1861
How medieval astronomers made trig tables
Clever tricks used by medieval astronomers to tabulate sines at every degree, before calculators and before calculus.
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,391 posts.
1862
1863
Maximum likelihood estimation and loss functions
When I started learning about loss functions, I could always understand the intuition behind them. For example, the mean squared error (MSE) for regression seemed logical—penalizing large deviations from the ground-truth makes sense. But one thing always bothered me: I could never come up with those loss functions on…
1864
Homotopy Type Theory and Higher Inductive Types
In this article, we explore the possibilities allowed by higher inductive types. They enable a much more intuitive formalization of integers and new mind-blowing definitions of the (homotopical) ci…
1865
Nonograms: a practical guide with interactive examples
This is a very important technique: only fill cells when you’re certain; no guessing.
1866
Not so fast, Mr. Fourier
A real explanation of discrete Fourier transform (DFT, FFT), discrete cosine transform (DCT), and their inverses.
1867
Painting with math: A gentle study of raymarching
A compilation of my Raymarching and Signed Distance Field learnings and work. In it, I teach you how to leverage those techniques along with lighting models, smoothmin, soft shadows, and some math to create beautiful 3D raymarched scenes ranging from abstract shapes to infinite realistic-looking landscapes.
1868
Dijkstra's Algorithm
I was at SCNA the other day, and someone approached me about TDD and Dijkstra’s algorithm. He wondered if you could find a sequence of tests that would lead you to the algorithm. This sounded like a fun little exercise, so I decided to give it a try here.
1869
Solving Programming Puzzles Without Using Your Brain
This post is a write-up of a solution to part of a programming puzzle I did yesterday. It’s a little different than the usual “solution + theory” approach, though: I’m going to talk about the actual steps you’d need to take to get to the solution (i.e. what to google, what intermediate code looks like, etc.). Often…
1870
1871
Smaller than Bloom filters
I've been looking at what would be needed in order to have a global view of CRLs in browsers. At the moment revocation has three problems: privacy (by asking the CA about the status of a certificate you're revealing to them what you're looking at), performance (OCSP checks take hundreds of milliseconds which adds up…
1872
1873
Strange Attractors (2018)
Interactive Mathematical Applets and Animations
1874
Learning to solve hard problems in RL for LLMs by never giving up
This is a blog post for my recent paper on RL post-training of LLMs: introducing the Matthew Effect and proposing to solve it with Never Give Up. It is presented interactively and less formally, more like how I give the talk. For a deeper, more technical dive, check out the paper on arxiv and code on github. The…
1875
Singular Value Decomposition for Programmers
Today's article is a short one. Not because Singular Value Decomposition (SVD) is not important, but because it is so ubiquitous that we'll touch it in other...
1876
An Algorithm for Polygon Intersections
In this post we'll work our way towards an algorithm that can compute convex polygon intersections. We'll also explore a method for intersections between axis-aligned rectangles, a function that can determine the intersection of two line segments, as well as a point in polygon test.
1877
Heritability of human life span is ~50% when heritability is redefined
ratios will be ratios
1878
Loop invariants can give you coding superpowers
A loop invariant is a simple yet powerful tool for designing, testing, modifying, documenting and proving code correct.
1879
The Math I Learned After I Thought Had Already Learned Math
True story: it’s possible to fly through your own secondary math education — honor roll bumper sticker on your mom’s minivan and all —Â but miss some of the Very Big Ideas of secondary …
1880
Cylinders in Spheres
What is the largest volume cylinder it is possible to carve from a solid sphere? Also, so you know about the napkin ring problem?
1881
1882
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…
1883
1884
Sets, types and type checking
My currently understanding of types
1885
A Lisp interpreter implemented in Conway's Game of Life (2021)
Lisp in Life is a Lisp interpreter implemented in Conway’s Game of Life.
1886
A New Way To Solve Linear Equations (over finite fields)
Impossible but true: a new approach to linear systems Prasad Raghavendra is an expert in many aspects of complexity theory, especially the foundations of approximation theory. He recently was a col…
1887
Map Simplification with Visvalingam's Algorithm
An interesting challenge in cartography is getting data of the appropriate resolution. As Lewis Fry Richardson observed , the more precisely you measure the length of a coastline, the longer it appears; geographic shapes have infinite complexity. Digital displays, in contrast, are limited by pixels. Choosing too high…
1888
Dumb statistical models, always making people look bad
This is Jessica. In my Prediction for Decision-making class last quarter we talked about human predictions and decisions relative to algorithmic ones. This led to a discussion about why it’s often hard to demonstrate the value of human knowledge once you have a decent statistical model.
1889
Alpha Compositing
Interactive article explaining alpha compositing concepts.
1890
