Syzygy

Posted on 15 July 2013 by John

Syzygy must be really valuable in some word games. Such an odd little word.

I’ve run into the word syzygy in diverse contexts and wondered what the meanings had in common. According to the Online Etymology Dictionary, the word comes from

Greek syzygia “yoke, pair, union of two, conjunction”

It is used in biology to denote a pairing of chromosomes. Jung uses it to denote a pairing of opposites.

In astronomy it refers to an alignment of three objects in a gravitational system. In math it denotes an alignment of sorts, a linear combination of module generators that sums to 0.

Bayes : Python :: Frequentist : Perl

Posted on 13 July 2013 by John

Bayesian statistics is to Python as frequentist statistics is to Perl.

Perl has the slogan “There’s more than one way to do it,” abbreviated TMTOWTDI and pronounced “tim toady.” Perl prides itself on variety.

Python takes the opposite approach. The Zen of Python says “There should be one — and preferably only one — obvious way to do it.” Python prides itself on consistency.

Frequentist statistics has a variety of approaches and criteria for various problems. Bayesian critics call this “adhockery.”

Bayesian statistics has one way to do everything: write down a likelihood function and prior distribution, then add data and compute a posterior distribution. This is sometimes called “turning the Bayesian crank.”

Triangular numbers and simplices

Posted on 11 July 2013 by John

A couple weeks ago I posted a visual proof that

$1 + 2 + 3 + \cdots + n = {n+1 \choose 2}$

This says that the nth triangular number equals C(n+1, 2), the number of ways to choose two things from a set of n + 1 things.

I recently ran across a similar proof here. A simplex is a generalization of a triangle, and you can prove the equation above by counting the number of edges in simplices.

A 0-simplex is just a point. To make a 1-simplex, add another point and connect the two points with an edge. A 1-simplex is a line segment.

To make a 2-simplex, add a point not on the line segment and add two new edges, one to each vertex of the line segment. A 2-simplex is a triangle.

To make a 3-simplex, add point above the triangle and add three new edges, one to each vertex of the triangle. A 3-simplex is a tetrahedron.

Now proceed by analogy in higher dimensions. To make an n-simplex, start with an n-1 simplex and add one new vertex and n new edges. This construction shows that the number of edges in an n simplex is 1 + 2 + 3 + … + n.

Another way to count edges is to note that an n-simplex has n+1 vertices and an edge between every pair of vertices. So an n simplex has C(n+1, 2) edges. So C(n+1, 2) must equal 1 + 2 + 3 + … + n.

How to subscribe to a Twitter account via RSS now

Posted on 9 July 2013 by John

Twitter turned off their RSS support last month. This page gives several ways to create new RSS feeds for Twitter accounts.

Update (October 27, 2014): Here is a cost-free and ad-free Android app that is an RSS feed generator for Twitter.

Update (April 25, 2015): Here is a list of RSS feeds for each of my Twitter accounts, hosted by BazQux.

Update (February 6, 2017): Subscribing to Twitter via RSS is a losing battle. I’ve deleted the rest of this post because it doesn’t work anymore.

Disappointing title

Posted on 3 July 2013 by John

I caught a glimpse of a book in a library this morning and thought the title was “Statistics for People Who Think.” Sounds like a great book!

But the title was actually “Statistics for People Who (Think They) Hate Statistics” which is far less interesting.

Antihubrisines

Posted on 3 July 2013 by John

From John Tukey’s Sunset Salvo:

Our suffering sinuses are now frequently relieved by antihistamines. Our suffering philosophy — whether implicit or explicit — of data analysis, or of statistics, or of science and technology needs to be far more frequently relieved by antihubrisines.

To the Greeks hubris meant the kind of pride that would be punished by the gods. To statisticians, hubris should mean the kind of pride that fosters an inflated idea of one’s powers and thereby keeps one from being more than marginally helpful to others.

Tukey then lists several antihubrisines. The first is this:

The data may not contain the answer. The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data.

A couple definitions of applied math

Posted on 2 July 2013 by John

My advisor in grad school used to say that applied mathematics is an attitude, not a subject classification. You can’t take an area of math and say whether it is or isn’t applied. Any area of math can be applied, or not, though some areas are applied more frequently and more directly than others.

Here’s a possible definition of applied math:

An area of math is applied, for you, if you’ve been paid to use it and not just to teach it or write about it.

By this definition, some rarefied areas of pure math are applied, but only for some people and not for others.

Here’s a less personal definition, and one that’s fuzzy rather than binary:

An area of math is applied in proportion to the amount of money people have made applying it.

Why the emphasis on money? Because that’s the common way people express their desires quantitatively. It’s a way of determining how much value the problem owner, not the mathematician, finds in the solution. Applied is in the eye of the client.

An interesting feature of both definitions is that they can change over time, especially in the personal definition. I’ve applied parts of math that I never thought I would. And there are also things I thought I’d find more use for than I have.

Month: July 2013