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Optimizing a bignum library for fun
Can I make math operations run 100x faster on really, really big numbers?
New
The latest blog posts to take off on Hacker News. 2,391 posts.
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The Second Law of Thermodynamics (2011)
Web site content explains the modern view of entropy change and the dispersal of energy in a process (at a specific temperature). It has been selected for instructors in general and physical chemistry by Dr. Frank L. Lambert, Professor Emeritus (Chemistry) of Occidental College, Los Angeles.
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Win your fantasy league using operations research
I’ve never been good at playing football 1 . I started playing again last year and I have scored more own goals than goals for my team. Also, I support the RCD Espanyol 2 , which has spent last season in the second division and has miraculously ascended to the first division last week. And to be honest, I only watch…
484
General Theory of Neural Networks
From gene regulatory networks to artificial neural networks
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Scoped Propagators
A programming model for spatial canvases
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The zombie misconception of theoretical computer science
In Michael Sipser’s Introduction to the Theory of Computation textbook, he has one Platonically perfect homework exercise, so perfect that I can reconstruct it from memory despite not having …
487
The Invention of Zero
“If you look at zero you see nothing; but look through it and you will see the world.”
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Finding near-duplicates with Jaccard similarity and MinHash
How do you find near-duplicates in a massive collection of documents? An exploration of the Jaccard similarity metric, and the MinHash hashing trick used to efficiently approximate it at web scale.
489
Building a data compression utility in Haskell using Huffman codes
In this post we will implement a data compression program in about 150 lines of Haskell. It will use Huffman coding and handle arbitrary binary files using constant memory for encoding and decoding.
490
Diffusion Forcing: Next-Token Prediction Meets Full-Sequence Diffusion
Official Website of Diffusion Forcing
491
How random are TOTP codes?
I'm pretty sure that the 2FA codes generated by my bank's TOTP app have a bias towards the number 8 - because eight is an auspicious number. But is that just my stupid meaty brain noticing patterns where none exist? The TOTP algorithm uses HMAC, which in turn uses SHA-1. My aforementioned brain is not clever enough to…
492
Trying Kolmogorov-Arnold Networks in Practice
There's been a fair bit of buzz about Kolmogorov-Arnold networks online lately. Some research papers were posted around claiming that they offer better accuracy or faster training compared to traditional neural networks/MLPs for the same parameter count.
493
A proof of proof by infinite descent
WARNING: the following contains a whole lot of pedantry about proving theorems at a level of detail such that you could likely convince a co...
494
Conway's Game of Life for curved surfaces (2012)
Conway’s Game of Life is one of the most popular and iconic cellular automata. It is so famous that googling it loads up a working simulation right in your browser! The rules for the Game o…
495
Convolutions, Fast Fourier Transform and polynomials (2022)
You may remember from high school what a polynomial is. If so, you may also remember how to multiply two of them. But what if I told you that the method you were taught is slow as F? In this post we will connect polynomials with the Fourier Transform and convolutions, and show you how to multiply polynomials with…
496
Quaternion Differentiation (2012)
I wanted to point someone to a short explanation of this today and noticed, with some surprise, that I couldn’t find something concise within 5 minutes of googling. So it seems worth writing …
497
The Point of the Banach Tarski Theorem (2015)
One of my favourite Limited Audience Jokes (although technically it's actually a riddle) goes:
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A brief introduction to interval arithmetic
Why x^2 isn't always x*x.
499
A reckless introduction to Hindley-Milner type inference (2019)
(I've been editing this post on and off for almost a year. I'm not really happy with it, but I suspect I never will be.)
500
A railroad simulation using discrete event simulation
In our previous post, we introduced how to utilize Discrete Event Simulation (DES) in PicoLisp. Now, let's explore another application: a railroad model…
501
Solving puzzles faster than humanly possible
Can anyone solve 1000 Opus Magnum puzzles in 24 hours? What about with assistance from bots? Will the solutions be any good? Let's find out!
502
How does a computer/calculator compute logarithms?
Summer of Math Exposition 3 - How does a computer/calculator compute logarithms?
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Reconstructing Public Keys from Signatures
One weird hobby of mine is reasonable properties of cryptographic schemes that nobody promised they do or don’t have. Whether that’s invisible salamanders or binding through shared secr…
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There's more to mathematics than rigour and proofs (2007)
The history of every major galactic civilization tends to pass through three distinct and recognizable phases, those of Survival, Inquiry and Sophistication, otherwise known as the How, Why, and Wh…
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Harvard Railroad Economics Exam (1906)
Final exam from Dr. Stuart Daggett's Harvard economics course on Railroad Practice taught in 1906-07.
507
AI for math resources, and erdosproblems.com
This post contains two unrelated announcements. Firstly, I would like to promote a useful list of resources for AI in Mathematics, that was initiated by Talia Ringer (with the crowdsourced assistan…
508
Exponentially Better Rotations (2022)
If you’ve done any 3D programming, you’ve likely encountered the zoo of techniques and representations used when working with 3D rotations. Some of them are better than others, depending on the situation.
509
Does anybody know this fractal? (2012)
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…
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