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Reinforcement Learning with Prediction-Based Rewards
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The latest blog posts to take off on Hacker News. 2,851 posts.
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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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The Waiting Time Paradox, Or, Why Is My Bus Always Late?
If you, like me, frequently commute via public transit, you may be familiar with the following situation:
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The Strangest Book on the Theory of Computation (2009)
Based on the description of the book in the World Scientific Press catalogue, I asked my university library to order a book entitled Automat...
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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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Advanced techniques to implement fast hash tables
Array and hash table are probably the most important data structures. Some programming languages such as Perl, Lua and Javascript, almost build the language core on top of the two data structures. …
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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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Let’s talk about PAKE
The first rule of PAKE is: nobody ever wants to talk about PAKE. The second rule of PAKE is that this is a shame, because PAKE — which stands for Password Authenticated Key Exchange — is actually o…
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Algorithms tutorial series for beginners
As a developer, you have the power to change the world! You can write programs that enable new technologies. For instance, develop software to find an earlier diagnosis of diseases. But that’s not the only way. You might do it indirectly by creating projects that make people more productive and help them free up time…
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Decision Tables
I really like decision tables but they’ve fallen out of common knowledge. Let’s fix that. A decision table is a means of concisely representing branching and conditional computations. In the most basic form, you have some columns that represent the “inputs” as booleans and some columns that represent outputs and…
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A Long Peek into Reinforcement Learning
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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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Constraint Solving with MiniZinc
This is part one of a two-part article. Part two is here. A while back somebody told me to check out MiniZinc. Eventually I did and really enjoyed it, so figured I’d write about it here. This is actually going to be a two part article. Right now we’re talking about what it is and how it works, and in the next post…
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Twenty Questions Of Maddening, Delicious Geometry
The geometry puzzles that are lighting up Twitter.
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A Gentle Introduction to Markov Chain Monte Carlo (2012)
Applying probabilistic models to data usually involves integrating a complex, multi-dimensional probability distribution. For example, calculating the expectation/mean of a model distribution invol…
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What Made Gödel’s Incompleteness Theorem Hard to Prove
Roughly speaking, Gödel’s Incompleteness Theorem states that there are true mathematical statements that cannot be proven. When I was in 11-th grade, my geometry teacher Mr. Olsen, my friend …
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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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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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Worst Puzzle Ever (2009)
It breaks my heart to write this post because the puzzle in question was 1) very expensive and 2) given to me by someone very dear to me who...
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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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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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How to Be Wrong (2016)
“To be wrong, or not to be wrong?” That is the wrong question. You are going to spend a lot of your time being wrong, especially if you become a scientist or mathematician. The question…
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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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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…
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The algebra and calculus of algebraic data types
Just as algebra is fundamental to the whole of mathematics, algebraic data types (ADTs) are fundamental to many common functional programming languages. They’re the primitives upon which all of our richer data structures are built, including everything from sets, maps, and queues, to bloom filters and neural networks .