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GPS and Relativity
People often ask me "What good is Relativity?" It is a commonplace to think of Relativity as an abstract and highly arcane mathematical theory that has no consequences for everyday life. This is in fact far from the truth.
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The latest blog posts to take off on Hacker News. 107 posts.
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Cylinders in Spheres
What is the largest volume cylinder it is possible to carve from a solid sphere? Also, so you know about the napkin ring problem?
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Dijkstra’s algorithm and the Fibonacci heap
A couple of Sundays ago, I wrote an implementation of Dijkstra’s algorithm in Clojure. The core algorithm came to twenty-five lines. I banged out the code as...
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How a mathematician constructed a decision tree to solve a medical problem
Here’s an excerpt from Love and Math, a book by Edward Frenkel. The author writes about mathematics and his career. One of the stories is about …
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World Cup Follow-Up: Update of Winning Probabilities and Betting Results
An update on the winning probabilities for the remaining World Cup teams, and an analysis of how our predictor performed on the group-phase matches.
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The Lambda Calculus for Absolute Dummies (2012)
If there is one highly underrated concept in philosophy today, it is computation . Why is it so important? Because computationalism is t...
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Eigenmorality
This post is about an idea I had around 1997, when I was 16 years old and a freshman computer-science major at Cornell. Back then, I was extremely impressed by a research project called CLEVER, wh…
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How to be a Bayesian in Python
See also Frequentism and Bayesianism: A Python-driven Primer , a peer-reviewed article partially based on this content.
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How to Fold a Julia Fractal
A tale of numbers that like to turn: a different look at complex numbers and the strange things they do.
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The Largest Black Hole in the Known Universe
It’s a huge surprise, and shows up in the most unlikely of places!
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Math for seven-year-olds
As a guest today in my daughter’s second-grade classroom, full of math-enthusiastic seven-and-eight-year-old girls, I led a mathematical investigation of graph coloring, chromatic numbers, ma…
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Selection bias and bombers (2008)
During WWII, statistician Abraham Wald told the RAF to add armor where it didn't seem planes needed it. But he was right.
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Categories from scratch
Note The latest version of this document can be found online at https://dr-knz.net/categories-from-scratch.html. Alternate formats: Source, PDF. Prologue The concept of category from mathematics happens to be useful to computer programmers in many ways. Unfortunately, all “good” explanations of categories so far have…
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Programming with Nothing (2011)
I love Ruby! I’ve used it every day for years and I’m not sick of it yet. It’s an easy language to love: it’s expressive, flexible and syntactically beautiful ; it has a unique combination of useful features like mixins , metaclasses and blocks ; it comes with a useful core library and comprehensive standard library …
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Elsevier journals – some facts
Update: figures now in from Imperial. See below. Further update: figures in from Nottingham too. Further update: figures now in from Oxford. Final update: figures in from LSE. A little over two yea…
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Analysis of suspected MH370 pings recorded by Ocean Shield
So this is a bit of a deviation from my normal MATLAB oriented posts. In-fact MATLAB was not used once in this analysis! I've been followi...
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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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Evolutionary algorithm to find Quake III's fast inverse square hack with Python
Curiosity killed the cat I've always been amazed by early game developers. Unlike today, they had to bend and twist software to its extre...
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Why 'gallons per mile' is better than 'miles per gallon'
Why we should really be quoting fuel consumption figures as 'gallons per mile' and not 'miles per gallon'.
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0^0
Clever student: I know! $latex x^{0}$ = $latex x^{1-1}$ = $latex x^{1} x^{-1}$ = $latex \frac{x}{x}$ = $latex 1$. Now we just plug in x=0, and we see that zero to the zero is one! Cleverer …
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Why are roller coaster loops not circular?
Why are the loops on roller coasters never circular?
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New partition function record: p(10^20) computed
The partition function p ( n ) counts the number of partitions of n , i.e. the number of ways n can be written as a sum of positive integers when disregarding the order of the terms. For example, 4 has the five distinct partitions 4, 3+1, 2+2, 2+1+1, 1+1+1+1, so p (4) = 5. This week, I set a new record by computing…
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Overkilling the 8-queens Problem
Last night, a fellow Hacker Schooler challenged me to a running-time contest on the classic eight queens puzzle. Naturally, I pulled up my trusty …