Blog Profile / The Endeavour
| URL : | http://www.johndcook.com/blog/ | |
|---|---|---|
| Filed Under: | Academics | |
| Posts on Regator: | 754 | |
| Posts / Week: | 6.7 | |
| Archived Since: | April 26, 2011 | |
Blog Post Archive
Gelfand’s question
Gelfands’s question asks whether there is a positive integer n such that the first digits of jn base 10 are all the same for j = 2, 3, 4, …, 9. (Thanks to @republicofmath for pointing out this problem.) This … Read more ›
What have you been doing?
Several people have asked me what kind of work I’ve been doing since I went out on my own earlier this year. So far I’ve done a lot of fairly small projects, though I have one large project that’s just … Read more ›
Continuous quantum
David Tong argues that quantum mechanics is ultimately continuous, not discrete. In other words, integers are not inputs of the theory, as Bohr thought. They are outputs. The integers are an example of what physicists call an emergent quantity. In … Read more ›
Mean residual time
If something has survived this far, how much longer is it expected to survive? That’s the question answered by mean residual time. For a positive random variable X, the mean residual time for X is a function eX(t) given by … Read mo...
No use for old things
From Brave New World: “But why is [Shakespeare] prohibited?” asked the Savage. … The Controller shrugged his shoulders. “Because it’s old; that’s the chief reason. We haven’t any use for old things here.” “Even when they’re beautiful?” “Particularly when they’re … Read more ›
Pure math and physics
From Paul Dirac, 1938: Pure mathematics and physics are becoming ever more closely connected, though their methods remain different. One may describe the situation by saying that the mathematician plays a game in which he himself invents the rules while … Read more ›
Example of unit testing R code with testthat
Here’s a little example of using Hadley Wickham’s testthat package for unit testing R code. You can read more about testthat here. The function below computes the real roots of a quadratic. All that really matters for our purposes is … Read more ›
Singular Value Consulting, LLC
The name of my business is Singular Value Consulting, LLC. Math people may catch the allusion to singular value decomposition (SVD). I hope that non-math folks will interpret “singular value” to mean something like “singularly valuable.” One way to think … Read more ›
Computing skewness and kurtosis in one pass
If you compute the standard deviation of a data set by directly implementing the definition, you’ll need to pass through the data twice: once to find the mean, then a second time to accumulate the squared differences from the mean. … Read more ›
A statistical problem with “nothing to hide”
One problem with the nothing-to-hide argument is that it assumes innocent people will be exonerated certainly and effortlessly. That is, it assumes that there are no errors, or if there are, they are resolved quickly and easily. Suppose the probability … Read more ›
The weight of code
From Bjorn Freeman-Benson’s talk Airplanes, Spaceships, and Missiles: Engineering Lessons from Famous Projects Bjorn is discussing the ferrite core memory of the Apollo guidance system. These are very, very robust memory systems. … But the problem is that they actually … Read more ›
Bottom-up exposition
I wish more authors followed this philosophy: The approach I have taken here is to try to move always from the particular to the general, following through the steps of the abstraction process until the abstract concept emerges naturally. … … Read more ›
Orwellian vs Huxleyian
Orwell and Huxley wrote contrasting dystopian books. In Orwell’s 1984, people are controlled by overt totalitarian power. In Huxley’s Brave New World, people are lulled into submission. Orwellian became a common adjective: But Huxleyian didn’t: Neither did Huxleyan: Orwellian gets … Read more ›
Seven dogmas of category theory
Joseph Goguen gave seven dogmas in his paper A Categorical Manifesto. To each species of mathematical structure, there corresponds a category whose objects have that structure, and whose morphisms preserve it. To any natural construction on structures of one species, … Read more ›
SymPy book
There’s a new book on SymPy, a Python library for symbolic math. The book is Instant SymPy Starter by Ronan Lamy. As far as I know, this is the only book just on SymPy. It’s only about 50 pages, which … Read more ›
All models are wrong …
Merger of two tweets from Nassim Taleb: All models are wrong but some are deadly. One does not judge a model on whether it is wrong, rather how costly the error, period.
How many lights can you turn on?
Suppose you have a large n × n grid of lights, some turned on and some turned off. Along the side of each row is a switch that can toggle the lights in that row, turning on lights that were … Read more ›
Sum-free subset results
This posts gives some results for the sum-free subset problem in the previous post. Paul Erd?s proved in 1965 that a set of n non-zero integers contains a sum-free subset of size larger than kn where k = 1/3. The … Read more ›
Sum-free subset challenge
A set of integers is called sum-free if no element of the set is the sum of any other pair of elements in the set. For example, {1, 10, 100} is sum-free. Let’s look at pulling out a sum-free subset … Read more ›
Blueberry season
I took a couple of my kids blueberry picking this morning at Chmielewski Blueberry Farm. It’s a little early in the season, so some of the berries are ripe but a lot are not. Here’s a post I wrote four … Read more ›