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The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
Rasmus Kyng has written the near-perfect algorithm. It computes the maximum transport flow at minimum cost for any kind of network – be it rail, road or electricity – at a speed that is, mathematically speaking, impossible to beat.
I’m excited to share a 3 state, 3 symbol Turing Machine that cannot be proven to halt or not (when starting on a blank tape) without solving a Collatz-like problem. Therefore, solving the \(BB(3, 3)\) problem is at least as hard as solving this Collatz-like problem, a class of problem for which Paul Erdős famously…
Sleuthing into the history of a 1930 book on quantum mechanics previously owned by Alan Turing and a lambda calculus note tucked inside.
Some connections between things, which I have not seen elsewhere. Maybe they mean something?
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.
Principal component analysis (PCA) is a technique used to emphasize variation and bring out strong patterns in a dataset. It's often used to make data easy to explore and visualize.
Applying Principal Component Analysis to a data-set of short electronic music loops
I spent 2022 learning to draw and was blindsided by the rise of AI art There is lots to say about this, whether it has been or will be a good thing for artists and society in the long run. I hope to write about it in another post. models like Stable Diffusion. Suddenly, the computer was a better artist than I could…
Note that some of the wrong answers can be fixed with various workarounds. For example Common–Lisp gives the correct answer for:
Update (Dec. 16): If you’re still following this, please check out an important comment by Alex Selby, the discoverer of Selby’s algorithm, which I discussed in the post. Selby querie…
Thoughts on software engineering from Rob Bell
Finding provably optimal strategies for 2048 using Markov Decision Processes
what can language model embeddings tell us about whales speech, and decoding ancient texts? (on The Platonic Representation Hypothesis and the idea of *universality* in AI models)
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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New : You can now watch a recording of my talk on my YouTube channel ! Or you can just click "play" below, I suppose.
Leverage is actually reasonably easy to understand, both in the math and in the implications for financial firms.
Imagine we want to compute the square root of a number n n n . The basic idea of Heron’s method , named after the mathematician and engineer, Heron of Alexandria, is to find a number g g g that is close to n \sqrt{n} n and to then average that with the number n / g n/g n / g , which corrects for the fact that g g g…
A traditional subjective Bayesian will assume a data generating distribution (aka a likelihood when viewed as a function of the parameters). Then, conditional on this assumption, they encode their prior beliefs as a prior distribution over parameters. After this, they turn the crank on posterior inference and don’t…
Since spring, and even before that, I have participated in a great collaborative effort on writing a book on Homotopy Type Theory. It is finally finished and ready for public consumption. You can get the book freely at http://homotopytypetheory.org/book/ . Mike Shulman has written about the contents of the book , so I…
If you've ever graphed equations, chances are you have only ever graphed equations in what I refer to as "Binary mode" - which draws a line where the equation is EXACTLY equal, and leaves white everywhere else.
I’ve been talking a lot recently about how quantum algorithms don’t work. But last week JR Minkel, an editor at Scientific American, asked me to write a brief essay about how quantum al…
Engineering at Forward | UCLA CS '19
