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Degenerate matter: How reality deals with uncertainty
Casual introduction to the uncertainty principle from quantum mechanics and how it leads to neutron stars and superfluids
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The latest blog posts to take off on Hacker News. 171 posts.
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Algorithms to Live By – The Computer Science of Human Decisions
What does the math tell us about how many job applicants we should look at before hiring one? While onboarding our new employees, how can ideas from the TCP networking protocol help us to identify the optimal workload for them? Why would giving employees unlimited vacation days most likely lead to less vacation being…
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Visually symmetric words
The word "kayak" is a palindrome, but it isn't visually symmetric. The word "bud" is visually symmetric, but not a palindrome.
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Challenging algorithms and data structures every programmer should try
Bored of algorithms? Here are my recommendations that are exciting, understandable, and sometimes even useful!
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Do simpler machine learning models exist and how can we find them?
The above is the title of a talk by computer scientist Cynthia Rudin. here’s the abstract:
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Signed distance functions in 46 lines of Python
A walkthrough of 46 lines of code that render a 3D ASCII donut using signed distance functions.
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Special Relativity and Middle-Earth
This post is an unofficial sequel to one of my first blog posts from 2007, which was entitled “Quantum mechanics and Tomb Raider”. One of the oldest and most famous allegories is Plato&…
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Vintage-Style Map of the Mandelbrot Set
Bill Tavis designed this lovely vintage-style map of the familiar fractal shape, the Mandelbrot set. He is selling a poster version of the map, starting at the
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A trip through the Graphics Pipeline
Welcome. This is the index page for a series of blog posts I’m currently writing about the D3D/OpenGL graphics pipelines as actually implemented by GPUs. A lot of this is well known among gra…
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A neat XOR trick
Looking over the solutions mega-thread , it seems like not many people discovered this trick; when I posted about it , people found it to be noteworthy.
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Fast midpoint between two integers without overflow
Let us say that I ask you to find the number I am thinking about between -1000 and 1000, by repeatedly guessing a number. With each guess, I tell you whether your guess is correct, smaller or larger than my number. A binary search algorithm tries to find a value in an interval by repeating … Continue reading Fast…
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A homework question in someone’s 11th grade statistics class
My son is in 11th grade. Below you’ll find a HW question which was given in my son’s statistics class. How would you answer?
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Understanding Convolutions in Probability
In this post we take a look a how the mathematical idea of a convolution is used in probability. In probability a convolution is a way to add two random variables. Using a slightly ridiculous, mad-science, example we walk through multiple way to compute a convolution and ultimate arrive at the formu
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Experiment with Penrose Tilings and other patterns
Create And Share Mathematical Tiling Patterns
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Why I am learning category theory
Category theory is a domain of mathematics that exerts a strange influence over programmers. One thing that can be said for sure about category theory is tha...
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How thick is a three-sided coin?
Matt Parker, employing the enviably pithy prose typical of a content creator forged on the unforgiving fires of social media, asked the simple question back in 2018: > How thick is a three-sided coin? Translated into mathematician-ese, this means > What aspect ratio of a flipped coin leads to the chance of landing on…
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CRDT: Fractional Indexing
Collaborative peer-to-peer applications sometimes need to operate on sequences of objects with a consistent order across all peers. For example, a peer-to-peer photo album application might need to sync the order in which photos appear in an album.
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Making all your integers positive with zigzag encoding
You sometimes feel the need to make all of your integers positive, without losing any information. That is, you want to map all of your integers from 'signed' integers (e.g., -1, 1, 3, -3) to 'unsigned integers' (e.g., 3,2,6,7). This could be useful if you have a fast function to compress integers that fails to ……
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Torsors (2010)
When you first read about "torsors", they're bound to seem a bit too darn sophisticated for their own good. Mostly this is because nobody explains them very well. So, I want to convince you that they're actually very simple and natural. I'll do this by giving you three examples from physics:
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Demystifying Fourier analysis
I've started learning about spectrum analysis a long time ago at university, but failed to gain a true insight in how it works under the hood. For me, it was just some magical math formulas I had to memorize and know about. I knew the theory but it didn't really click .
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Twenty questions is a weird game
Let’s play a game. I’m thinking of a number from 1 to 100. You guess, and I tell you whether my number is higher or lower.
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Demystifying financial leverage
Leverage is actually reasonably easy to understand, both in the math and in the implications for financial firms.
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Binary Lambda Calculus (2020)
Binary lambda calculus ( BLC ) is a minimal, pure functional programming language invented by John Tromp in 2004, 1 based on a binary encoding of the untyped lambda calculus in De Bruijn index notation.
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What is an eigenvalue?
An eigenvalue of a square matrix $LATEX A$ is a scalar $latex \lambda$ such that $latex Ax = \lambda x$ for some nonzero vector $latex x$. The vector $latex x$ is an eigenvector of $LATEX A$ and it…
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The essence of Reed-Solomon coding
Let’s say we want to store some data on multiple drives, so that we can recover from drive failures.
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Nearly all binary searches and mergesorts are broken (2006)
Posted by Joshua Bloch, Software EngineerI remember vividly Jon Bentley's first Algorithms lecture at CMU, where he asked all of us incoming Ph.D. ...