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Why does 0.1 and 0.2 = 0.30000000000000004?
Why does 0.1 + 0.2 = 0.30000000000000004?
New
The latest blog posts to take off on Hacker News. 2,391 posts.
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They say that stocks go down during the day and up at night
Prompted by your blog post this morning, I attach a plot from Figure 3 of They Still Haven’t Told You showing overnight and intraday returns to AIG (with logarithmic vertical scale, updated with data through the end of October).
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Math breakdown: Anime homing missiles
Tech Notes on Cubic Bezier Curves, Perlin Noise, and Minimal Rotation Frames
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Estimating square roots in your head
Imagine we want to compute the square root of a number n n n . The basic idea of Heron’s method , named after the mathematician and engineer, Heron of Alexandria, is to find a number g g g that is close to n \sqrt{n} n and to then average that with the number n / g n/g n / g , which corrects for the fact that g g g…
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Cistercian Numerals
Cistercian numerals were invented by the Cistercian order of monks in the 13th century. Giuseppe Frisella explains how the notation system works: A vertical str
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A baffling scale transform on a chart of university course selection trends
Harvard Magazine printed the following chart that confirms a trend in undergraduate majors that we all know about: students are favoring STEM majors at the expense of humanities.
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An intutive counterexample to the axiom of choice
Time for some hard-core geeking-out. This comment on HN by /u/jiggawatts struck me as a brilliant idea: it's an intuitive counter-example t...
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The Point of the Banach-Tarski Theorem
One of my favourite Limited Audience Jokes (although technically it's actually a riddle) goes:
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Formalising a new proof that the square root of two is irrational
Recently, somebody shared on Twitter a new proof of the irrationality of √2. Its claimed advantage is that “it requires no knowledge of mathematics above the definition of what it means for a number to be irrational, and can be written almost in one line.” These claims are dubious: the usual proof, which I’ve…
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Reverse engineering a neural network's clever solution to binary addition
While training small neural networks to perform binary addition, a surprising solution emerged that allows the network to solve the problem very effectively. This post explores the mechanism behind that solution and how it relates to analog electronics.
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Bayesian statistics and machine learning: How do they differ?
My colleagues and I are disagreeing on the differentiation between machine learning and Bayesian statistical approaches. I find them philosophically distinct, but there are some in our group who would like to lump them together as both examples of machine learning. I have been favoring a definition for Bayesian…
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Tetris is capable of universal computation
This text presents a method for embedding a programmable, general-purpose, digital computer into Tetris. It describes the capabilities and performance of an implementation that runs Tetris on Tetris.
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The Art of LaTeX: Common mistakes and advice for typesetting proofs
When was the first time you had to use LaTeX? If you are like most people, it was probably suddenly forced upon you during your first math or CS class where you had to start writing proofs, with minimal guidance on how to get started. Unfortunately, this meant that while many people have good operational knowledge of…
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U.S. stock market returns – a history from the 1870s to 2022
Facts and figures on U.S. stock market returns from 1871 to 2024. Annual returns, likelihood of losing money, best / worst months, and more.
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A Lisp interpreter implemented in Conway's Game of Life (2021)
Lisp in Life is a Lisp interpreter implemented in Conway’s Game of Life.
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Cargo Cult Quantum Factoring
Just days after we celebrated my wife’s 40th birthday, she came down with COVID, meaning she’s been isolating and I’ve been spending almost all my time dealing with our kids. But …
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Breaking RSA with a quantum computer?
A group of Chinese researchers have just published a paper claiming that they can—although they have not yet done so—break 2048-bit RSA. This is something to take seriously. It might not be correct, but it’s not obviously wrong. We have long known from Shor’s algorithm that factoring with a quantum computer is easy…
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Competitive programming in Haskell: better binary search
Binary search is a workhorse of competitive programming. There are occasional easy problems where binary search is the solution in and of itself; more often, it’s used as a primitive building block…
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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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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