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Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 179 posts.
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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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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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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…
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The 8000th Busy Beaver number eludes ZF set theory (2016)
I’ve supervised a lot of great student projects in my nine years at MIT, but my inner nerdy teenager has never been as personally delighted by a project as it is right now. To…
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Using k-d trees to efficiently calculate nearest neighbors in 3D vector space
What would the world look like if there were only 16 colors? I use k-d trees to perform nearest neighbor search to find out.
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City street orientations around the world
This post is adapted from this research paper that you can read/cite for more info. It analyzes and visualizes 100 cities around the world.
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Gamifying propositional logic: QED, an interactive textbook
About six years ago on this blog, I started thinking about trying to make a web-based game based around high-school algebra, and ended up using Scratch to write a short but playable puzzle game in …
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How to explain infinity to kids
From the highly eclectic blog of Mark Dominus
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Math and Analogies
Here's a talk on "Math And Analogies" I did for the Center on Contemporary Art (CoCA) in Seattle. What's this? Well, it's a number. Probably written down a…
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Towards λ-calculus
lambdaway is built on a wiki engine, lambdatank, and a small Lisp dialect, lambdatalk.
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The Federalist Papers: Author Identification Through K-Means Clustering
Using K-means clustering on writing style to classify disputed Federalist Papers authorship.
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The secret life of NaN
The floating point standard defines a special value called Not-a-Number (NaN) which is used to represent, well, values that aren’t numbers. Double precision ...
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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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Algebras we love
If you work with anything that can be modeled mathematically, you most likely know that many things you work on can be expressed with algebras. However, if you are not a graduate of a computer science course or similar you might not know how ubiquitous they are and how often you rely on some of them. (And I don’t mean…