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Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,391 posts.
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The bunkbed conjecture is false
What follows is an unusual story of perseverance. We start with a conjecture and after some plot twists end up discussing the meaning of truth. While the title is a spoiler, you might not be able t…
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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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Gödel's Incompleteness Theorem in Bash
Gödel’s first incompleteness theorem states that there are mathematical statements that can neither be proven or disproven. His proof is fairly difficult to ...
935
Primitive Recursive Functions for a Working Programmer
Programmers on the internet often use Turing-completeness terminology. Typically, not being Turing-complete is extolled as a virtue or even a requirement in specific domains. I claim that most such discussions are misinformed --- that not being Turing complete doesn't actually mean what folks want it to mean, and is…
936
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.
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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 Basic Introduction to Neural Networks (2007)
Although the mathematics involved with neural networking is not a trivial matter, a user can rather easily gain at least an operational understanding of their structure and function.
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City street orientations around the world
This post is adapted from this research paper that you can read/cite for more info. It analyzes and visualizes 100 cities around the world.
940
Exact Polygonal Filtering: Using Green's Theorem and Clipping for Anti-Aliasing
Efficient filtering of polygonal shapes with closed-form solutions based on Green’s theorem with piecewise-polynomial filters (e.g. box/bilinear/bicubic).
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Are polynomial features the root of all evil? (2024)
High-degree polynomial features aren’t inherently unstable: the power basis and unscaled inputs are. This post shows how regularization and Bernstein polynomials make polynomial regression behave.
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A new Sudoku layout with 81 uniquely shaped cells
My journey making a Sudoku variant that doesn’t have rows or columns
943
Dissecting Lemire's nearly divisionless random number generator
A very late blog post announcing the readability contest winners, a new (very) annotated implementation, and a surprising sort-of security issue found along the way.
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Rolling Shutter Simulation in C
The most recent Smarter Every Day (#172) explains a phenomenon that results from rolling shutter . You’ve likely seen this effect in some of your own digital photographs. When a CMOS digital camera captures a picture, it reads one row of the sensor at a time. If the subject of the picture is a fast-moving object…
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What Monoids teach us about software
Monoids are a pretty interesting concept in software development. Monoids are everywhere. Monoids are simple yet powerful. And Monoids have a lot to teach us about software, in particular about com…
948
40k coin tosses yield ambiguous evidence for dynamical bias
However, no experiment with actual coin-tosses has been done to investigate whether the predicted effect is empirically observed. Diaconis et al noted, correctly, that to estimate the probability with a S.E. of 0.1% would require 250,000 tosses, but this seems unnecessarily precise. Let's work with numbers of tosses…
949
Non-Transitive Dice
We describe a set of very unusual dice, and a two player game where you will always have the advantage. You can even teach your opponent how the game works, yet still win again! Finally, we will describe a new game for three players where you can expect to beat both players at the same time! Watch James Grime and…
950
Quick, How Might the Alien Spacecraft Work?
How Stephen Wolfram helped with the theory of interstellar travel, communication with aliens and questions from the actors in “Arrival”, the movie.
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Egoless Mathematics in the AI Era
[This is a guest post by Karthik C. S., Amit Sahai, and Jie Xue. This blog post was initially written in a different file format and converted using AI. — T.] This is a good time for mathemat…
953
Alligator Eggs
In 2007, I met Philip Wadler at a conference, who mentioned to me that he wanted to teach lambda calculus to his eight-year-old children.
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Analysis of suspected MH370 pings recorded by Ocean Shield
So this is a bit of a deviation from my normal MATLAB oriented posts. In-fact MATLAB was not used once in this analysis! I've been followi...
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Role of Algorithms
This is lobste.rs comment as an article, so expect even more abysmal editing than usual.
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Adventures in algorithmic trading on the Runescape Grand Exchange
Runescape has been a game near and dear to my heart since I was a child. Though I do not actively play anymore, it still functions as an interesting programming project substrate. Most recently, I created a bot that automatically executes trades on the Grand Exchange in order to conduct market making via common…
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Palomar: A registry of Lean verified mathematics
In recent months there has been a proliferation of AI-generated proofs of various old and new results, some of which have been formalized in the proof assistant language Lean. However, checking tha…
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Gravity's Oldest Puzzles
Every now and then the orbital motion of a body doesn’t match our prediction. And that might lead to interesting discoveries.
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Converting a fisheye image into a panoramic, spherical or perspective projection
The source code implementing the projections below is only available on request for a small fee. It includes a demo application and an invitation to convert an image of your choice to verify the code does what you seek. For more information please contact the author .
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Gamifying propositional logic: QED, an interactive textbook
About six years ago on this blog, I started thinking about trying to make a web-based game based around high-school algebra, and ended up using Scratch to write a short but playable puzzle game in …