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Going Critical
Learn how things spread with playable simulations
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I found two identical packs of Skittles among 468 packs
This article was discussed on Hacker News, and was cited in The Mathematical Gazette. Introduction This is a follow-up to a post from earlier this year discussing the likelihood of encountering two…
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93% of Paint Splatters Are Valid Perl Programs
TLDR: read the paper and view the gallery of pretty Perl programs. In this paper, we aim to answer a long-standing open problem in the programming languages community: is it possible to smear paint on the wall without creating valid Perl?
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Mitchell Feigenbaum (1944–2019), 4.66920160910299067185320382…
Stephen Wolfram shares his memories of mathematical physicist Mitchell Feigenbaum. Also a detailed discussion of his work and big discovery of a universal constant for functions approaching chaos via period doubling.
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Visual Information Theory (2015)
I love the feeling of having a new way to think about the world. I especially love when there’s some vague idea that gets formalized into a concrete concept. Information theory is a prime example of this.
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Eigenvectors from eigenvalues
Peter Denton, Stephen Parke, Xining Zhang, and I have just uploaded to the arXiv the short unpublished note “Eigenvectors from eigenvalues”. This note gives two proofs of a general eige…
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Steve Wozniak's floating point routines for the 6502
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Think in Math, Write in Code
Programmers love to discuss programming languages. We not only debate their technical merits and aesthetic qualities, but they become integrated into our personal identities, along with the values and traits that we associate with them. Some even defend a form of Linguistic Determinism that thinking is confined to…
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New pathfinding algorithm
New pathfinding algorithm Oxyd Last week we mentioned the change to make biters not collide with each other, but that wasn’t the only biter-related update we released this past week. Somewhat coincidentally, this week’s updates have included something I’d been working on for a few weeks before – an upgrade to the…
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Elliptic Curve Cryptography Explained
Fang-Pen Lin's blog about programming
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Dynamic Programming for Technical Interviews
Probably the first in a multi-part series on DP.
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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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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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Knuth on Huang's Sensitivity Proof: “I've got the proof down to one page” [pdf]
The Sensitivity Conjecture, which I blogged about here, says that, for every Boolean function f:{0,1}n→{0,1}, the sensitivity of f—that is, the maximum, over all 2n input strings x∈{0,1}n, of…
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Xor Filters: Faster and Smaller Than Bloom Filters
In software, you frequently need to check whether some objects is in a set. For example, you might have a list of forbidden Web addresses. As someone enters a new Web address, you may want to check whether it is part of your black list. Or maybe you have a large list of already used … Continue reading Xor Filters…
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A generalised solution to distributed consensus
A generalised solution to distributed consensus Howard & Mortier, arXiv’19 This is a draft paper that Heidi Howard recently shared with the world via Twitter, and here’s the accompanying …
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Random Forests for Complete Beginners
The definitive guide to Random Forests and Decision Trees.
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An Almost-Secret Algorithm Researchers Used to Break Thousands of RSA Keys
RSA encryption allows for anyone to send me messages that only I can decode. To set this up, I select two large random primes $latex p$ and $latex q$ (each of which is hundreds of bits long), and r…
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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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Cities: Skylines Is Turing Complete
(Non-clickbait title: building a 4-bit adder in Cities:Skylines.)
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Second-Order Thinking: What Smart People Use to Outperform (2016)
Second-order thinking is a mental model that smart people like Warren Buffett & Howard Marks use to avoid problems. Read this article to learn how it works.
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Simpson’s Paradox (2016)
A riveting tale of how good data can lead to bad decisions.
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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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How random can you be?
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