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Cities: Skylines Is Turing Complete
(Non-clickbait title: building a 4-bit adder in Cities:Skylines.)
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The latest blog posts to take off on Hacker News. 2,391 posts.
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Steve Wozniak's floating point routines for the 6502
Create beautiful emails, automate campaigns, and track performance. Try it now and see how our tools can drive your business.
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It’s Time for Some Queueing Theory
Queueing theory is the scientific study of waiting in line. It can apply to familiar lines like those at the grocery store or bank but also to things like web s
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Real-world dynamic programming: seam carving
Dynamic programming has a reputation as a technique you learn in school, then only use to pass interviews at software companies. Indeed, most developers do not regularly work on problems where dynamic programming is needed. Ultimately, dynamic programming is a technique for efficiently solving problems that can be…
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What is ergodicity? (2016)
Why are election polls often inaccurate? Why is racism wrong? Why are your assumptions often mistaken? The answers to all these questions and to many others have a lot to do with the non-ergodicity…
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Adventure Games and Eigenvalues (2017)
Do adventure games have dead ends? The author of The Teeny Tiny Mansion proves the absence of dead ends in that game via formal verification (in particular, with the help of the cbmc model-checking program ). Here I’ll demonstrate how to prove the same thing via Markov theory. The Markov approach requires more…
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Logistic Regression from Bayes’ Theorem
In this post we’ll explore how we can derive logistic regression from Bayes’ Theorem. Starting with Bayes’ Theorem we’ll work our way to computing the log odds of our problem and the arrive at the inverse logit function. After reading this post you’ll have a much stronger intuition for how logistic
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Quantum transitions take time – the news is its experimental demonstration
A number of people have asked me to weigh in on this story in Quanta Magazine (based on this paper [ PDF version ] and also reported in t...
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Solving Programming Puzzles Without Using Your Brain
This post is a write-up of a solution to part of a programming puzzle I did yesterday. It’s a little different than the usual “solution + theory” approach, though: I’m going to talk about the actual steps you’d need to take to get to the solution (i.e. what to google, what intermediate code looks like, etc.). Often…
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Interview on ”Bayesian Statistics the Fun Way”
Lambdaclass's blog about distributed systems, machine learning, compilers, operating systems, security and cryptography.
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A Visual Introduction to Morse Theory
In a previous article , I already introduced manifolds and their, ahem, manifold ways. Among the many interesting comments I received about this article, some were dealing with a basic question, namely how to measure the properties of a manifold. In this article, I want to present a few concepts from Morse theory …
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Exponential Economist Meets Finite Physicist (2012)
[ An updated treatment of some of this material appears in Chapter 2 of the Energy and Human Ambitions on a Finite Planet (free) textbook, also mirrors a 2022 article in Nature Physics . . ]
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Translating math into code with examples in Java, Racket, Haskell, Python (2011)
These structures are so universal that most research papers in the theory of computation, programming languages and formal methods present concepts in terms of discrete mathematics rather than code.
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Logical fallacies in software engineering
How our mind falls short trying to short cut.
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Von Neumann’s critique of automata theory and logic in computer science (1947)
These remarks from “THE GENERAL AND LOGICAL THEORY OF AUTOMATA” 1947 are enormously insightful – no surprise. Von Neumann essentially predicts the emergence of the field of analysis of algorithms and algorithmic complexity. Not only does he point out the importance of understanding how many steps it will take to carry…
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What's the difference between 0/0 and 1/0?
From the highly eclectic blog of Mark Dominus
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Notes on Weight Initialization for Deep Neural Networks
Neural networks involve long sequence of multiplications, usually between a matrix and a vector, say \(a*x\). The result of this sequence of multiplications will either have a huge magnitude or be reduced to 0. We can divide \(a\) by a number ( scaling_factor ) to scale down its magnitude to the right level. Proper…
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Modern SAT solvers: fast, neat and underused
In the previous two parts we used a SAT solver as a black box that we feed input into, and it will (usually quickly) spit out an answer. In this part, we will look at how SAT solvers work and what heuristics and other tricks they employ in their quest for performance.
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I Got a Knuth Check for 0x$3.00
Donald Knuth is a computer scientist who is so committed to the correctness of his books that he offers one US hexadecimal dollar ($2.56, 0x$1.00) for any “bug” found in his books, where a bug is anything that is “technically, historically, typographically, or politically incorrect”. I wanted to get a Knuth check for…
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Matrices as Tensor Network Diagrams
In the previous post, I described a simple way to think about matrices, namely as bipartite graphs. Today I'd like to share a different way to picture matrices—one which is used not only in mathematics, but also in physics and machine learning. Here's the basic idea. An $m\times n$ matrix $M$ with real entries…
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Going Critical
Learn how things spread with playable simulations
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Faster arithmetic by flipping signs
Over the years, I picked up a number of tricks to optimize code. Today I’ll talk about one of them.