2191
Time to Abolish "Statistical Significance"?
The idea of "statistical significance" has been a basic concept in introductory statistics courses for decades. If you spend any time lookin...
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,393 posts.
2192
JPEG XL would be Turing-complete without the 1024×1024 pixel limitation
You can construct the Rule 110 cellular automaton in JPEG XL.
2193
Mastering The Fourier Transform in One Day
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2194
2195
Entropy and Algebra and Topology = ?
Today I'd like to share some math connecting ideas from information theory, algebra, and topology. It's all in a new paper I've recently uploaded to the arXiv (https://arxiv.org/abs/2107.09581), which describes a correspondence between Shannon entropy and functions on topological simplices that obey a version of the…
2196
How to design co-programs
I recently attended the Matthias Felleisen Half-Time Show, a symposium held in Boston on 3rd November in celebration of Matthias’s 60th birthday. I was honoured to be able to give a talk ther…
2197
Empirical Bayes for multiple sample sizes
The James-Stein Estimator with unequal variances
2198
Measuring the size of the Earth by watching a shadow on a wall
Recently I've been discussing the details of measuring the size of the Earth by watching a shadow descending a wall at sunrise, or ascending at sunset. The sums are easy enough if you do it at either Equinox, and at the Equator, and you can read about it here:
2199
Penrose Mazes (2020)
Mazes are typically constructed on regular grids: square, triangular, hexagonal, etc. But what if you generate a maze on top of a Penrose tiling, which is guaranteed to be irregular? (It is an aperiodic tiling .) The resulting mazes have a very characteristic appearance: they are filled with circles and stars, but the…
2200
The beauty of mixed-radix bases
On the relationship between mixed-radix bases and array indexing
2201
Fuzzy string search
Intro Fuzzy search algorithms (also known as similarity search algorithms) are a basis of spell-checkers and full-fledged search engines lik...
2202
The theory of concatenative combinators (2007)
This article attempts to outline, in informal terms, a new theory of combinators, related to the theory of Combinatory Logic pioneered by Moses Schonfinkel, Haskell Curry, and others in the 1930s. Although not essential, an understanding of the classical theory of combinators may be helpful (see the links at the…
2203
Creatively Misusing TLA+
Five not-quite-normal uses
2204
Why Python's integer division floors (2010)
I was asked (again) today to explain why integer division in Python returns the floor of the result instead of truncating towards zero like...
2205
Formalising a new proof that the square root of two is irrational
Recently, somebody shared on Twitter a new proof of the irrationality of √2. Its claimed advantage is that “it requires no knowledge of mathematics above the definition of what it means for a number to be irrational, and can be written almost in one line.” These claims are dubious: the usual proof, which I’ve…
2206
The Algorithm Behind Jim Simons's Success
Reflections on a Wall Street legend.
2207
Multiplying and dividing with Hindu-Arabic numerals and with Roman ones
Last Sunday the eminent British historian of the twentieth century, Richard Evans, tweeted the following: Let’s remember we use Arabic numerals – 1, 2, 3 etc. Try dividing MCMLXVI by XX…
2208
2209
Computing the number of digits of an integer even faster
I my previous blog post, I documented how one might proceed to compute the number of digits of an integer quickly. E.g., given the integer 999, you want 3 but given the integer 1000, you want 4. It is effectively the integer logarithm in base 10. On computers, you can quickly compute the integer logarithm … Continue…
2210
Understanding Stein's Paradox (2021)
An intuitive explanation of the James-Stein estimator.
2211
Fold-... and Monoids
A blog about computers, functional languages, Lisp, and Scheme.
2212
2213
Finding an Optimal Keyboard Layout for Swype
An overview of my work on optimizing phone keyboard layouts for Swype and T9. There's some interesting history here as well as a novel simulation-based approach to keyboard optimization.
2214
Brainfuck Optimization Strategies
In almost every computation a great variety of arrangements for the succession of the processes is possible, and various considerations must influence the selection amongst them for the purposes of a Calculating Engine. One essential object is to choose that arrangement which shall tend to reduce to a minimum the time…
2215
Why are amplitudes complex?
[By prior agreement, this post will be cross-posted on Microsoft’s Q# blog, even though it has nothing to do with the Q# programming language. It does, however, contain many examples th…
2216
Estimating Logarithms
While reading through the fantastic book *[The Lost Art of Logarithms](https://www.lostartoflogarithms.com/)* by [Charles Petzold](https://www.charlespetzold.com/) I was nerd-sniped by a [simple method](https://www.lostartoflogarithms.com/chapter04/) of estimating the logarithm of any number base 10. According to the…
2217
TLA from First Principles
Building an intuition for the mathematics behind the "TLA" in "TLA+"
2218
Fast and Easy Levenshtein distance using a Trie (2011)
<img src="http://stevehanov.ca/blog/images/acer.jpg"/> If you have a web site with a search function, you will rapidly realize that most mortals are terrible typists. Many searches contain mispelled words, and users will expect these searches to magically work. This magic is often done using levenshtein distance. In…
2219
PigPaxos: Removing the Scalability Bottlenecks in Paxos
This is our most recent work, started and led by Aleksey Charapko . (This is a joint post with him.) You can get the paper at arxiv.org . Th...
2220
Minimal Boolean Formulas (2011)
28 . That's the minimum number of AND or OR operators you need in order to write any Boolean function of five variables. Alex Healy and I computed that in April 2010. Until then, I believe no one had ever known that little fact. This post describes how we computed it and how we almost got scooped by Knuth's Volume 4A…