URL : | http://www.johndcook.com/blog/ | |
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Filed Under: | Academics | |

Posts on Regator: | 1454 | |

Posts / Week: | 4.6 | |

Archived Since: | April 26, 2011 |

As much as we admire simplicity and strive for simplicity, something in us isn’t happy when we achieve it. Sometimes we’re disappointed with a simple solution because, although we don’t realize it yet, we didn’t properly frame the problem it solves. I’ve been in numerous conversations where someone says effectively, “I understand that 2+3 = […]

A Menger sponge is created by starting with a cube a recursively removing chunks of it. Draw a 3×3 grid on one face of the cube, then remove the middle square, all the way through the cube. Then do the same for each of the eight remaining squares. Repeat this process over and over, and do it […]

The harmonic numbers are defined by Harmonic numbers are sort of a discrete analog of logarithms since As n goes to infinity, the difference between Hn and log n is Euler’s constant ? = 0.57721… [1] How would you compute Hn? For small n, simply use the definition. But if n is very large, there’s a way […]

I’ve written quite a few pages that are separate from the timeline of the blog. These are a little hidden, not because I want to hide them, but because you can’t make everything equally easy to find. These notes cover a variety of topics: Math diagrams Numerical computing Probability and approximations Differential equations Python Regular expressions […]

I’ve updated the icons for my Twitter accounts.

The study of the planet Mercury provides two examples of the bandwagon effect. In her new book Worlds Fantastic, Worlds Familiar, planetary astronomer Bonnie Buratti writes The study of Mercury … illustrates one of the most confounding bugaboos of the scientific method: the bandwagon effect. Scientists are only human, and they impose their own prejudices […]

This post serves two purposes. It will empirically explore question in number theory and demonstrate quantile-quantile (q-q) plots. It will shed light on a question raised in the previous post. And if you’re not familiar with q-q plots, it will serve as an introduction to such plots. The previous post said that for almost all x > 1, the […]

A few days ago I wrote about how powers of the golden ratio are nearly integers but powers of ? are not. This post is similar but takes a little different perspective. Instead of looking at how close powers are to the nearest integers, we’ll look at how close they are to their floor, the largest […]

One of the case studies in Michael Beirut’s book How to is the graphic design for the planned community Celebration, Florida. The logo for the town’s golf course is an illustration of the bike shed principle. C. Northcote Parkinson observed that it is easier for a committee to approve a nuclear power plant than a bicycle […]

Last week I wrote a blog post showing that powers of the golden ratio are nearly integers. Specifically, the distance from ?n to the nearest integer decreases exponentially as n increases. Several people pointed out that the golden constant is a Pisot number, the general class of numbers whose powers are exponentially close to integers. […]

When I first saw ring theory, my impression was that there were dozens of kinds of rings with dozens of special relations between them—more than I could keep up with. In reality, there just a few basic kinds of rings, and the relations between them are simple. Here’s a diagram that shows the basic kinds of […]

In his paper Mindless statistics, Gerd Gigerenzer uses a Freudian analogy to describe the mental conflict researchers experience over statistical hypothesis testing. He says that the “statistical ritual” of NHST (null hypothesis significance...Show More Summary

This morning I was reading Terry Tao’s overview of the work of Yves Meyer and ran across this line: The powers ?, ?2, ?3, … of the golden ratio lie unexpectedly close to integers: for instance, ?11 = 199.005… is unusually close to 199. I’d never heard that before, so I wrote a little code […]

In a recent interview, Tyler Cowen discusses complacency, (neruo-)diversity, etc. Let me give you a time machine and send you back to Vincent van Gogh, and you have some antidepressants to make him better. What actually would you do, should you do, could you do? We really don’t know. Maybe he would have had a […]

Radim ?eh??ek of Rare Technologies just posted an interview he and I did a few days ago. We mostly talk about consulting: getting started, finding work, good and bad leads, etc.

The canonical examples of natural and unnatural transformations come from linear algebra, namely the relation between a vector space and its first and second duals. We will look briefly at the finite dimensional case, then concentrate on the infinite dimensional case. Two finite-dimensional vector spaces over the same field are isomorphic if and only if […]

The ladder of abstractions in category theory starts with categories, then functors, then natural transformations. Unfortunately, natural transformations don’t seem very natural when you first see the definition. This is ironic since...Show More Summary

Eight blog posts based on the work of the intriguing mathematician Srinivasa Ramanujan: Ramanujan series for computing ? Ramanujan ? approximation Ramanujan’s nested radical Ramanujan approximation for circumference of an ellipse Ramanujan’s most beautiful identity Ramanujan’s factorial approximation Sums of fourth powers Algorithm used for world record pi calculations

Larry Wall, creator of the Perl programming language, created a custom degree plan in college, an interdisciplinary course of study in natural and artificial languages, i.e. linguistics and programming languages. Many of the features of Perl were designed as an attempt to apply natural language principles to the design of an artificial language. I’ve been […]

A blog post by Evelyn Lamb yesterday introduced Thomas Baruchel’s web site by of images from complex analysis. I wondered what a collage of these images would look like, so I used the ImageQuilts software by Edward Tufte and Adam Schwartz to create the image below. Related: Applied complex analysis

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