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An Interactive Guide to the Fourier Transform (2012)
The Fourier Transform is one of the deepest insights ever made. Unfortunately, the meaning is buried within dense equations:
Most cited
Posts that commenters keep linking to, ranked by how many different people have cited them in Hacker News comments. 417 posts.
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Kill Math
The power to understand and predict the quantities of the world should not be restricted to those with a freakish knack for manipulating abstract symbols.
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The Fermi Paradox
The Fermi Paradox: There should be 100,000 intelligent alien civilizations in our galaxy — so why haven't we found any of them?
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Alligator Eggs
In 2007, I met Philip Wadler at a conference, who mentioned to me that he wanted to teach lambda calculus to his eight-year-old children.
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Ten Signs a Claimed Mathematical Breakthrough is Wrong
Yesterday several people asked my opinion of a preprint claiming to solve the Graph Isomorphism problem in deterministic polynomial time. I responded: If I read all such papers, then I wouldn’t hav…
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Galactic-Scale Energy (2011)
[ An updated treatment of this material appears in Chapter 1 of the Energy and Human Ambitions on a Finite Planet (free) textbook , and also appears as part of an article in Nature Physics in 2022.]
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D-Wave: Truth finally starts to emerge
Wrap-Up (June 5): This will be my final update on this post (really!!), since the discussion seems to have reached a point where not much progress is being made, and since I’d like to oblige …
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Ssss: Shamir's Secret Sharing Scheme (2006)
Shamir's Secret Sharing Scheme
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PHYS771 Quantum Computing Since Democritus
University of Waterloo, Fall 2006 Tuesdays and Thursdays, 1:00-2:30pm BFG Building, 2nd floor seminar room (BFG2125)
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Let's remove quaternions from every 3D engine (2018)
To represent 3D rotations graphics programmers use Quaternions . However, Quaternions are taught at face value . We just accept their odd multiplication tables and other arcane definitions and use them as black boxes that rotate vectors in the ways we want. Why does $\mathbf{i}^2=\mathbf{j}^2=\mathbf{k}^2=-1$ and…
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Chesterton’s Fence: A Lesson in Second Order Thinking
A core component of making great decisions is understanding previous decisions. If we don’t understand how we got “here,” we run the risk of making things much worse.
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There are only four billion floats, so test them all (2014)
A few months ago I saw a blog post touting fancy new SSE3 functions for implementing vector floor, ceil, and round functions. There was the inevitable proud proclaiming of impressive performance an…
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Fibonacci Flim-Flam.
physics, history of science, pseudoscience, hoaxes, writing, education, skepticisism, humor, quotes, illusions, 3d stereo photography.
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Kolmogorov Complicity and the Parable of Lightning (2017)
A good scientist, in other words, does not merely ignore conventional wisdom, but makes a special effort to break it. Scientists go looking for trouble. — Paul Graham, What You Can’t Sa…
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From 1,000,000 to Graham's Number
Graham's number is so big, we need a whole new set of tools to even discuss it.
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Probabilistic Programming and Bayesian Methods for Hackers (2013)
Bayesian Methods for Hackers : An intro to Bayesian methods + probabilistic programming with a computation/understanding-first, mathematics-second point of view.
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Neural Networks, Manifolds, and Topology
Recently, there’s been a great deal of excitement and interest in deep neural networks because they’ve achieved breakthrough results in areas such as computer vision. 1
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Using spaced repetition systems to see through a piece of mathematics
By Michael Nielsen, January 2019
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Analysis of bank PIN numbers
Is your PIN number too predictable? Detailed analysis on PIN number databases.
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Quantum Computing for the Curious
Presented in an experimental mnemonic medium that makes it almost effortless to remember what you read
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Warning Signs in Experimental Design and Interpretation (2007)
When an experimental study states "The group with treatment X had significantly less disease ( p = 1%)", many people interpret this statement as being equivalent to "there is a 99% chance that if I do treatment X it will prevent disease." This essay explains why these statements are not equivalent. For such an…
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Regular Expression Matching: the Virtual Machine Approach
Name the most widely used bytecode interpreter or virtual machine. Sun's JVM? Adobe's Flash? .NET and Mono? Perl? Python? PHP? These are all certainly popular, but there's one more widely used than all those combined. That bytecode interpreter is Henry Spencer's regular expression library and its many descendants.
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Finite state machines as data structure for representing ordered sets and maps
It turns out that finite state machines are useful for things other than expressing computation. Finite state machines can also be used to compactly represent ordered sets or maps of strings that can be searched very quickly.
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Mona Lisa in 50 polygons, using a genetic algorithm (2008)
This weekend I decided to play around a bit with genetic programming and put evolution to the test, the test of fine art 🙂
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Data Compression Explained (2012)
Copyright (C) 2010-2012, Dell, Inc . You are permitted to copy and distribute material from this book provided (1) any material you distribute includes this license, (2) the material is not modified, and (3) you do not charge a fee or require any other considerations for copies or for any works that incorporate…