991
Why do arrays start at 0?
It's not the reason you think. No, it's not that reason either.
New
The latest blog posts to take off on Hacker News. 2,851 posts.
992
Visual Sum of Cubes
This article discusses a ‘visual’ derivation of the formula for 1³+2³+…+n³.
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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 …
995
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…
996
Quaternions: A Practical Guide
AnyLeaf Articles: Quaternions: A practical guide
997
Efficient simulation through linear algebra
I spent a lot of time working on a project in which physically plausible simulation of soft materials with pressure chambers was a key part, and in doing so, we managed to improve a part of our simulation by a significant amount. I was very happy with how this small part of the whole system turned out, and I've been…
998
Algorithms you should know before you take system design interviews
I put together a list and explained why they are important.
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1000
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.
1001
Let's Talk SkipList
the forgotten data structure (not really)
1002
Juris Hartmanis 1928–2022
A sure foundation for Computational Complexity source—wonderful 2015 CACM interview Juris Hartmanis passed away this morning. He was a professor in Cornell’s computer science department…
1003
Shor, I’ll do it (2007)
I’ve been talking a lot recently about how quantum algorithms don’t work. But last week JR Minkel, an editor at Scientific American, asked me to write a brief essay about how quantum al…
1004
The Fourth Operation: What Comes After Exponentiation
Tetration -- repeated exponentiation a fractional number of times.
1005
Knuth changes his mind on Bernoulli number B_1
(I thank Yoshiyuki Kotani for this identity. We'll be able to use the same idea again in 2024 and 2027!)
1006
Timsort (2019)
Timsort: A very fast , O(n log n), stable sorting algorithm built for the real world — not constructed in academia. Timsort is a sorting algorithm that is efficient for real-world data and not created in an academic laboratory. Tim Peters created Timsort for the Python programming language in 2001.
1007
Is the Kalman filter just a low-pass filter?
Exploring the relationship between Kalman filtering and optimal frequency domain filtering.
1008
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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“Burning Ship” fractal
The images described here are generated by analysing the following series for each point (c x ,c y ) on the plane.
1011
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.]
1012
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.
1013
New method identifies the root causes of statistical outliers
Amazon ICML paper proposes information-theoretic measurement of quantitative causal contribution.
1014
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
1015
The Algorithm for Hard Problems: Shake and Pull Gently
(Or, “regularized greedy algorithms and their applications.”) James Gilles “Algorithm” is one of those words that sounds fancier than it really deserves. We hear all the time about the “facebook algorithm”, the “youtube algorithm”, “high frequency trading algorithms”, “artificial intelligence algorithms”, and so on…
1016
I disagree with Turing and Kahneman regarding statistical evidence (2014)
It’s funny. I’m the statistician, but I’m more skeptical about statistics, compared to these renowned scientists.
1017
Einstein-Bohr debate settled once and for all
In Steven Pinker’s guest post from last week, there’s one bit to which I never replied. Steve wrote: After all, in many areas Einstein was no Einstein. You [Scott] above all could speak…
1018
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.
1019
Math on GitHub: Following Up
About six weeks ago, on May 19, 2022, GitHub released Math support on Markdown. At the time of the release, it received criticism for being ill-designed and buggy. I, too, wrote a blog post about it.
1020
A Random Distribution of Wealth (2017)
W hat happens, if 100 persons in a room are given $100 each and give away a Dollar to one randomly chosen person in this room each tick of the clock? How is wealth distributed over time by pure chance?