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The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
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…
I read a good post by one of the authors of the Isabelle theorem prover, that got me thinking. The author, Lawrence Paulson, observed that most math proofs are trivial, but writing them (preferably with a proof assistant) is a worthwhile activity, for reasons similar to safety checklists - “Not every obvious statement…
Personal website of David R Hagen, scientific software engineer
In this post we’ll try to make sense of what we’re seeing, and try to understand what it means to invert a circle!
[This essay in Spanish] [This essay in French] [This essay in Chinese] In an old joke, two noblemen vie to name the bigger number. The first, after ruminating for hours, triumphantly announces "Eighty-three!" The second, mightily impressed, replies "You win." A biggest number contest is clearly pointless when the…
A recent paper The Reversal Curse points out an apparent failure in large large language models like GPT-4. From the abstract: We expose a surprising failure of generalization in auto-regressive large language models (LLMs). If a model is
Note: These pages make extensive use of the latest XHTML and CSS Standards . They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in…
The Fermi Paradox: There should be 100,000 intelligent alien civilizations in our galaxy — so why haven't we found any of them?
Clever student: I know! $latex x^{0}$ = $latex x^{1-1}$ = $latex x^{1} x^{-1}$ = $latex \frac{x}{x}$ = $latex 1$. Now we just plug in x=0, and we see that zero to the zero is one! Cleverer …
A deep dive into spectral analysis of diffusion models of images, revealing how they implicitly perform a form of autoregression in the frequency domain.
Rush Hour is a 6x6 sliding block puzzle invented by Nob Yoshigahara in the 1970s. It was first sold in the United States in 1996.
Every now and again you come across something that stretches your brain in a new direction. Last week I stumbled on a magic trick of a Choose Your Own Adventure: Al Leonardi’s Ace of Aces, a paper …
Discover the secrets behind hit music with our popular song chords analysis from 1300 tracks. Your songwriting journey begins here!
Recently, after being awake for longer than I should have, I started thinking about methods of remembering the number of days in each month of the year. There is a rhyme for it, and a way to count on your knuckles, but these didn’t satisfy me. I wondered if there was a mathematical formula for the problem, and upon…
Once upon a time we were creatures in the wilderness and we evolved the ability to hear sounds. Now here's an interesting thing, if you hear a sound of frequency f and others of frequency 2f, 3f, etc then there's a good chance these sounds come from the same object, due to the physical principle of resonance . And so…
Lambdaclass's blog about distributed systems, machine learning, compilers, operating systems, security and cryptography.
I wore my Prime Factorization Sweater to KidlitCon09 , and it shows up in all my pictures, so I think it’s time for me to explain it.
This post is about the magic constant 0x5f3759df and an extremely neat hack, fast inverse square root, which is where the constant comes from.
Learn cryptography in Go by building ciphers, hashes, password security, and encryption tools. Understand security beneath the library call.
An interactive exploration of quadtrees. Start with brute-force spatial search, build recursive space partitioning step by step, then use it for point lookups, range queries, nearest-neighbor search, collision detection, and image compression.
If you would like me to grade your answers, please send an email to cperciva-exam-part1@tarsnap.com [EDIT: I have now finished marking part 1 answers; please do not send me any more] with your answers to the above questions along with the following two:
Why x^2 isn't always x*x.
From the highly eclectic blog of Mark Dominus
"He's done it again!" was my first thought as I looked at the back of a postcard sized Pixar flier [1] which was covered in code. In the lower right corner, the blob of statements and expressions had been signed by none other than Andrew Kensler. For those who are not familiar with him, Andrew is the programmer who…
