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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.
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Reinforcement Learning – Bandit Problems
Table of Contents
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An Introduction to Cache-Oblivious Data Structures
If you read my recent post about Postgres you may have noted that Postgres operates primarily with fixed-size blocks of memory called “pages.” By default, Postgres pages are 8KB. This number is tuned to match operating system page sizes which are tuned to match hardware cache sizes. If you were to run Postgres on…
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Mapping the internet with Hilbert curves
The internet is big. Really big . You just won’t believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think the /22 you got as a LIR was big, but that’s just peanuts to the internet.
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Death of the sampling theorem?
tl;dr: A team from Columbia University led by Ken Shepard and Rafa Yuste claims to beat the 100 year old Sampling Theorem [1,2]. Apparently anti-aliasing filters are superfluous now because one can…
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How 4000 Physicists Gave a Vegas Casino Its Worst Week (2015)
Learn about public engagement activities from the American Physical Society
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Shamir’s Secret Sharing Scheme
Consider a scenario in which you are tasked with managing the security of a bank's vault. The vault is considered impenetrable without a key, which you are g...
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Hamiltonian Monte Carlo explained
Understanding an effective way of sampling from complex distributions with 3d-demonstrations
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I simulated California housing and learned about simulators
Back in the early 2000s, XML was all the rage. An unusual evolution from HTML, which itself was an evolution (devolution?) from SGML, XML w...
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Understanding Quaternions
Quaternions are used to represent an orientation in 3D space. This article attempts to demystify the complexities of quaternions.
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Glow: Better Reversible Generative Models
Stay up to speed on the rapid advancement of AI technology and the benefits it offers to humanity.
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Planets evenly spaced on log scale
The distances to the planets are fairly evenly distributed on a logarithmic scale, not only in our solar system but in extrasolar systems as well.
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What the Four Color Theorem Can Teach Us About Writing Software
A visual exploration of what The Four Color Theorem can say about software complexity.
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Why Y? Deriving the Y Combinator in JavaScript
In this essay, after a brief review of the work we’ve already done on the Mockingbird, we’ll derive the Why Bird, known most famously as the Y Combinator . The why bird provides all the benefits of the mockingbird, but allows us to write more idiomatic JavaScript. We’ll see that one of the benefits of writing…
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Gödel and the unreality of time
In 1949, in a festschrift devoted to Einstein , Kurt Gödel published a very short but profound paper titled “A Remark About the Relati...
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Shortest bit sequence that's never been sent over the Internet (2017)
We can never know for sure because we don't have a comprehensive list of all the data. But what can we say probabilistically? Restating it like so:
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Mathematical Patterns That Eventually Fail
Sometimes patterns can lead you astray. For example, it’s known that $latex \displaystyle{ \mathrm{li}(x) = \int_0^x \frac{dt}{\ln t} }$ is a good approximation to $latex \pi(x),$ the number …
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Has an uncomfortable truth been suppressed?
Update to post, added 11th September. As expected, there is another side to the story discussed below. See this statement about the decision by the Mathematical Intelligencer and this one about the…