subject of game AI generally begins with so-called perfect information games. These are turn-based games where the players have no information hidden from each other and there is no element of chance in the game mechanics (such as by rolling dice or drawing cards from a shuffled deck). Tic Tac Toe, Connect 4…
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Path Tracing 3D Fractals
In some ways path tracing is one of the simplest and most intuitive ways to do ray tracing.
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Algorithmic surrealism: A slow-motion guide to high-frequency trading
Please note: Part 1 of this essay appeared in the Feb 2015 edition of Contributoria . It is published and modified here under a...
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Deriving the Reddit Formula
A few things about Reddit’s hot formula have always bothered me. The formula has obviously been a success when it comes to setting the Internet on fire, but I have to wonder:
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Impossible Escape?
Can you use math to escape from, what seems like, an impossible prison escape problem based on coins and a chessboard?
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Google’s S2, geometry on the sphere, cells and Hilbert curve
Update - 05 Dec 2017: Google just announced that it will be commited to the development of a new released version of the S2 library, amazing news, repository can be found here. Google's S2 library is a real treasure, not only due to its capabilities for spatial indexing but also because it is a library that
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Bayesian ranking of items with up and downvotes or 5 star ratings
Evan Miller wrote a great article How Not To Sort By Average Rating . He shows that simple formulas like score = upvotes - downvotes or score = upvotes / (upvotes + downvotes) don’t work. He proposes to use the lower bound of the Wilson score confidence interval. The formula is complicated and somewhat of a hack…
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How did Einstein Think?
John D. Norton Department of History and Philosophy of Science and Center for Philosophy of Science University of Pittsburgh http://www.pitt.edu/~jdnorton This page at http://www.pitt.edu/~jdnorton/Goodies Prepared to accompany cityLIVE! "everything einstein" November 15, 2007, 6:30 pm The New Hazlett Theater…
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A riddle wrapped in a curve
If you’re looking for a nice dose of crypto conspiracy theorizing and want to read a paper by some very knowledgeable cryptographers, I have just the paper for you. Titled “A Riddle Wrapped in an E…
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Is Extended Random a Malicious NSA Plot?
Dual_EC was almost certainly an NSA backdoor. Extended Random is the TLS extension that would have made it practical to exploit. Did NSA plant that one too? A look at the evidence.
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What the Next Generation Needs Is Math, Not Programming
It is the intelligent analysis of information that would be critical in a decade from now.
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Will Our Understanding of Math Deteriorate Over Time?
Scientific American writes about rescuing the enormous theorem (classification of finite simple groups) before the proof vanishes. How can...
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Bayes' Theorem with Lego
Find Bayes' Theorem confusing? Let's break down this famous formula using Lego to help you build up a better intuition for this foundational concept!
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Regression to the mean is the main reason ineffective treatments appear to work
Jump to follow-up “Statistical regression to the mean predicts that patients selected for abnormalcy will, on the average, tend to improve. We argue that most improvements attributed to the p…
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Quasi-Polynomial Algorithm for Graph Isomorphism
Update (Dec. 14): The long wait is over! Here’s Laci’s paper on the arXiv. So far, I’ve read it only deeply enough to note that it contains the following sentence: A group G ≤ S…
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Clifford Algebra: A visual introduction (2014)
Clifford Algebra, a.k.a. Geometric Algebra, is a most extraordinary synergistic confluence of a diverse range of specialized mathematical fields, each with its own methods and formalisms, all of wh…