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Are You Living In a Computer Simulation? (2003)
The original paper that introduced the simulation argument
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,394 posts.
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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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Donald Knuth's letter about teaching O notation in calculus classes
Continuing the theme of alternative approaches to teaching calculus, I take the liberty of posting a letter sent by Donald Knuth to to the Notices of the American Mathematical Society in March, 199…
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Why the secret to speedier highways might be closing some roads: the Braess paradox
"All will be well if you use your mind for your decisions, and mind only your decisions." Help me make more videos and posts! A monthly membership directly supports the channel and allows me to make more videos that inspire students and teachers around the world. You also get early access to new videos. Support with a…
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Automatic Differentiation: The most underused tool in the machine learning toolbox?
Update: (November 2015) In the almost seven years since writing this, there has been an explosion of great tools for automatic differentiation and a corresponding upsurge in its use. Thus, happily,…
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Viktor T. Toth
This page contains a JavaScript calculator of Hawking radiation and other parameters of a Schwarzschild black hole.
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Implementing Regular Expressions
This page collects resources about implementing regular expression search efficiently.
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An Intuitive (and Short) Explanation of Bayes’ Theorem
Bayes’ theorem was the subject of a detailed article. The essay is good, but over 15,000 words long — here’s the condensed version for Bayesian newcomers like…
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Why FTL implies time travel
In science fiction, it is pretty standard fare to introduce some form of faster-than-light communication or travel. After all, space is big, and you can't write your swashbuckling Hornblower-in-space novel if you have to wait for a generation ship to crawl painfully slowly between the nearest stars,
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Stephen Wolfram, A New Kind of Science
Attention conservation notice : Once, I was one of the authors of a paper on cellular automata . Lawyers for Wolfram Research Inc. threatened to sue me, my co-authors and our employer, because one of our citations referred to a certain mathematical proof, and they claimed the existence of this proof was a trade secret…
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The Patriot Missile Failure
On February 25, 1991, during the Gulf War, an American Patriot Missile battery in Dharan, Saudi Arabia, failed to track and intercept an incoming Iraqi Scud missile. The Scud struck an American Army barracks, killing 28 soldiers and injuring around 100 other people. A report of the General Accounting office…
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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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Peter Selinger: MD5 Collision Demo
C:\TEMP> md5sum hello.exe cdc47d670159eef60916ca03a9d4a007 C:\TEMP> .\hello.exe Hello, world! (press enter to quit) C:\TEMP>
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P.S.: The Best of Intentions
Operations in Lisp, Scheme, and other dynamically-typed languages typically dispatch on representational type information rather than intentional type information. Several broad classes of bugs and confusions can be traced to improper attempts to recover intentional type information from representation types.
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Surprisingly Turing-Complete
A catalogue of software constructs, languages, or APIs which are unexpectedly Turing-complete; implications for security and reliability.
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The Three Projections of Doctor Futamura
Introduction The Three Projections of Futamura are a sequence of applications of a programming technique called 'partial evaluation' or 'sp...
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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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The Relativistic Rocket
Thanks to Alan R. Wilson for correcting a two-word typo involving GPS satellites. Thanks to Aron Yoffe for suggesting the newtonian comparison. Thanks to Tom Fuchs for suggesting the analogy to the stone thrown upwards. Fuel numbers added by Don Koks, 2004. Updated by Phil Gibbs, 1998. Thanks to Bill Woods for…
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Chicago undergraduate mathematics bibliography
Somehow I became the canonical undergraduate source for bibliographical references, so I thought I would leave a list behind before I graduated. I list the books I have found useful in my wanderings through mathematics (in a few cases, those I found especially un useful), and give short descriptions and comparisons…
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What if You Only Invested at Market Peaks?
What happens when you only invest at the peaks of the market by being the world's worst market timer.