The latest blog posts to take off on Hacker News. 173 posts.
A global pandemic, apocalyptic fires, and the possible descent of the US into violent anarchy three days from now can do strange things to the soul. Bertrand Russell—and if he’d done no…
The Fibonacci series is a famous example of an object with a simple mathematical description, but a nearly inexhaustable list of bizarre and complicated properties. Originally, the series was described by Fibonacci in the 15th century in connection with the following problem:
In this first post of Tweag’s four-part series on Markov chain Monte Carlo sampling algorithms, you will learn about why and when to use them and the theoretical underpinnings of this powerful class of sampling methods. We discuss the famous Metropolis-Hastings algorithm and give an intuition on the choice of its free…
We’ve been writing a bit about some odd tail behavior in the Fivethirtyeight election forecast, for example that it was giving Joe Biden a 3% chance of winning Alabama (which seemed high), it was displaying Trump winning California as in “the range of scenarios our model thinks is possible” (which didn’t seem right)…
What does matrix multiplication mean? Here's a few common intuitions: This is useful when first learning about vectors: vectors go in, new ones come out.…
Why models always get better when they are bigger and deeper, even when the amount of data they consume stays the same or gets smaller.
A new (and better) version of the GOL computer is available here : https://github.com/nicolasloizeau/scalable-gol-computer
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A few months ago I saw a blog post touting fancy new SSE3 functions for implementing vector floor, ceil, and round functions. There was the inevitable proud proclaiming of impressive performance an…
Several years ago, I developed a public lecture on the cosmic distance ladder in astronomy from a historical perspective (and emphasising the role of mathematics in building the ladder). I previous…
I’m excited to announce Swift Algorithms, a new open-source package of sequence and collection algorithms, along with their related types.
It’s this simple: Do you want what’s behind one door or the other nine?
Towards an API for the real numbers, Boehm, PLDI’20 Last time out we saw that even in scientific computing applications built by experts, problems with floating point numbers are commonplace. …
A very late blog post announcing the readability contest winners, a new (very) annotated implementation, and a surprising sort-of security issue found along the way.
Science News, Physics, Science, Philosophy, Philosophy of Science
The following table shows diagrams of identity, the booleans, some standard combinators, some Church numerals, the predecessor function on Church numerals, and Omega. term definition diagram alternative I/1 λx.x K/true λx.λy.x false/0 λx.λy.y S λx.λy.λz.(x z)(y z) Y λf.(λx.x x)(λx.f(x x)) 2 λf.λx.f(f x) 3 λf.λx.f(f(f…
As you all may know, I watched and posted my lecture notes of the whole MIT Introduction to Algorithms course. In this post I want to summarize all the topics that were covered in the lectures and point out some of the most interesting things in them. Actually, before I wrote this article, I had started writing an...
Words by Rob Rix.
The Game of Life is based on very simple rules, but artificial neural networks struggle to learn its rules through the classic deep learning training process.
Before ‘cyber’ was a prefix for everything internet and computers, it was how mathematicians were going to conquer the world.
Decision tables are easy, simple, and powerful. You can teach them in five minutes and write one in half that time. You can look at a table and understand what it’s saying, see if it matches your problem, and check for design flaws. So it’s kinda weird that there’s basically nothing about them online. I wrote an…
Bayesian statistics rely heavily on Monte-Carlo methods. A common question that arises is “isn’t there an easier, analytical solution?” This post explores a bit more why this is by breaking down the analysis of a Bayesian A/B test and showing how tricky the analytical path is and exploring more of t
(Updated 2020-09-06 with pointers to related work and a bit more explanation)
In this course we explain how category theory—a branch of mathematics known for its ability to organize the key abstractions that structure much of the mathematical universe—has become useful for writing elegant and maintainable code. In particular, we'll use examples from the Haskell programming language to motivate…
With this year’s International Conference on Machine Learning (ICML) being over, it is time to have another instalment of this series. Similar to last year’s post , I shall cover several papers that caught my attention because of their use of topological concepts—however, unlike last year, I shall not restrict the…
What log scales tell us.
A few years ago I came across this video, showing a complex machine built entirely in Conway’s Game of Life:
Patrick Honner tweeted a few days ago: My 7 yo pointed out that our 300 piece puzzle actually contains 18 x 18 = 324 pieces and I just don’t know what to believe anymore. — Patrick Honner (@M…
