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Court of Appeal bans Bayesian probability
As of the 23rd May 2022 this website is archived and will receive no further updates .
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How to make fake data look meaningful
If you are trying to trick somebody with your data, never share the raw data; only share the conclusions. Bonus points if you can’t share the data because it is somehow priviledged or a trade secret. The last thing you want is to allow other people to evaluate your analysis and possibly challenge your conclusions.
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Why Hacker News should use a different Deterministic Algorithm, Not a Random One
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What is algebra?
NOVEMBER 20, 2011. We hear a lot about the importance that all children master algebra before they graduate from high school. But what exactly is algebra, and is it really as important as everyone …
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Gödel, Turing and Cantor: The Math
This is mathematical section of the parent essay Gödel Incompleteness for Startups Gödel Numbering A formal system is just a collection of axioms and rules. Just like we did before we can record ax…
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Feynman vs. The Abacus
A Japanese man came into the restaurant. I had seen him before, wandering around; he was trying to sell abacuses. He started to talk to the waiters, and challenged them: He said he could add numbers faster than any of them could do.
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Elsevier journals: has anything changed?
Greg Martin, a number theorist at UBC (the University of British Columbia in Vancouver) doesn’t think so, so he has decided to resign from the editorial board of Elsevier’s Journal of N…
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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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Let's Play Ancient Greek Geometry
Today I’m releasing Let’s Play: Ancient Greek Geometry . It’s a Compass and Straightedge tool/puzzle game written in JavaScript. I’ve always thought Geometric Construction felt like a puzzle, so to me this pairing was quite natural. Compass and Straight edge is a technique for constructing shapes out of circles…
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How to escape a monster (using calculus)
You are sitting in a rowing boat in the middle of a circular lake. How do you escape from a smart monster on the shore who can run four times faster than you can row?
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Computer scientists develop 'mathematical jigsaw puzzles' to encrypt software
The "software obfuscation" system encrypts software so that it only allows someone to use a program as intended while preventing any deciphering of the code behind it.
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Algorithms Every Data Scientist Should Know: Reservoir Sampling
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Short algorithm, long-range consequences
A new technique for solving ‘graph Laplacians’ is drastically simpler than its predecessors, with implications for a huge range of practical problems.
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The Median-of-Medians Algorithm
In this post, we consider the problem of selecting the \(i\)-th smallest element from an unsorted list of \(n\) elements. Somewhat surprisingly, there is an algorithm that solves this problem in linea
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Understanding the FFT Algorithm
The Fast Fourier Transform (FFT) is one of the most important algorithms in signal processing and data analysis. I've used it for years, but having no formal computer science background, It occurred to me this week that I've never thought to ask how the FFT computes the discrete Fourier transform so quickly. I dusted…
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You've heard of Markov chains. But who was Markov?
Harvard celebrates the 100th anniversary of a computational principle that was little noticed in its time, but that underlies all of modern science.
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Modelling a Basic Income with Python and Monte Carlo Simulation
Basic Income is a popular policy floating around the internet lately. The idea consists of declaring that the government will pay each living adult a fixed amount of money every month - an amount comparable to a minimum wage job. This policy would then replace all current welfare programs - welfare, unemployment …
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How to build an Anti Aircraft Missile: Bayes’ Theorem and the Kalman Filter
Ever wondered how an Anti Aircraft Missile works? A plane can move at different speeds and altitudes, so how do you know when to fire your missile? Well you need to know two things: where the aircr…
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Stochastic Superoptimization
An “optimizer” should really be called an “improver”, and a “superoptimizer” should be called an “optimizer” 🙂
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What are the 'real numbers', really?
The short, simple answer used in calculus courses is that a real number is a point on the number line . That's not the whole truth, but it is adequate for the needs of freshman calculus. The freshman calculus course (at most universities nowadays) follows the 17th century style of Newton and Leibniz, emphasizing…
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The Existential Risk of Mathematical Error
Mathematical mistake/error-rates limit our understanding of rare risks and ability to defend against them.
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The Elsevier boycott one year on
A few days ago was the anniversary of the beginning of the Cost of Knowledge boycott of Elsevier. It seems a good moment to take stock of what the boycott has achieved and to think about what progr…