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Sorry ARIMA, but I’m Going Bayesian
When people think of “data science” they probably think of algorithms that scan large datasets to predict a customer’s next move or interpret unstructured te...
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To approximate 52! by hand, compute 54! and divide by 3000
Some time ago I gave a talk in which I showed that something unexpected happened with a deck of playing cards. I had some volunteers try it, and while they did so I talked about just how many orderings there are for 52 cards. I computed (an approximation to) $52!$ (52 factorial) by hand. It's not so hard - you just…
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How to assign partial credit on an exam of true-false questions?
Note: the following is a record of some whimsical mathematical thoughts and computations I had after doing some grading. It is likely that the sort of problems discussed here are in fact well studi…
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Category Theory and Declarative Programming
This is part 11 of Categories for Programmers. Previously: Natural Transformations. See the Table of Contents. Introduction to Part II In the first part of the book I argued that both category theo…
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Experimenting with Post-Quantum Cryptography
Posted by Matt Braithwaite, Software Engineer Quantum computers are a fundamentally different sort of computer that take advantage of aspec...
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Fast Fourier transform in x86 assembly
I have a simple fast Fourier transform implementation on the page Free small FFT in multiple languages , whose asymptotic time complexity is the optimal Θ( n log n ). I wanted to know how much additional speed-up could be obtained by reorganizing memory access patterns and using SIMD vector arithmetic instructions…
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Logical Induction
MIRI is releasing a paper introducing a new model of deductively limited reasoning: “Logical induction,” authored by Scott Garrabrant, Tsvi Benson-Tilsen,
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The Three Cultures of Machine Learning
Everyone should read Leo Breiman's 2001 article, Statistical Modeling: The Two Cultures . (Summary: Traditional statisticians start with a distribution. They try to identify the parameters of the distribution from data that were actually generated from it. Applied statisticians start with data. They have no idea where…
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Combinatorial Music Theory (1991)
graph theory, music theory
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2D Terrain generation using midpoint displacement
Today I will present how to implement in Python a simple yet effective algorithm for proceduraly generating 2D landscapes. It is called Midpoint Displacement (or Diamond-square algorithm,…
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Hash Functions all the way down
Update! I tested more hash functions in a follow-up post. See More Hash Function Tests .
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A Natural Law for Rotating Galaxies: What Does This Mean for Dark Matter?
Learn about public engagement activities from the American Physical Society
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How Hamming codes work
Detecting (and correcting) errors in digital signals.
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SeaHash: Explained
I explain how SeaHash works.
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Interactive Numerical Optimization Tutorial
Numerical Optimization is one of the central techniques in Machine Learning. For many problems it is hard to figure out the best solution directly, but it is relatively easy to set up a loss function that measures how good a solution is - and then minimize the parameters of that function to find the solution.
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How should mathematics be taught to non-mathematicians? (2012)
Michael Gove, the UK’s Secretary of State for Education, has expressed a wish to see almost all school pupils studying mathematics in one form or another up to the age of 18. An obvious quest…
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Three and a half degrees of separation
At Meta, research permeates everything we do. We believe the most interesting research questions are derived from real world problems.
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Black Hole Tech?
In celebration of the detection of gravitational waves, Stephen Wolfram looks forward and discusses what technology black holes could make possible.
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Zero Knowledge Proofs: An illustrated primer (2014)
One of the best things about modern cryptography is the beautiful terminology. You could start any number of punk bands (or Tumblrs) named after cryptography terms like ‘hard-core predicate&#…
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Some thoughts about the reports of supposed evidence of election irregularities
The Internet lit up on Monday over the news, reported in New York Magazine , that a team of computer scientists and lawyers had reported to the Clinton campaign that “they’ve found persuasive evidence that results in Wisconsin, Michigan, and Pennsylvania may have been manipulated or hacked. ”
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Why Don't Computer Scientists Learn Math?
I recently attended the Heidelberg Laureate Forum , in which some older researchers--mainly Fields Medalists and Turing Award winners--talked to and with young researchers. The young researchers ranged from a few students just entering university to young faculty members, most being graduate students. They came from…
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Don’t invert that matrix (2010)
There is hardly ever a good reason to invert a matrix. What do you do if you need to solve Ax = b where A is an n x n matrix? Isn't the solution A−1 b? Yes, theoretically. But that doesn't mean you need to actually find A−1. Solving the equation Ax = b is