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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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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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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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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…
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Hash-based Signatures: An illustrated Primer
Over the past several years I’ve been privileged to observe two contradictory and fascinating trends. The first is that we’re finally starting to use the cryptography that researchers h…
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Probabilistic Filters By Example
Probablistic filters are high-speed, space-efficient data structures that support set-membership tests with a one-sided error. These filters can claim that a given entry is definitely not represented in a set of entries, or might be represented in the set. That is, negative responses are conclusive, whereas positive…
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How to read a mathematics textbook (2016)
Reading maths textbooks linearly doesn't work; here's what to do instead.
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Getting started with linear algebra
I'd like to introduce a series of blog posts and their corresponding Python Notebooks gathering notes on the Deep Learning Book from Ian Goodfellow, Yoshua B...
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A study of musical scales (2017)
PREFACE. This essay was written in 2009. Since then, a few errata have been corrected and I embedded the youtube videos, but there have been no substantial additions. I think it still holds up fairly well, but if I were to rewrite it today, I would change some things. My main regret is using the criteria of maximum…
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Show HN: Solving Rush Hour, the 6x6 Sliding Block Puzzle
Rush Hour is a 6x6 sliding block puzzle invented by Nob Yoshigahara in the 1970s. It was first sold in the United States in 1996.
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Deciphering the postcard-sized raytracer
"He's done it again!" was my first thought as I looked at the back of a postcard sized Pixar flier [1] which was covered in code. In the lower right corner, the blob of statements and expressions had been signed by none other than Andrew Kensler. For those who are not familiar with him, Andrew is the programmer who…
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Secrets of smooth Béziers
I haven’t posted here much lately, and I admit, it’s because I’ve gotten sidetracked thinking about curves again. I did my PhD thesis on curves, so spent years thinking about them, then put that on hold for a while, aside from some work in crunching font file sizes down.
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Programmer's guide to polynomials and splines
This is a brief introduction into polynomials. From how to make a polynomial run through your set of points to how to make it into a spline.
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Attacking Merkle Trees with a second preimage attack
Hacking, hardware, software, and general curiosities of computing machinery! Docendo discumus.