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The polls messed up
To continue our post-voting, pre-vote-counting assessment (see also here and here ), I want to separate two issues which can get conflated: 1. Problems with poll-based election forecasts.
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The latest blog posts to take off on Hacker News. 2,851 posts.
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Fast Inverse Square Root
The famous fast inverse square root is some mysterious code not written by programming legend John Carmack to calculate a fast approximation of $1/\sqrt{x}$:
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Simple Image Vectorization
This is an example of an image vectorization algorithm. It shows the bilinear interpolation, polynomial approximation, differential analysis, and iterative algorithms working together to solve a practical problem
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The Complete Idiot’s Guide to the Independence of the Continuum Hypothesis
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…
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The Remarkable Number 1/89 (2004)
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:
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Markov Chain Monte Carlo (MCMC) Sampling, Part 1: The Basics (2019)
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…
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Reverse-engineering the problematic tail behavior of Fivethirtyeight forecast
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)…
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A Programmer’s Intuition for Matrix Multiplication
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.…
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Why deep learning works even though it shouldn’t
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.
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Building a computer in Conway's game of life
A new (and better) version of the GOL computer is available here : https://github.com/nicolasloizeau/scalable-gol-computer
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Gravity is not a force – free-fall parabolas are straight lines in spacetime
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There are only four billion floats, so test them all (2014)
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…
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Climbing the cosmic distance ladder: Terence Tao book announcement
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…
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Swift Algorithms
I’m excited to announce Swift Algorithms, a new open-source package of sequence and collection algorithms, along with their related types.
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Making the Monty Hall problem weirder but obvious
It’s this simple: Do you want what’s behind one door or the other nine?
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Toward an API for the Real Numbers
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. …
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Dissecting Lemire's nearly divisionless random number generator
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.
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What are Differential Equations and how do they work?
Science News, Physics, Science, Philosophy, Philosophy of Science
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Lambda Calculus Diagrams (2015)
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…
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Summary of all the MIT Introduction to Algorithms lectures (2009)
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...
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All you need is λ, part one: booleans
Words by Rob Rix.
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Why neural networks struggle with the Game of Life
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.
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A Software Engineer’s Guide to Cybernetics
Before ‘cyber’ was a prefix for everything internet and computers, it was how mathematicians were going to conquer the world.
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Decision Table Patterns
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…
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Why Bayesian Stats Needs Monte-Carlo Methods
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
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The Stack Monoid
(Updated 2020-09-06 with pointers to related work and a bit more explanation)
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Programming with Categories
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…
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A round-up of topology-based papers at ICML 2020
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…
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How to Read a Log Scale
What log scales tell us.