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Basic skeletal animation with geometric algebra
Klein - Realtime Projective Geometric Algebra
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 173 posts.
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A Pretty Good Mathematical Model of Perfectionism
I struggle with perfectionism. Well, not so much “struggle with” — I’m f*cking great at it. It comes naturally. There are some upsides, but perfectionism is also associated …
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Why numbering should start at zero (1982)
To denote the subsequence of natural numbers 2, 3, ..., 12 without the pernicious three dots, four conventions are open to us
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Chesterton’s Fence: A Lesson in Second Order Thinking
A core component of making great decisions is understanding previous decisions. If we don’t understand how we got “here,” we run the risk of making things much worse.
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Finding Mona Lisa in the Game of Life
Using a SAT solver to find Game of Life states that turn into pictures.
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Cofactor Explained: Clearing Elliptic Curves' dirty little secret
Efficient elliptic curves tend not to have a prime order. This discusses the problems this causes, and the solutions.
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Binary Decision Diagrams (2010)
Suppose you want to visit every state capitol exactly once, traveling on highways. Which route is shortest? Which route is longest? What is the mean and standard deviation of all the routes?
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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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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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Summary of all the MIT Introduction to Algorithms lectures (2009)
As you all may know, I watched and posted my lecture notes of the whole MIT Introduction to Algorithms course. In this post I want to summarize all the topics that were covered in the lectures and point out some of the most interesting things in them. Actually, before I wrote this article, I had started writing an...
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Logistic regression from scratch
Deep dives into Cryptography and Privacy.
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Plotting patterns in music with a fantasy record player
A blog about signals, programming, music, and other stuff.
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Back-of-the-envelope estimates of next quarter’s unemployment rate
Layoffs are certainly one of the effects of battling COVID-19. What sort of unemployment rate might we see in the second quarter of 2020?
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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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Don't bet on the most likely winner
It's all relative
109
Learning to Play the Chaos Game
I, Thomasina Coverly, have found a truly wonderful method whereby all the forms of nature must give up their numerical secrets and draw themselves through number alone…
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Peter Montgomery Has Died
Peter was born in San Francisco, California, on September 25, 1947. He went to UC Berkeley in 1967 and received a BA in Mathematics in 1969 and an MA in 1971. Peter’s undergraduate advisor was Derrick H. Lehmer, an excellent match given Peter’s research interests since high school: integer factorization.
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Markov Chain Monte Carlo (MCMC) Sampling, Part 1: The Basics (2019)
In this first post of Tweag’s four-part series on Markov chain Monte Carlo sampling algorithms, you will learn about why and when to use them and the theoretical underpinnings of this powerful class of sampling methods. We discuss the famous Metropolis-Hastings algorithm and give an intuition on the choice of its free…
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The polls messed up
To continue our post-voting, pre-vote-counting assessment (see also here and here ), I want to separate two issues which can get conflated: 1. Problems with poll-based election forecasts.
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Machine Learning, Kolmogorov Complexity, and Squishy Bunnies (2019)
Computer Science, Machine Learning, Programming, Art, Mathematics, Philosophy, and Short Fiction
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Options for giving math talks and lectures online
As part of social distancing efforts to slow down the spread of the novel coronavirus, several universities have now transitioned, or begun transitioning, to online teaching models. (My home unive…
116
Transformers Are Graph Neural Networks
Engineer friends often ask me: Graph Deep Learning sounds great, but are there any big commercial success stories? Is it being deployed in practical applications? Besides the obvious ones–recommendation systems at Pinterest, Alibaba and Twitter–a slightly nuanced success story is the Transformer architecture, which…
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Why neural networks struggle with the Game of Life
The Game of Life is based on very simple rules, but artificial neural networks struggle to learn its rules through the classic deep learning training process.
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The Complete Idiot’s Guide to the Independence of the Continuum Hypothesis
A global pandemic, apocalyptic fires, and the possible descent of the US into violent anarchy three days from now can do strange things to the soul. Bertrand Russell—and if he’d done no…
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Doing a math assignment with the Lean theorem prover
Note: this post was written for Lean 3; the latest version, Lean 4, is a very different language. Turn back the clock to 2009: a confused physics major newly infatuated with math and computer science, I enrolled in MATH 273: Numbers and Proofs at the University of Calgary. This wasn’t my first encounter with…
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An equation that takes Pythagoras to a new level
Unbelievably enough, it all comes back to Pythagoras.