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What if You Only Invested at Market Peaks?
What happens when you only invest at the peaks of the market by being the world's worst market timer.
Most cited
Posts that commenters keep linking to, ranked by how many different people have cited them in Hacker News comments. 32 posts.
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Nearly All Binary Searches and Mergesorts Are Broken (2006)
Posted by Joshua Bloch, Software EngineerI remember vividly Jon Bentley's first Algorithms lecture at CMU, where he asked all of us incoming Ph.D. ...
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Backblaze Releases the Reed-Solomon Java Library for Free
Today we are releasing our latest open-source project: Backblaze Reed-Solomon Java library for erasure coding. Click for details on how to use and download.
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Zero Knowledge Proofs: An illustrated primer (2014)
One of the best things about modern cryptography is the beautiful terminology. You could start any number of punk bands (or Tumblrs) named after cryptography terms like ‘hard-core predicate&#…
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The Relativistic Rocket
Thanks to Alan R. Wilson for correcting a two-word typo involving GPS satellites. Thanks to Aron Yoffe for suggesting the newtonian comparison. Thanks to Tom Fuchs for suggesting the analogy to the stone thrown upwards. Fuel numbers added by Don Koks, 2004. Updated by Phil Gibbs, 1998. Thanks to Bill Woods for…
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Music theory for nerds
Not music nerds, obviously. I don’t know anything about music. I know there are letters but sometimes the letters have squiggles; I know an octave doubles in pitch; I know you can write a pop song with only four chords. That’s about it. The rest has always seemed completely, utterly arbitrary. Why do we have twelve…
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Don’t invert that matrix (2010)
There is hardly ever a good reason to invert a matrix. What do you do if you need to solve Ax = b where A is an n x n matrix? Isn't the solution A−1 b? Yes, theoretically. But that doesn't mean you need to actually find A−1. Solving the equation Ax = b is
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The Holy Trinity: Logic, Languages, Categories (2011)
The Christian doctrine of trinitarianism states that there is one God that is manifest in three persons, the Father, the Son, and the Holy Spirit, who together form the Holy Trinity. The doctrine…
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Linear algebra for game developers – Part 1 (2009)
When I posted about decals last week, a number of readers commented that they would be interested in posts about linear algebra as it…
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How to assign partial credit on an exam of true-false questions?
Note: the following is a record of some whimsical mathematical thoughts and computations I had after doing some grading. It is likely that the sort of problems discussed here are in fact well studi…
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Experimenting with Post-Quantum Cryptography
Posted by Matt Braithwaite, Software Engineer Quantum computers are a fundamentally different sort of computer that take advantage of aspec...
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Operation Costs in CPU Clock Cycles
Quote: Back in 80s, it was possible to calculate the speed of the program just by looking at assembly. Another Quote: keep in mind that these days compilers ...
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Base-122 – A space efficient alternative to base-64
A space efficient UTF-8 binary-to-text encoding
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Quick, How Might the Alien Spacecraft Work?
How Stephen Wolfram helped with the theory of interstellar travel, communication with aliens and questions from the actors in “Arrival”, the movie.
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Logical Induction
MIRI is releasing a paper introducing a new model of deductively limited reasoning: “Logical induction,” authored by Scott Garrabrant, Tsvi Benson-Tilsen,
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Combinatorial Music Theory (1991)
graph theory, music theory
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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…
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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…
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Fast Fibonacci Algorithms (2015)
Definition: The Fibonacci sequence is defined as \(F(0) = 0\), \(F(1) = 1\), and \(F(n) = F(n-1) + F(n-2)\) for \(n ≥ 2\). So the sequence (starting with \(F(0)\)) is 0, 1, 1, 2, 3, 5, 8, 13, 21, ….
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Image Kernels explained visually
An image kernel is a small matrix used to apply effects like the ones you might find in Photoshop or Gimp, such as blurring, sharpening, outlining or embossing. They're also used in machine learning for 'feature extraction', a technique for determining the most important portions of an image. In this context the…
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Tools for thought: graphical algebra and Fourier analysis
" I think a lot of mathematics is really about how you understand things in your head. […]
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A beginner's guide to Big O notation (2009)
Thoughts on software engineering from Rob Bell
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The rectangularness of countries
What is the most rectangular country?
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How convolutional neural networks see the world
Note: this post was originally written in January 2016. It is now very outdated. Please see this example of how to visualize convnet filters for an up-to-date alternative, or check out chapter 9 of my book "Deep Learning with Python (2nd edition)".
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The Beauty of Roots (2011)
Around 2006, my friend Dan Christensen created a fascinating picture of all the roots of all polynomials of degree ≤ 5 with integer coefficients ranging from -4 to 4: