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New
The latest blog posts to take off on Hacker News. 173 posts.
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Peter Montgomery Has Died
Peter was born in San Francisco, California, on September 25, 1947. He went to UC Berkeley in 1967 and received a BA in Mathematics in 1969 and an MA in 1971. Peter’s undergraduate advisor was Derrick H. Lehmer, an excellent match given Peter’s research interests since high school: integer factorization.
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Calculating Pi: My Attempt at Breaking the Pi World Record
Before I go into the specifics of my record attempt, it is important for you to have some background information. Over the past few years I have been steadily acquiring server hardware to increase my knowledge of system administration and cyber security. This is not only for personal growth: it has also helped me…
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Introduction to Clifford Algebra (2006)
Clifford algebra gives a unified view of many things that otherwise would need to be understood separately.
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How to Tell a Mathematician You Love Them (2017)
For those who love numbers, and those who love them.
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Pathfinding Demystified (2014)
Pathfinding is one of these topics that usualy baffles game developers. The A* algorithm in particular is poorly understood, and the general belief seems to be that it’s arcane magic.
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Palindrome Day 20200202
Sonstiges - Learn more about palindromic dates in 2020 and in the near future. 2020-02-02 (YYYMMDD) or 02.02.2020 (DDMMYYY) and others.
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Let's remove quaternions from every 3D engine (2018)
To represent 3D rotations graphics programmers use Quaternions . However, Quaternions are taught at face value . We just accept their odd multiplication tables and other arcane definitions and use them as black boxes that rotate vectors in the ways we want. Why does $\mathbf{i}^2=\mathbf{j}^2=\mathbf{k}^2=-1$ and…
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Some Useful Probability Facts for Systems Programming
Probability problems come up a lot in systems programming, and I’m using that term loosely to mean everything from operating systems programming and networking, to building large online services, to creating virtual worlds like in games. Here’s a bunch of rough-and-ready probability rules of thumb that are deeply…
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Why numbering should start at zero (1982)
To denote the subsequence of natural numbers 2, 3, ..., 12 without the pernicious three dots, four conventions are open to us
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Entropy in the Universe
If you click on this picture, you’ll see a zoomable image of the Milky Way with 84 million stars: But stars contribute only a tiny fraction of the total entropy in the observable Universe. If…
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Projective Geometric Algebra Done Right
[This is part one of a two-part series. The second part can be found here: Symmetries in Projective Geometric Algebra .]
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Gamedev Tutorial: Dot Product, Rulers, and Bouncing Balls
[latexpage] 本文之中文翻譯在此 Prerequisites Trignometry Basics – Sine & CosineTrigonometry Basics – Tangent, Triangles, And CannonballsInverse Trigonometric Functions, Slope Angles, And Facing Objects Overview The dot product is a simple yet extremely useful mathematical tool. It encodes the relationship between two vectors'…
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Algorithm for Drawing Trees
I recently wanted to take a hierarchy of items and draw them in a nice tree structure. For example, a Family Tree. At the time, I thought “This will be easy, I’ll just Google for an alg…
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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...
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Using neural networks to solve advanced mathematics equations
Facebook AI has developed the first neural network that uses symbolic reasoning to solve advanced mathematics problems.
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Images Created from Prime Numbers
Inspired by James McKee’s Trinity Hall prime, physics researcher Gilles Esposito-Farese (of the self-descriptive pangram) has worked out that this 2,258-digit prime number: 53084469288402965415857953902888840109250315594591772197851275320 59910735745658243457138160802170063601085186072703319516241231606…
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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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Want to make good business decisions? Learn causality
In some organizations, earnest efforts to be “data-driven” devolve into a culture of false certainty in which the influence of metrics is dictated not by the...
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How strong is your knot?
MIT mathematicians and engineers have developed a mathematical model that predicts how stable a knot is, based on several key properties, including the number of crossings involved, and the direction in which the rope segments twist as the knot is pulled tight.
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Calculate the day of the week for any date in your head
The Doomsday Algorithm gives the day of the week for any date (and you can do it in your head)