1951
Evolution of Random Number Generators
Prime powers have a kinda chaotic pattern in their bits. We bootstrap this idea into a good random number generator, recapitulating history.
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
1952
1953
LU Factorization and Linear Systems for Programers
Solving systems of linear equations is a staple food of linear algebra. It can be applied as a part of many machine learning tasks, although it is not always...
1954
1955
Unicode's transliteration rules are Turing-complete
Claim: as specified, the UTS #35 transliteration-rule language is Turing-complete. This is an exception in Unicode, where algorithms are deliberately bounded and always terminate. The specification defines a revisiting cursor with no rewrite limit. ICU's implementation implements a per-call cap, but the spec itself…
1956
Four pitfalls of hill climbing
An animated look at local maxima, novelty effects, differentiation, emergent maxima.
1957
Fast Lossless Color Image Compression
In the research field of compression, the usual goal is to achieve the best possible compression rate. The best known algorithms, however, are very slow, and sometimes impractical for real-world ap…
1958
Space Emerging from Quantum Mechanics
The other day I was amused to find a quote from Einstein , in 1936, about how hard it would be to quantize gravity: “like an attempt to breathe in empty space.” Eight decades later, I think we can still agree that it’s hard.
1959
Rolling hash; Rabin-Karp string search
This is yet another string search algorithm. (Previously my readers have read about Knuth-Morris-Pratt .)
1960
Raytracing diamonds
This comes from a question posed to me and others in 2019 by Stefan Langerman, a computational geometer who also happens to be a diamond dealer. The classic ...
1961
Competitive programming in Haskell: better binary search
Binary search is a workhorse of competitive programming. There are occasional easy problems where binary search is the solution in and of itself; more often, it’s used as a primitive building block…
1962
Learning Lean: Part 1
Motivation I’ve been captivated by the recent movement to popularize mathematics formalization through the Lean theorem prover, and this year I’m diving deeper into learning it. For those unfamiliar with this revolution, I highly recommend watching Kevin Buzzard’s talks on YouTube for an overview of why formal…
1963
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
1964
Singular Value Decomposition Part 2: Theorem, Proof, Algorithm
I’m just going to jump right into the definitions and rigor, so if you haven’t read the previous post motivating the singular value decomposition, go back and do that first. This post will be theorem, proof, algorithm, data. The data set we test on is a thousand-story CNN news data set. All of the data, code, and…
1965
An interactive guide to Fourier series (2022)
Drawing with the Fourier Series
1966
Tversky Neural Networks
Psychologically Plausible Deep Learning with Differentiable Tversky Similarity
1967
Faster arithmetic by flipping signs
Over the years, I picked up a number of tricks to optimize code. Today I’ll talk about one of them.
1968
1969
Was Knuth Really Framed?
Recently, the formal methods specialist Hillel Wayne posted an interesting article discussing whether Donald Knuth was actually framed when Jon Bentley asked him to demonstrate literate programming . (Knuth came up with an 8-page long monolithic listing, whereas in a critique Doug McIlroy provided a six line shell…
1970
Understanding is a poor substitute for convexity (2012)
Something central, very central, is missing in historical accounts of scientific and technological discovery. The discourse and controversies focus on the role of luck as opposed to teleological programs (from telos, "aim"), that is, ones that rely on pre-set direction from formal science. This is a faux-debate: luck…
1971
Optimizing hash tables: hiding the hash code
Several JavaScript data structures such as Map, Set, WeakSet, and WeakMap use hash tables under the hood. This article explains how V8 v6.3 improves hash table performance.
1972
Parrondo's Paradox: How two ugly parents can make a beautiful baby
"How two ugly parents (mathematically) can make a beautiful baby"
1973
Math Symbols Explained with Python
Learn the meaning behind mathematical symbols used in Machine Learning using your knowledge of Python.
1974
A pair of dice which never roll 7 (2004)
Some friends of mine play the board game Settlers Of Catan . In this game, each player rolls two ordinary dice on their turn, and the number which comes up determines what resources people get for the turn. When a seven is rolled, something special happens: no resources are generated, and instead a robber moves on the…
1975
Scarcity, Inventory, and Inequity: A Deep Dive into Airline Fare Buckets
Airline pricing may seem mystifying, but behind every airfare is a complex system of fare buckets and inventory controls. Airlines don't just sell seats - they manage a dynamic inventory of fares, divided into booking classes (fare buckets) with different prices and rules. For the technically curious, understanding…
1976
1977
The inspection paradox is everywhere (2015)
I have updated this article with new data, better code, and friendlier data visualization. You can read the new version here . Th...
1978
1979
So You Think You Have a Power Law (2007)
Regular readers who care about such things — I think there are about three of you — will recall that I have long had a thing about just how unsound many of the claims for the presence of power law distributions in real data are, especially those made by theoretical physicists, who, with some honorable exceptions…
1980
Reasonable Effectiveness of the Multiplicative Weights Update Algorithm (2017)
papad Hard to believe Sanjeev Arora and his coauthors consider it “a basic tool [that should be] taught to all algorithms students together with divide-and-conquer, dynamic programming, and random sampling.” Christos Papadimitriou calls it “so hard to believe that it has been discovered five times and forgotten.” It…