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The simple geometry behind any road
How does the geometry of a road unfold?
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
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How Hamming codes work
Detecting (and correcting) errors in digital signals.
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LLMs don't do formal reasoning
Important new study from Apple
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Saving Jet Fuel
Benchmarks & Tips for Big Data, Hadoop, AWS, Google Cloud, PostgreSQL, Spark, Python & More...
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Will Our Understanding of Math Deteriorate Over Time?
Scientific American writes about rescuing the enormous theorem (classification of finite simple groups) before the proof vanishes. How can...
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Why Mathematica does not simplify sinh(arccosh(x))
When Mathematica seems to not to know how to simplify an expression, it may be doing the right thing, being more sophisticated than you expect.
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Starting from scratch: Training a 30M Topological Transformer
Tauformer is a topological transformer (see paper ) that replaces dot‑product attention with a Laplacian-derived scalar (taumode) per token/head, then attends using distances in that scalar space. Below is a post-style overview of the idea and the first training signals from a 30M-parameter run.
1419
Trying to improve buffet lines using simulations
I have suspected for years that the classic buffet line system is a deeply flawed method, so I decide to simulate different methods to find out better ways
1420
Using Fibonacci Numbers to Convert from Miles to Kilometers and Vice Versa
I recently learned an interesting fact about Fibonacci numbers while watching a random number theory video on YouTube. Fibonacci numbers can be used to approximately convert from miles to kilometers and back. Here is how. Take two consecutive Fibonacci numbers, for example 5 and 8. And you're done converting. No...
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Generating all permutations, combinations, and power set of a string (2012)
Combinatorics is a branch of mathematics that deal with counting of discrete structures. Two concepts that often come up in the study of c...
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John Conway's FRACTRAN, a ridiculous, yet surprisingly deep language (2020)
On April 8, 2020, John Horton Conway developed symptoms of COVID-19. On April 11, 2020, he succumbed to the disease. 1 2 3 4
1423
50 years of proof assistants
Crackpots ranging from billionaire Peter Thiel to random YouTube influencers claim that science has been stagnating for the past 50 years. They admit that computing is an exception: they don’t pretend that my personal 32GB laptop is not an advance over the 16MB mainframe that served the whole Caltech community when I…
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Speech to Birdsong Conversion
A blog about signals, programming, music, and other stuff.
1425
A back-projection algorithm to extract 3D volume from shadows
If you'd rather read python than english you can go straight to the code on github: https://github.com/jminardi/volume-from-shadow
1426
Deep Learning in the Real World: Dealing with Non-Differentiable Loss Functions
Over the past few years, deep learning has been taking by storm many industries. From voice recognition to image analysis and synthesis, neural networks have turned out to be very efficient at solv…
1427
The polls messed up
To continue our post-voting, pre-vote-counting assessment (see also here and here ), I want to separate two issues which can get conflated: 1. Problems with poll-based election forecasts.
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Gödel's Theorem
A much-abused result in mathematical logic , supposed by many authors who don't understand it to support their own favored brand of rubbish, and even subjected to surprisingly rough handling by some who really should know better.
1430
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…
1431
The Three Ways of XOR
We all know the XOR operation. It’s the cousin of NOT, AND and OR. Like AND and OR, it is a binary boolean function. Unlike them, most programming languages ...
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Machine Learning, Kolmogorov Complexity, and Squishy Bunnies (2019)
Computer Science, Machine Learning, Programming, Art, Mathematics, Philosophy, and Short Fiction
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Options for giving math talks and lectures online
As part of social distancing efforts to slow down the spread of the novel coronavirus, several universities have now transitioned, or begun transitioning, to online teaching models. (My home unive…
1439
Monte Carlo Crash Course: Quasi-Monte Carlo
We’ve learned how to define and apply Monte Carlo integration—fundamentally, it’s the only tool we need. In the remaining chapters, we’ll explore ways to reduce variance and successfully sample difficult distributions.
1440
TLA+ in Practice and Theory, Part 4: Order in TLA+
We learn how to encapsulate and compose TLA+ specifications, of the precise mathematical definition of abstraction, and compare TLA+'s notion of abstraction with those of other formalisms. Plus some various cool stuff.