The latest blog posts to take off on Hacker News. 266 posts.
Experimenting with the "divisibility" of complex numbers, I stumbled across this thingy. It looks like a fractal. Although the formula does not do any iterations. It reminds me of something. But I dont know what. Doing a Google image search brings up a couple of galaxies :) This image shows the region from (-1/-1) to…
About a weird, lovely short story
This morning, I came accross Cameron Sun’s Probabilistic Tic-Tac-Toe on HN . However, the comments were disappointing, with people proposing probabilistic models, linear programming, minimax algorithms, and heuristic evaluations to develop AI approaches for the game, none of which quite correct. In this post, I’ll…
If an expert can't understand your explanation, you've dumbed it down too much!
This article will be part of an extensive series in which I plan to explore various aspects of Fourier Mathematics. I will take notes, create some visuals (a good pretext to learn more about graphics), and hope that it will be helpful to anyone looking for a clear, visual introduction to these concepts. The article…
An Intuitive and Visual Guide to Maxwell's Equations
A useful theorem attributed to the probably first mathematician ever, Thales of Miletus (ca. 624 BC-ca. 546 BC) is one of most elementary and intuitive ever stated.
There are few things I think about more than the essays on gwern.net, and there are few with as satisfying a theoretical payout to contemplate in my orb as his essay on “leaky pipelines”, aka log-normal distributions. The skulk: Say you’re working on a Laravel web app. You’re about 90% sure you know how to start the…
Reflections on a Wall Street legend.
Suppose you have an array of floating-point numbers, and wish to sum them. You might naively think you can simply add them, e.g. in Rust:
Or how to find the largest power of 2 that divides x?
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…
A letter from Lewis Carroll to Nature, March 31, 1887: Having hit upon the following method of mentally computing the day of the week for any given date, I send it you in the hope that it may interest some of your readers. I am not a rapid computer myself, and as I find my average time for doing any such question is…
Pavel has found a new 3-state 4-symbol Busy Beaver champion which can compute an “Ackermann-level” function and halts with exactly
This is a tale of two approaches to regular expression matching. One of them is in widespread use in the standard interpreters for many languages, including Perl. The other is used only in a few places, notably most implementations of awk and grep. The two approaches have wildly different performance characteristics:
Using transformed ellipses to estimate perspective transformations of text.
This is a set of notes for learning calculus using the Julia language. Julia is an open-source programming language with an easy to learn syntax that is well suited for this task.
APT 2.9.3 introduces the first iteration of the new solver codenamed solver3, and now available with the –solver 3.0 option. The new solver works fundamentally different from the old one. How does it work? Solver3 is a fully backtracking dependency solving algorithm that defers choices to as late as possible. It…
Pets do the darndest things, especially if you teach them a bit of math.
In a paper published in Physical Review X on May 13, a quartet of physicists and computer scientists expand the modern theory of the thermodynamics of computation. By combining approaches from statistical physics and computer science, the researchers introduce mathematical equations that reveal the minimum and maximum…
Are you kidding? Edward Barbeau is now a professor emeritus of mathematics at the University of Toronto. Over the years he has been working to increase the interest in mathematics in general, and e…
About two years ago, I switched teams at Google to focus on fully homomorphic encryption (abbreviated FHE, or sometimes HE). Since then I’ve got to work on a lot of interesting projects, learning along the way about post-quantum cryptography, compiler design, and the ins and outs of fully homomorphic encryption. If…
An intuitive explanation of the James-Stein estimator.
On the one hand they are easy to explain, they are just numbers that have no factors other than one and themselves, but on the other hand they contain endless complexity. They show up in numerous places, ranging from mathematical concepts and conjectures to interesting looking visualizations and cryptography…
A free, self-contained introduction to neural networks and differentiable programming, from automatic differentiation to transformers, with additional chapters on advanced topics.
