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The future of interactive theorem proving?
This is a guest post, written by Zhangir Azerbayev. Zhangir is an undergraduate at Yale, majoring in computer science and mathematics. He completed this work while visiting Carnegie Mellon’s …
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Why are mathematicians so bad at arithmetic? (2017)
18 x 93 is… hey, look over there!
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Special Relativity and Middle-Earth
This post is an unofficial sequel to one of my first blog posts from 2007, which was entitled “Quantum mechanics and Tomb Raider”. One of the oldest and most famous allegories is Plato&…
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Making all your integers positive with zigzag encoding
You sometimes feel the need to make all of your integers positive, without losing any information. That is, you want to map all of your integers from 'signed' integers (e.g., -1, 1, 3, -3) to 'unsigned integers' (e.g., 3,2,6,7). This could be useful if you have a fast function to compress integers that fails to ……
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Visually symmetric words
The word "kayak" is a palindrome, but it isn't visually symmetric. The word "bud" is visually symmetric, but not a palindrome.
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Film grain synthesis in AV1 (2019)
Description of the film grain synthesis algorithm in AV1. This page provides information on the film grain synthesis algorithm and links for further study
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New method identifies the root causes of statistical outliers
Amazon ICML paper proposes information-theoretic measurement of quantitative causal contribution.
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The Fourth Operation: What Comes After Exponentiation
Tetration -- repeated exponentiation a fractional number of times.
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The Philosophy of Linear Algebra (2021)
Whenever a student wonders why linear algebra, matrices, and vectors are important, the response from teachers usually sounds like this:
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Where to wait for an elevator (2010)
Where do you stand in order to minimize the expected distance to walk to catch the first elevator that arrives? Maybe not where you think.
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Some neurons are active when adding, others when subtracting
Most elementary school children probably already know that three apples plus two apples add up to five apples. However, what happens in the brain during such calculations is still largely unknown. The current study by the Universities of Bonn and Tübingen now sheds light on this issue.
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Why a Slide Rule Works
Why does lining up two scales of a slide rule let you multiply numbers?
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Deconstructing Bézier Curves
Graphists, animators, game programmers, font designers, and other graphics professionals and enthusiasts are often working with Bézier curves. They're popular, extensively documented, and used pretty much everywhere. That being said, I find them being explained almost exclusively in 2 or 3 dimensions, which can be a…
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Explanation of Bitcoin’s Elliptic Curve Digital Signature Algorithm
Elliptic Curve Cryptography (ECC) has grown to be very popular in public-key cryptographic systems, most popularly used in Bitcoin. ECC is…
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Noether's Theorem in a Nutshell (2020)
Noether's theorem is an amazing result which lets physicists get conserved quantities from symmetries of the laws of nature. Time translation symmetry gives conservation of energy; space translation symmetry gives conservation of momentum; rotation symmetry gives conservation of angular momentum, and so on.
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Flipping until you are lost
Start with any triangulation of a convex polygon, and then repeatedly choose a random diagonal and flip it, replacing the two triangles it borders with two d...
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What use is mental math in 2022?
The ability to quick estimates is still valuable, maybe more valuable than it used to be.
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The examples in the textbooks are not representative of real world problems
Bill Harris points to this cartoon from Randall Munroe. I think he (Munroe) is really on to something here. Not about Bayes’s theorem but about the sorts of examples that are in textbooks.
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Galactic-Scale Energy (2011)
[ An updated treatment of this material appears in Chapter 1 of the Energy and Human Ambitions on a Finite Planet (free) textbook , and also appears as part of an article in Nature Physics in 2022.]
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Torsors (2010)
When you first read about "torsors", they're bound to seem a bit too darn sophisticated for their own good. Mostly this is because nobody explains them very well. So, I want to convince you that they're actually very simple and natural. I'll do this by giving you three examples from physics: