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Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,391 posts.
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SymPy makes math fun again
An introduction into symbolic computations in Python. Don't worry, it's much simpler than it sounds. It's about making Python do your math for you with very little investment in the technology.
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The Rule of 72 (2007)
The Rule of 72 is a great mental math shortcut to estimate the effect of any growth rate, from quick financial calculations to population estimates. Here’s…
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Less is more: Recursive reasoning with tiny networks
|| Paper | Code ||
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What every computer programmer should know about floating point, part 1
Author’s note: this article used to be called “What Every ComputerProgrammer Should Know About Floating Point, part 1”. Some peoplenoted that this was perh...
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Jupyter, Mathematica, and the Future of the Research Paper
Economist. Policy Entrepreneur. Geek. Co-recipient of the 2018 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. University Professor at NYU. Focused on urbanization; cooperation at scale of millions and billions; science; technology; economic development; long-term growth; code as language.
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Outperforming everything with anything: Python? Sure, why not?
A 100 lines of Python code that substitute the compiler front-end for a specific computation. This shows that you don't need a “fast” compiling language to write efficient code. In fact, a compilation is only one of the multiple ways to achieve speed.
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Free and Open-Source Mathematics Textbooks
Mathematics, Teaching, & Technology
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Medical researcher discovers integration, gets 75 citations
(Note: this post is `just for fun;’ no premeds, doctors, researchers, or nobel laureates were meant to be offended in the writing of this post.) The bane of many American physics grad student…
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Why are QR Codes with capital letters smaller than QR codes with lower case?
Take a look at these two QR codes. Scan them if you like, I promise there's nothing dodgy in them. Left is upper-case HTTPS://EDENT.TEL/ and right is lower-case https://edent.tel/ You can clearly see that the one on the left is a "smaller" QR as it has fewer bits of data in it. Both go to the same URl, the only…
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3Blue1Brown Calculus Blog Series
Mathematics with a distinct visual perspective. Linear algebra, calculus, neural networks, topology, and more.
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Neglected machine learning ideas
This post is inspired by the “metacademy” suggestions for “leveling up your machine learning.” They make some halfway decent suggestions for beginners. The problem is, thes…
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Hashing
A visual, interactive introduction to hash functions.
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Optimal Strategy for Connect 4
The graph, the viewer, and the verification tooling all live in the WeakC4 repository on GitHub .
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What is the inverse of a vector?
If vector multiplication were invertible, we could treat vectors just like any other variable. We could do simple algebra like:
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Six Math Essentials
Just a brief announcement that I have been working with Quanta Books to publish a short book in popular mathematics entitled “Six Math Essentials”, which will cover six of the fundament…
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BB(3, 3) is Hard
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…
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A book from Alan Turing and a mysterious piece of paper
Sleuthing into the history of a 1930 book on quantum mechanics previously owned by Alan Turing and a lambda calculus note tucked inside.
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Everything is logarithms
Some connections between things, which I have not seen elsewhere. Maybe they mean something?
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Neural network training makes beautiful fractals
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.
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Principal Component Analysis Explained Visually (2015)
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.
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Eigentechno – Principal Component Analysis applied to electronic music
Applying Principal Component Analysis to a data-set of short electronic music loops
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Diffusion Models
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…
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9999999999999999.0 – 9999999999999998.0
Note that some of the wrong answers can be fixed with various workarounds. For example Common–Lisp gives the correct answer for:
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Google, D-Wave, and the case of the factor-10^8 speedup
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…
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A beginner's guide to Big O notation (2009)
Thoughts on software engineering from Rob Bell
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The Mathematics of 2048: Optimal Play with Markov Decision Processes
Finding provably optimal strategies for 2048 using Markov Decision Processes
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All AI models might be the same
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)
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