The political duality of rep and dem

by: OpenLeft

Sat Jan 02, 2010 at 10:00

A Paul Rosenberg Golden Oldie
From Sat Oct 06, 2007. Original HERE.

There's a rather far-flung concept in mathematics known as "duality."  A few days ago it struck me how this concept can illuminate something very fundamental about the current state of American politics.  It's a powerful, and far-reaching concept, but fortunately you don't have to grasp a great deal about it in order to get my point.

As Wikipedia explains:

Generally speaking, dualities translate concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion. Duality is characteristically an involution operation: if the dual of A is B, then the dual of B is A. As involutions sometimes have fixed points, the dual of A is sometimes A itself.

Ohhhh-kay.  Let's try bringing that down to Earth a little bit, shall we?

A simple example comes from graph theory:

In mathematics, a dual graph of a given planar graph G has a vertex for each plane region of G, and an edge for each edge joining two neighboring regions. The term "dual" is used because this property is symmetric, meaning that if G is a dual of H, then H is a dual of G; in effect, these graphs come in pairs.

That may still sound like Greek to you, but it's a whole lot simpler when see it pictured like this:

See?  Each blue vertex (dot) is alone within a plane region defined by red edges (lines), and visa versa.  Each red line intersects one blue line, and visa versa.

In effect, the dual graph of G is sort of like turning G inside out.

So what's this got to do with politics?  With Democrats and Republicans?

Simple....

The Political Duality Of Rep and Dem

by: Paul Rosenberg

Sat Oct 06, 2007 at 06:00

As Wikipedia explains:

Generally speaking, dualities translate concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion. Duality is characteristically an involution operation: if the dual of A is B, then the dual of B is A. As involutions sometimes have fixed points, the dual of A is sometimes A itself.

Ohhhh-kay.  Let's try bringing that down to Earth a little bit, shall we?

A simple example comes from graph theory:

In mathematics, a dual graph of a given planar graph G has a vertex for each plane region of G, and an edge for each edge joining two neighboring regions. The term "dual" is used because this property is symmetric, meaning that if G is a dual of H, then H is a dual of G; in effect, these graphs come in pairs.

That may still sound like Greek to you, but it's a whole lot simpler when see it pictured like this:

See?  Each blue vertex (dot) is alone within a plane region defined by red edges (lines), and visa versa.  Each red line intersects one blue line, and visa versa.

In effect, the dual graph of G is sort of like turning G inside out.

So what's this got to do with politics?  With Democrats and Republicans?

Simple....