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How long is that Bézier?
Blog of Raph Levien.
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
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An automatic theorem proving project
I am very happy to say that I have recently received a generous grant from the Astera Institute to set up a small group to work on automatic theorem proving, in the first instance for about three y…
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Reversible computing with mechanical links and pivots
With the concern that “Moore’s Law is dead,” new interest has grown for unconventional forms of computing. This includes:
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Lindenmayer systems
A Lindemayer system or LSystem for short consists of an alphabet of symbols that can be used to make strings, a collection of production that expand each symbol into some larger string of symbols, an initial “axiom” string from which to begin construction, and a mechanism for translating the generated strings into…
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Pseudo-bandlimited pixel art filtering in 3D: A mathematical derivation
Recently, I’ve been playing Octopath Traveler, and I’m very disappointed with the poor texture filtering seen in this game. It is PS1-level, with severe shimmering artifacts, which ruins the nice pixel art. Tastefully merging retro pixel art with 3D environment is a very cool aesthetic to me, so I want it to look…
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What should we tell our students?
[This is a guest post by Álvaro Lozano-Robledo. This blog post was initially written in a different file format and converted using AI. — T.] TL;DR: Keep calm and carry on studying math. I wo…
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The Greedy Doctor Problem
TL;DR: How to reason about people who are smarter than you. A few proposals, interspersed with reinforcement learning and humorous fiction. Ending on a surprising connection to logical inductors.
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The Advisory Group on Mathematics and Artificial Intelligence
[This is a guest post by the Advisory Group on Mathematics and Artificial Intelligence. This blog post was initially written in a different file format and converted using AI. — T.] We would …
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Dividing unsigned 8-bit numbers
Division is quite an expensive operation. For instance, latency of the 32-bit division varies between 10 and 15 cycles on the Cannon Lake CPU, and for Zen4 this range is from 9 to 14 cycles. The latency of 32-bit multiplication is 3 or 4 cycles on both CPU models.
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Learning math? Think like a cartoonist
What's the essential skill of a cartoonist? Drawing ability? Humor? A deep well of childhood trauma? I'd say it's an eye for simplification, capturing the…
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Everything Is Correlated
Anthology of sociology, statistical, or psychological papers discussing the observation that all real-world variables have non-zero correlations and the implications for statistical theory such as ‘null hypothesis testing’.
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Bayesian ranking of items with up and downvotes or 5 star ratings
Evan Miller wrote a great article How Not To Sort By Average Rating . He shows that simple formulas like score = upvotes - downvotes or score = upvotes / (upvotes + downvotes) don’t work. He proposes to use the lower bound of the Wilson score confidence interval. The formula is complicated and somewhat of a hack…
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A reasonably speedy Python ray tracer
Cyrille Rossant's small ray-tracer is an nice self-contained Python program (using NumPy) that renders this 400×300 image in about 15 seconds on a fast PC:
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History of Maths for Beginners
In the comments on my recent post on books on the history of maths Fernando Q. Gouvêa jumped in to draw attention to the book Math Through the Ages: A Gentle History for Teachers and Othe…
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Elo sucks – better multiplayer rating systems for smaller games (2019)
Elo does not work when different skill levels must play against each other. Can we make a better system?
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Is Matrix Multiplication Ugly?
A few weeks ago I was minding my own business, peacefully reading a well-written and informative article about artificial intelligence, when I was ambushed by a passage in the article that aroused …
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What if you had bought Apple stock instead of that iPod?
Currently, Apple's stock is at an all time high. A share today is worth over 40 times its value seven years ago. So, how much would you have today if you purchased stock instead of an Apple product? See for yourself in the table below. A huge thanks to everymac.com for the original prices and release dates. All values…
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"The worst algorithm in the world?"
You know the Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, … Each number is the sum of the previous two. Let’s say the zeroth Fibonacci number is zero, so: $latex \begin{array}{r@{\…
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Entropy of a Large Language Model output
Large language models like ChatGPT & Claude have become ubiquitous in today’s world. I visited a friend for the New years eve and was impressed by how ChatGPT was being extensively used within the family. The friend’s little kid is going to grow up in a world, where turning to large language models (LLM) for quick…
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Simulating and Visualising the Central Limit Theorem
Update: this post was discussed on Hacker News I completed a Computer Science degree at uni, and bundled a lot of maths subjects in as electives: partial differential equations, vector calculus, discrete maths, linear algebra.
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Where do those undergraduate divisibility problems come from?
Chris Grossack's math blog and professional website.
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Gradient Descent Models Are Kernel Machines
This paper shows that models which result from gradient descent training (e.g., deep neural nets) can be expressed as a weighted sum of simi...