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New
The latest blog posts to take off on Hacker News. 151 posts.
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How much math you need for programming (2014)
Whenever I wanted to learn Algorithms, Mathematics used there somehow seemed to be an obstacle. I admit my Math is not that good but it ain’t that bad either but this “ain’t bad&#…
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Learning to Play the Chaos Game
I, Thomasina Coverly, have found a truly wonderful method whereby all the forms of nature must give up their numerical secrets and draw themselves through number alone…
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Plotting patterns in music with a fantasy record player
A blog about signals, programming, music, and other stuff.
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How to Think about Correlation?
I am an economist at the Federal Trade Commission with a very basic statistics question, one that I have put to several fairly high-powered econometricians, and to which no one has had a satisfying answer.
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Scaling Down Deep Learning
A blog by Sam Greydanus
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Interval Tree Clocks
Notes on Interval Tree Clocks
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Is Probability Real?
Today, I want to address an issue with statements involving chance. To demonstrate, let’s first consider a statement that doesn’t involve chance:
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How Rainbow Tables Work
I found the creator of Rainbow Table's paper, aimed at cryptanalysts, was pretty inaccessible considering the simplicity and elegance of Rainbow Tables, so this is an overview of it for a layman.
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Convolution Is Fancy Multiplication
Like making engineering students squirm? Have them explain convolution and (if you're barbarous) the convolution theorem. They'll mutter something about…
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Test for Divisibility by 13
How to manually test whether a large number is divisible by 7, 11, and 13 all at the same time.
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All Hail Geometric Algebra
Rotate a cube by 90 degrees around the \(x\)-axis, then rotate it by 90 degrees around the \(z\)-axis. This is equivalent to a single rotation. What is the axis and angle of this single rotation?
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The Most Common Errors in Undergraduate Mathematics (2009)
This page describes the errors that I have seen most frequently in undergraduate mathematics, the likely causes of those errors, and their remedies.
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Ramanujan's Easiest Formula
A while ago I decided to figure out how to prove one of Ramanujan’s formulas. I feel this is the sort of thing every mathematician should try at least once. I picked the easiest one I could f…
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What Gödel Discovered
In 1931, a 25-year-old Kurt Gödel wrote a proof that turned mathematics upside down. The implication was so astounding, and his proof so elegant that it was...kind of funny. I wanted to share his discovery with you. Fair warning though, I’m not a mathematician; I’m a programmer. This means my understanding is…
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DARPA’s 23 Challenge Questions
Research in Scientific Computing in Undergraduate Education2020117 points30 commentsMath & Algorithms details
DARPA challenges The Defense Advanced Research Projects Agency (DARPA) has issued 23 mathematical challenges. DARPA says the solution of any one of these challenges would have the effect of “…
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An Interactive Introduction to Fourier Transforms
Fourier transforms are a tool used in a whole bunch of different things. This is a explanation of what a Fourier transform does, and some different ways it can be useful.
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A Pretty Good Mathematical Model of Perfectionism
I struggle with perfectionism. Well, not so much “struggle with” — I’m f*cking great at it. It comes naturally. There are some upsides, but perfectionism is also associated …
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Introduction to Linear Algebra for Applied Machine Learning with Python
Linear algebra is to machine learning as flour to bakery: every machine learning model is based in linear algebra, as every cake is based in flour . It is not the only ingredient, of course. Machine learning models need vector calculus, probability, and optimization, as cakes need sugar, eggs, and butter. Applied…
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Two Workers Are Quadratically Better Than One
For latency, anyway. A common architecture pattern is the “task queue”: tasks enter an ordered queue, workers pop tasks and process them. This pattern is used everywhere from distributed systems to thread pools. It applies just as well to human systems, like waiting in line at a supermarket or a bank. Task queues are…
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The polls messed up
To continue our post-voting, pre-vote-counting assessment (see also here and here ), I want to separate two issues which can get conflated: 1. Problems with poll-based election forecasts.
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Fast Inverse Square Root
The famous fast inverse square root is some mysterious code not written by programming legend John Carmack to calculate a fast approximation of $1/\sqrt{x}$:
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Simple Image Vectorization
This is an example of an image vectorization algorithm. It shows the bilinear interpolation, polynomial approximation, differential analysis, and iterative algorithms working together to solve a practical problem
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The Complete Idiot’s Guide to the Independence of the Continuum Hypothesis
A global pandemic, apocalyptic fires, and the possible descent of the US into violent anarchy three days from now can do strange things to the soul. Bertrand Russell—and if he’d done no…
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The Remarkable Number 1/89 (2004)
The Fibonacci series is a famous example of an object with a simple mathematical description, but a nearly inexhaustable list of bizarre and complicated properties. Originally, the series was described by Fibonacci in the 15th century in connection with the following problem:
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Reverse-engineering the problematic tail behavior of Fivethirtyeight forecast
We’ve been writing a bit about some odd tail behavior in the Fivethirtyeight election forecast, for example that it was giving Joe Biden a 3% chance of winning Alabama (which seemed high), it was displaying Trump winning California as in “the range of scenarios our model thinks is possible” (which didn’t seem right)…