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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.
Most cited
Posts that commenters keep linking to, ranked by how many different people have cited them in Hacker News comments. 494 posts.
152
Intel Underestimates Error Bounds by 1.3 Quintillion
Intel’s manuals for their x86/x64 processor clearly state that the fsin instruction (calculating the trigonometric sine) has a maximum error, in round-to-nearest mode, of one unit in the last place…
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Why Do Buses Bunch?
Created by Lewis Lehe (of Setosa and UC Berkeley Trans. Eng. ) with design and art by Dennys Hess . Thanks to Ian Johnson for good advice. Tools: d3 , Angular Material , Coffeescript , Browserify , Gulp and Five-Hour Energy Drink .
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Why there is no Hitchhiker’s Guide to Mathematics for Programmers
For those who aren’t regular readers: as a followup to this post, there are four posts detailing the basic four methods of proof, with intentions to detail some more advanced proof techniques in the future. You can find them on this blog’s primers page. Do you really want to get better at mathematics? Remember when…
157
Algorithmic symphonies from one line of code
Lately, there has been a lot of experimentation with very short programs that synthesize something that sounds like music. I now want to sha...
158
The algebra and calculus of algebraic data types
Just as algebra is fundamental to the whole of mathematics, algebraic data types (ADTs) are fundamental to many common functional programming languages. They’re the primitives upon which all of our richer data structures are built, including everything from sets, maps, and queues, to bloom filters and neural networks .
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Nearly all binary searches and mergesorts are broken (2006)
Posted by Joshua Bloch, Software EngineerI remember vividly Jon Bentley's first Algorithms lecture at CMU, where he asked all of us incoming Ph.D. ...
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The power of two random choices
In many large-scale web services, multiple layers of stateless and stateful services are seperated by load balancers. Load balancing can be done with dedicated hardware, with dedicated software load balancers, using DNS trickery or through a load-balancing mechanism in the client. In large systems, the resources and…
162
So You Think You Have a Power Law (2007)
Regular readers who care about such things — I think there are about three of you — will recall that I have long had a thing about just how unsound many of the claims for the presence of power law distributions in real data are, especially those made by theoretical physicists, who, with some honorable exceptions…
163
A step by step backpropagation example (2015)
Background Backpropagation is a common method for training a neural network. There is no shortage of papers online that attempt to explain how backpropagation works, but few that include an example…
164
Eytzinger Binary Search
This tutorial is loosely based on a 46-page paper by Paul-Virak Khuong and Pat Morin “Array layouts for comparison-based searching” and describes one particular way of performing efficient binary search by rearranging elements of a sorted array in a cache-friendly way.
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Prospecting for Hash Functions
Update 2022 : TheIronBorn has found even better permutations using a smarter technique. That thread completely eclipses my efforts in this article.
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Binary Lambda Calculus (2020)
Binary lambda calculus ( BLC ) is a minimal, pure functional programming language invented by John Tromp in 2004, 1 based on a binary encoding of the untyped lambda calculus in De Bruijn index notation.
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Airfoil
Interactive article explaining the physics of an airfoil and what makes airplanes fly
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Going Critical
Learn how things spread with playable simulations
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Knuth's Art of Computer Programming, V 4B, has gone into print
(I'm still looking for the catchiest way to appreciate the number MMXXVI. Exercise 7.2.1.6–122 gives 1234+.5*6+789 and -1+2345*6/7+8+9 and 1+(2/3)*45*67.8-9 ; other suggestions are welcome. The most elegant that I've seen so far is a beauty that was suggested independently by Arnaud Lefebvre and by Evangelos…
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Too much efficiency makes everything worse (2022)
This blog is intended to be a place to share ideas and results that are too weird, incomplete, or off-topic to turn into an academic paper, but that I think may be important. Let me know what you think! Contact links to the left.
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Music theory for nerds
Not music nerds, obviously. I don’t know anything about music. I know there are letters but sometimes the letters have squiggles; I know an octave doubles in pitch; I know you can write a pop song with only four chords. That’s about it. The rest has always seemed completely, utterly arbitrary. Why do we have twelve…
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AlphaGeometry: An Olympiad-level AI system for geometry
Our AI system surpasses the state-of-the-art approach for geometry problems, advancing AI reasoning in mathematics
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Programming with Categories
In this course we explain how category theory—a branch of mathematics known for its ability to organize the key abstractions that structure much of the mathematical universe—has become useful for writing elegant and maintainable code. In particular, we'll use examples from the Haskell programming language to motivate…
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How you eat corn on the cob predicts whether you're an analyst or algebraist
I like learning about odd connections between disparate things. This probably is the oddest example that I know. Broadly speaking, mathemat...
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Fields medalist Tim Gowers: Elsevier — my part in its downfall
The Dutch publisher Elsevier publishes many of the world’s best known mathematics journals, including Advances in Mathematics, Comptes Rendus, Discrete Mathematics, The European Journal of Co…
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MathBox 2: PowerPoint Must Die
PowerPoint must die.
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The 8000th Busy Beaver number eludes ZF set theory (2016)
I’ve supervised a lot of great student projects in my nine years at MIT, but my inner nerdy teenager has never been as personally delighted by a project as it is right now. To…
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Down with Determinants (1995)
This paper was published in the American Mathematical Monthly 102 (1995), 139-154.
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Darts, Dice, and Coins: A beautiful article on a beautiful algorithm
Earlier this year, I asked a question on Stack Overflow about a data structure for loaded dice . Specifically, I was interested in answering this question: