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Discovering errors in Donald Knuth's TAOCP
As Donald Knuth has just published Volume 4, Fascicle 7 of The Art of Computer Programming (TAOCP), on constraint satisfaction, I would like to provide…
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,851 posts.
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Probability-generating functions
I have long struggled with understanding what probability-generating functions are and how to intuit them. There were two pieces of the puzzle missing for me, and we’ll go through both in this article.
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The infamous coin toss
In 2011 I gave a 15-minute talk to a lay audience in London. The topic I had chosen was ergodicity breaking, and the challenge was clear: how do you get this across? I invented a coin-toss gamble, which has since become a go-to illustration of ergodicity break
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Why are we even doing all this?
[This is a guest post by Rikab Gambhir. This blog post was initially written in a different file format and converted using AI. — T.] First, they came for the artists, and I did not speak out…
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US Army applying new areas of math
Many times on this blog I've argued that the difference between pure and applied math is motivation. As my graduate advisor used to say, “Applied mathematics is not a subject classification. It's an attitude.” Traditionally there was general agreement regarding what is pure math and what is applied. Number theory and…
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How to implement an algorithm from a scientific paper
This article is a short guide to implementing an algorithm from a scientific paper. I have implemented many complex algorithms from books and scientific publications, and this article sums up what I have learned while searching, reading, coding and debugging. This is obviously limited to publications in domains…
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World Cup Follow-Up: Update of Winning Probabilities and Betting Results
An update on the winning probabilities for the remaining World Cup teams, and an analysis of how our predictor performed on the group-phase matches.
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Clojure Linear Algebra Refresher: Eigenvalues and Eigenvectors
I stumble upon eigenvectors and eigenvalues regularly when reading about machine learning topics. They seem to be important. They are not introduced in those...
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Minesweeper thermodynamics
You know how sometimes you start a game of Minesweeper and immediately get stuck?
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Matrices from a geometric perspective
Graphics is all about geometry. In particular, there are points that have a certain color, and the pattern of colors gives you a certain picture. You can change the way the points are distributed by applying certain transformations like translation (movement), rotation and scaling. While most people familiar with the…
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A new kind of fractal?
Experimenting with the "divisibility" of complex numbers, I stumbled across this thingy. It looks like a fractal. Although the formula does not do any iterations. It reminds me of something. But I dont know what. Doing a Google image search brings up a couple of galaxies :) This image shows the region from (-1/-1) to…
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An Introduction to the Lambda Calculus (2015)
;; Done Twice as a "Dojo" at Villiers Park on Thursday 19th March 2015 ;; To groups of about 15 ultra-clever teenagers who were thi...
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Foldable Words
Packing up the household for a recent move, I was delving into shoeboxes, photo albums, and file folders that had not been opened in decades. One of my discoveries, found in an envelope at the back of a file drawer, was the paper sleeve from a drinking straw, imprinted with a saccharine message:
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When Big O Fools You
Big O notation is a great tool. It allows one to quickly make smart choices among various data structures and algorithms. But sometimes a casualBig O analy...
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Formalising Mathematics: An Introduction
An introduction to the TCC course “Formalising Mathematics”
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Planets evenly spaced on log scale
The distances to the planets are fairly evenly distributed on a logarithmic scale, not only in our solar system but in extrasolar systems as well.
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Matrices and Graph
The single most undervalued fact of linear algebra: matrices are graphs, and graphs are matrices
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Bezier Curves and Picasso
Pablo Picasso Simplicity and the Artist Some of my favorite of Pablo Picasso’s works are his line drawings. He did a number of them about animals: an owl, a camel, a butterfly, etc. This piece called “Dog” is on my wall: Dachshund-Picasso-Sketch (Jump to interactive demo where we recreate “Dog” using the math in this…
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Ideas in statistics that have powered AI
Andrew Gelman, a statistics professor at Columbia, and Aki Vehtari, a computer science professor at Finland’s Aalto University, recently published a list of the most important statistical ideas in the last 50 years. Here, they break it down in easy-to-understand terms.
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The Case for Bayesian Deep Learning
The Case for Bayesian Deep Learning Andrew Gordon Wilson Abstract Bayesian inference is especially compelling for deep neural networks. The key distinguishing property of a Bayesian approach is margin
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The Beauty of Roots (2011)
Around 2006, my friend Dan Christensen created a fascinating picture of all the roots of all polynomials of degree ≤ 5 with integer coefficients ranging from -4 to 4:
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Algorithmic symphonies from one line of code
Lately, there has been a lot of experimentation with very short programs that synthesize something that sounds like music. I now want to sha...
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A lazy way to solve differential equations
Looking at Taylor series as streams of real numbers, solving differential equations becomes as easy as writing them.