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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.
New
The latest blog posts to take off on Hacker News. 2,391 posts.
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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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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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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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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…
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Cache Oblivious Algorithms
Cache-Oblivious Algorithms Cache-oblivious algorithms seemed incredible to me when I first heard about it in 6.854 (Advanced Algorithms). It’s relatively straightforward to imagine algorithms that utilizes information about page size $B$ and cache size $M$ to create efficient data structures. However, cache-oblivious…
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Logistic regression from scratch
Deep dives into Cryptography and Privacy.
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The largest city in each 10x10 degree latitude/longitude box
From the highly eclectic blog of Mark Dominus
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Twenty Proofs of Euler's Formula: V-E+F=2
Many theorems in mathematics are important enough that they have been proved repeatedly in surprisingly many different ways. Examples of this include the existence of infinitely many prime numbers , the evaluation of \(\zeta(2)\), the fundamental theorem of algebra (polynomials have roots), quadratic reciprocity (a…
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A Graphical Introduction to Lattices
Here is my (extended) family tree: Everyone in the tree shares at least one common ancestor and at least one common descendant. This ...
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The Sun seen through the Earth in “neutrino light” (2007)
Physics blog quantum computation
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The Map Is Not the Territory (2015)
The map is not the territory reminds us that our mental models of the world are not the same as the world itself. It cautions against confusing our abstractions and representations with the complex, ever-shifting reality they aim to describe.