1951
One Plus One Equals Two (2006)
From the highly eclectic blog of Mark Dominus
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,394 posts.
1952
1953
Open Questions
Some anomalies/questions which are not necessarily important, but do puzzle me or where I find existing explanations to be unsatisfying.
1954
16-bit math look-up tables – the unexpected power of scaled-integer math
Floating-point math puts a big overhead on a computer that doesn't have a floating-point coprocessor; but we really do need floating-point for all but the simplest operations— or do we?? Can we really do things like trig, log, and square-root functions without floating point?
1955
When the bubble bursts
We are clearly not in a steady-state situation. Is this a bubble or a revolution? The answer surely includes a bit of revolution—the fields of vision and speech recognition have been turned over by great empirical successes created by deep neural architectures and more generally machine learning has found plentiful…
1956
Understanding the FFT Algorithm
The Fast Fourier Transform (FFT) is one of the most important algorithms in signal processing and data analysis. I've used it for years, but having no formal computer science background, It occurred to me this week that I've never thought to ask how the FFT computes the discrete Fourier transform so quickly. I dusted…
1957
Closed form arc length parametrization is impossible for quadratic Bézier curves
Bézier curves are widely used for defining vector graphics. They are basically polynomial parametric curves, but given in the Bernstein basis, which enables us to define the curve using control points. The first and last control point define the start and endpoint of the curves, the intermediate control points kind of…
1958
Compiling to λ-calculus
Though it contains forms only for function applications, variable references and anonymous functions, it is equivalent to a Turing machine.
1959
Optimizing a breadth-first search
Optimizing a breadth-first search of an implicit graph for secondary storage, and memory use in general.
1960
A Bayesian view of Amazon resellers (2011)
I was buying a used book through Amazon this evening. Three resellers offered the book at essentially the same price. Here were their ratings: 94% positive out of 85,193 reviews 98% positive out of 20,785 reviews 99% positive out of 840 reviews Which reseller is likely to give the best service? Before you assume it's
1961
Six (and a half) intuitions for KL divergence
KL-divergence is a topic which crops up in a ton of different places in information theory and machine learning, so it's important to understand well. Unfortunately, it has some properties which seem confusing at a first pass (e.g. it isn't symmetric like we would expect from most distance measures, and it can be…
1962
Introduction to Category Theory
The aim of this course is to teach the basics of category theory, in a way that is accessible and relevant to computer scientists. The emphasis is on gaining a good understanding the basic definitions, examples, and techniques, so that students are equipped for further study on their own of more advanced topics if…
1963
1964
Binary Lambda Calculus (2020)
Binary lambda calculus ( BLC ) is a minimal, pure functional programming language invented by John Tromp in 2004, 1 based on a binary encoding of the untyped lambda calculus in De Bruijn index notation.
1965
Collatz’s Ant
if $n \equiv 0 \, (\text{mod}\, 2)$ the ant turns 90º clockwise, else the ant turns 90º counter-clockwise. On both accounts, the state of the cell is flipped and the ant moves forward one unit. This is repeated until $n = 1$.
1966
Math with Bad Drawings
Now available for preorder.
1967
Does one have to be a genius to do maths?
Better beware of notions like genius and inspiration; they are a sort of magic wand and should be used sparingly by anybody who wants to see things clearly. (José Ortega y Gasset, “Notes on t…
1968
Master List of Logical Fallacies (2018)
Fallacies are fake or deceptive arguments, "junk cognition," that is, arguments that seem irrefutable but prove nothing. Fallacies often seem superficially sound and they far too often retain immense persuasive power even after being clearly exposed as false. Like epidemics, fallacies sometimes "burn through" entire…
1969
How a mathematician constructed a decision tree to solve a medical problem
Here’s an excerpt from Love and Math, a book by Edward Frenkel. The author writes about mathematics and his career. One of the stories is about …
1970
A Sober Look at Bayesian Neural Networks
by Carles Gelada and Jacob Buckman WARNING: This is an old version of this blogpost, and if you are a Bayesian, it might make you angry. Click here for an updated post with the same content. Context: About a month ago Carles asserted on Twitter that Bayesian Neural Networks make...
1971
What is Symbolic Computation?
I've been reading a lot of Lisp books lately, some more advanced than others. All of the introductory books I've seen cover the idea of symbolic computation, but most of them breeze past it with just a few pages about "symbols" and "quoting". For many programmers coming from non-Lisp languages these are new, foreign…
1972
Zero knowlege proof of compositeness
Testing whether a number is composite as an example of a zero knowledge proof. How ZKPs are used more generally.
1973
The Map Is Not the Territory (2015)
The map is not the territory reminds us that our mental models of the world are not the same as the world itself. It cautions against confusing our abstractions and representations with the complex, ever-shifting reality they aim to describe.
1974
Towards a Better Pythagorean Cup
There was an article on Hacker News the other day by David Richeson entitled Make Your Own Pythagorean Cup . A Pythagorean cup is a cup with a built-in siphon. Supposedly invented by Pythagoras, the cup functions just like an ordinary cup as long as it is only filled to a certain level. If anyone gets greedy and tries…
1975
Space-filling curves, constructively
In 1890 Giuseppe Peano discovered a square-filling curve , and a year later David Hilbert published his variation . In those days people did not waste readers’ attention with dribble – Peano explained it all on 3 pages, and Hilbert on just 2 pages, with a picture!
1976
Egyptian Fractions (2006)
From the highly eclectic blog of Mark Dominus
1977
1978
Perlin noise
I used Perlin noise for the fog effect and title screen in Under Construction. I tweeted about my efforts to speed it up, and several people replied either confused about how Perlin noise works or not clear on what it actually is. I admit I only (somewhat) understand Perlin noise in the first place because I’ve…
1979
Computational Geometry in Python
This post is a simplified version of the accompanying notebook to chapter 6 of my upcoming book Mastering SciPy. Click anywhere on this box for more information.
1980
John and Alicia Nash, 1928,1933-2015
Our condolences Awesome Stories source John Nash and his wife Alicia were killed in a taxi accident on the New Jersey Turnpike Saturday afternoon. They were on their way back from Norway where he a…