Posts that commenters keep linking to, ranked by how many different people have cited them in Hacker News comments. 417 posts.
Operations in Lisp, Scheme, and other dynamically-typed languages typically dispatch on representational type information rather than intentional type information. Several broad classes of bugs and confusions can be traced to improper attempts to recover intentional type information from representation types.
Thanks to Alan R. Wilson for correcting a two-word typo involving GPS satellites. Thanks to Aron Yoffe for suggesting the newtonian comparison. Thanks to Tom Fuchs for suggesting the analogy to the stone thrown upwards. Fuel numbers added by Don Koks, 2004. Updated by Phil Gibbs, 1998. Thanks to Bill Woods for…
If you read any personal finance forums late last year, there's a decent chance you ran across a question from someone who was desperately trying to lose money before the end of the year. There are a number of ways someone could do this; one commonly suggested scheme was to buy put options that were expected to expire…
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.
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…
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 .
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…
Lately, there has been a lot of experimentation with very short programs that synthesize something that sounds like music. I now want to sha...
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…
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…
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…
Update 2022 : TheIronBorn has found even better permutations using a smarter technique. That thread completely eclipses my efforts in this article.
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.
Interactive article explaining the physics of an airfoil and what makes airplanes fly
Learn how things spread with playable simulations
(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…
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.
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…
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…
I like learning about odd connections between disparate things. This probably is the oddest example that I know. Broadly speaking, mathemat...
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…
PowerPoint must die.
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…
This paper was published in the American Mathematical Monthly 102 (1995), 139-154.
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:
