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The Recursive Universe
A few years ago I came across this video, showing a complex machine built entirely in Conway’s Game of Life:
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The latest blog posts to take off on Hacker News. 2,851 posts.
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How many pieces can a puzzle have?
Patrick Honner tweeted a few days ago: My 7 yo pointed out that our 300 piece puzzle actually contains 18 x 18 = 324 pieces and I just don’t know what to believe anymore. — Patrick Honner (@M…
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A circuit-like notation for lambda calculus (2015)
Lately, I’ve been playing around with inventing a visual writing system for lambda calculus.
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Entropy explained, with sheep (2016)
An explorable blog post about entropy, with sheep.
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Banned math book
The applied math classic Courant & Hilbert was banned in Nazi Germany. The US seized the copyright and published an English edition.
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Bloom filters debunked: Dispelling 30 Years of bad math with Coq
There's this rather nifty feature of modern web browsers (such as Firefox or Chrome ) where the browser will automatically warn the user if they happen to navigate to a " malicious " URL:
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Is every game of Slay the Spire winnable?
There is a lot of randomness in a game of Slay the Spire. From the cards and relics offered, to the potions dropped, to the map layouts and random encounters, very little remains the same between two playthroughs. This is part of the beauty of the game, forcing you to adapt and make the most out of the resources you…
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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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Optimizing 128-bit Division
When it comes to hashing, sometimes 64 bit is not enough, for example, because of birthday paradox — the hacker can iterate through random $latex 2^{32}$ entities and it can be proven that wi…
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Continuations by example: Exceptions, time-traveling search, threads, and more
Continuations are the least understood of all control-flow constructs. This lack of understanding (or awareness) is unfortunate, given that continuations permit the programmer to implement powerful language features and algorithms, including exceptions, backtracking search, threads, generators and coroutines.
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How SHA-2 works step-by-step (SHA-256)
Learn to code from scratch with hands-on lessons, a structured curriculum, and real projects. Stop watching tutorials, start writing code for free now.
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Hindley-Milner Type Inference (2012)
Robin Milner's type system with parametric polymorphism was a significant advance over the systems of Russell and Church. Arguably it is the ability to use type-variables that makes higher order logic a practical vehicle for proving non-trivial theorems. The Hindley-Milner algorithm is used to automatically infer…
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The stable marriage problem and modern dating
Attempting to model modern dating using the lessons learned from the stable marriage problem
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Division by zero in type theory: a FAQ
How can a theorem prover use the convention that 1/0=0 and still be consistent?
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Don't bet on the most likely winner
It's all relative
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2+1=4, by quinoa
I was struck the other day by the following: The cooking instructions on my Bob’s tri-colored quinoa package said to combine 2 cups of water with 1 cup of dried quinoa, which would ultimately create 4 cups of cooked quinoa. See image above. My first reaction was to believe …
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Sphere Eversion
Topology is the study of the properties of geometric objects which aren’t changed by continuous deformation. A standard low-grade math joke is that toplogists consider a coffee mug and a doughnut equivalent because they’re both torii—(pauses for laughter)—one can be continuously deformed into the other, called a…
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Crooked to the Millimetre
The technology pioneered by the ETH spin-off incon.ai allows blocks to be positioned with pinpoint accuracy, creating structures with aesthetic designs and augmented acoustics.
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Weighing a Car with Tire Pressures
The first thing I wanted to do with my Saab 96 was to establish a baseline weight.
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Better Geometry Through Graph Theory (2018)
A few months ago, I decided to implement set operations on curved regions. I had the the canonical textbook on computational geometry , which described approaches for polygons comprised of straight lines, and it seemed like other projects had extended these techniques to parametric curves . I figured it would take a…
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GNU GCC does not round floating-point divisions to the nearest value
I know that floating-point arithmetic is a bit crazy on modern computers. For example, floating-point numbers are not associative: 0.1+(0.2+0.3) == 0.599999999999999978 (0.1+0.2)+0.3 == 0.600000000000000089 But, at least, this is fairly consistent in my experience. You should simply not assume fancy properties like…