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Introduction to A* (1997)
Movement for a single object seems easy. Pathfinding is complex. Why bother with pathfinding? Consider the following situation:
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Sin and Cos: The Programmer's Pals
In this article I shall discuss several game programming techniques, all revolving around a central theme: the sine and cosine functions. This article will explain sine, cosine, vectors, atan2, and some useful special effects such as how to make homing missiles and how bitmap rotation works. I shall start with the…
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Jupyter, Mathematica, and the Future of the Research Paper
Economist. Policy Entrepreneur. Geek. Co-recipient of the 2018 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. University Professor at NYU. Focused on urbanization; cooperation at scale of millions and billions; science; technology; economic development; long-term growth; code as language.
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The Mathematics of 2048: Optimal Play with Markov Decision Processes
Finding provably optimal strategies for 2048 using Markov Decision Processes
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The Wavefunction Collapse Algorithm Explained
The Wavefunction Collapse Algorithm teaches your computer how to riff. The algorithm takes in an archetypical input, and produces procedurally-generated outputs that look like it.
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Probabilistic Programming and Bayesian Methods for Hackers (2013)
Bayesian Methods for Hackers : An intro to Bayesian methods + probabilistic programming with a computation/understanding-first, mathematics-second point of view.
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Visualizing quaternions: An explorable video series
Explaining how quaternions, a four-dimensional number system, describe 3d rotation.
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For mathematicians, = does not mean equality
Every now and then I hear some ridiculous things about the equals symbol. Some large subset of programmers—perhaps related to functional programmers, perhaps not—seem to think that = should only and ever mean “equality in the mathematical sense.” The argument usually goes, Functional programming gives us back that…
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One model to learn them all
One model to learn them all Kaiser et al., arXiv 2017 You almost certainly have an abstract conception of a banana in your head. Suppose you ask me if I’d like anything to eat. I can say the word ‘…
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A puzzle that tiles infinitely across both sides, based on the Klein Bottle
Have you ever done a puzzle that has no beginning or end? Where you don’t know up from down? Get lost in the infinite galaxy puzzle. The infinity puzzles™ are a new type of jigsaw puzzle insp…
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Intuitive Understanding of Euler’s Formula
Euler's identity seems baffling: It emerges from a more general formula: Yowza -- we're relating an imaginary exponent to sine and cosine! And somehow…
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Introduction to Calculus with Derivatives
Aditya Bhargava's personal blog.
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A Global Optimization Algorithm Worth Using
Here is a common problem: you have some machine learning algorithm you want to use but it has these damn hyperparameters . These are number...
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Statistics, Fast and Slow
Written for and first published in the Financial Times on 13 April 2018. One way to understand China is to look at the statistics. Real income per person has increased nearly tenfold since 1990. Si…
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Direct Coupling of the Higgs Boson to the Top Quark Observed
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Generating random points inside a sphere
Visualization of different methods of generating random points inside a sphere
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Mathematics I Use (2012)
An explanation of the forms of mathematics I use on a daily basis as a working software engineer.
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The hacker's guide to uncertainty estimates
I made a New Year's resolution: every plot I make during 2018 will contain uncertainty estimates. Nine months in and I have learned a lot, so I put together a summary of some of the most useful methods.
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A collection of things that are Turing-complete by accident (2013)
A list of things that were not supposed to be Turing-complete, but are.
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Lost in Math
Sabine Hossenfelder’s new book Lost in Math should be starting to appear in bookstores around now. It’s very good and you should get a copy. I hope that the book will receive a lot of a…
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Any positive number can be written as a sum of three palindromes
This incredible mathematical hat-trick is based on the paper Every positive integer is a sum of three palindromes by Javier Cilleruelo, Florian Luca and Lewis Baxter.
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Proof-Of-Work is a Decentralized Clock
This is an explanation of the key function on Proof-of-Work in the Bitcoin blockchain. It focuses on the one feature of Proof-of-Work that is essential and shows that other features often talked about such as security are secondary side-effects, useful, but not essential. This explanation rests on illustrating a few…
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Prediction Markets: When Do They Work?
Epistemic Status: Resident Expert I’m a little late on this, which was an old promise to Robin Hanson (not that he asked for it). I was motivated to deal with this again by the launch of Augu…