Comments on: The World is Pointy: Thomas Friedman’s Geometry

By: Shlomo Angel

Shlomo Angel — Fri, 26 May 2006 22:58:38 +0000

A propos the average distance between two points in a circle: Can you prove that among all shapes of a given area, the circle is the shape with the minimum average distance between any two points within it?
Alternatively, can you direct me to a reference where I can find such a proof?
Your help will be highly appreciated.
Regards,
Dr. Shlomo Angel
Adjunct Professor of Urban Planning
New York University

By: Greg

Greg — Fri, 23 Dec 2005 13:36:45 +0000

First of all, I’m definitely playing things a littled tongue and cheek here (that’s why I said in the post that treating Friedman’s metaphor as serious math would entail using a “mode of argument as removed from (and arguably therefore as unfair to)” The World is Flat as possible.
That said, Friedman does have a big problem with metaphorical imprecision. In the section on the Ten Forces that Flattened the World (on p. 55) he talks about the west “downloading the future” while Bin Laden and other forces of Islamic terror are “uploading the past”. I know that he wants to talk about the way that the heightened connectivity of the internet age enables anti-modernist terrorism as much as it enables economic modernization and globalization, but this downloading/uploading metaphor is just gibberish. He’s not using the technical side of the metaphor in a semantically meaningful way.
I think that this kind of slopiness (which is systemic throughout what is otherwise an excellent and well-thought through book) endangers both the clarity of Friedman’s writing (it makes me less sure of what he is trying to argue) and potentially even his thought itself (in the case of the downloading/uploading example, he’s using the metaphor to draw buttress the contrast he’s making between Islamic terror and the advance of gloablization when one could very easily argue that they were not so ideologically opposite).
I don’t think it’s unreasonable to try to figure out if the title of his book itself suffers from this same sloppiness. And if you read the post carefully, you’ll notice that I found that it does, but not nearly as much as I expected when I set out.

By: Louis Abramson

Louis Abramson — Tue, 20 Dec 2005 23:52:27 +0000

Thomas Friedman makes it very clear that nobody can predict what the world will look like a decade from now. Since Friedman is a journalist and not a mathematician I believe you totally missed what he was trying to say. In layman’s terms “flat” just refers to a “plane” or two-dimensional environment thereby eliminating peaks and valleys that could become obstructions in seeing (line of sight) or moving from point A to point B. He uses the simili in order to make it easy for those that had trouble with geometry and other Math branches to understand the dynamic and frantic transformation of our trading world. Spherical or Plane the world is abstractically being flatten, period.

By: Ari

Ari — Tue, 20 Dec 2005 01:02:37 +0000

Yeah, at a certain point it’s just a metaphor — and a bad one, at that! If you’re curious, here is how flat maps of the earth are actually made: 1) Wrap a cylinder around the Earth so that it touches the equator. The cylinder’s axis goes through the north and south poles. 2) Project out from the axis onto the surface of the cylinder. We now have a cylindrical map of the earth. 3) Cut the cylinder wherever you’d like to get a rectangular map.
Who knows … maybe Friedman will be hanging out with a musician one day and decide that the earth is sharp. 😉

By: Greg

Greg — Mon, 19 Dec 2005 21:28:38 +0000

I guess it depends what you think of as a “flattened” version of the sphere. I was just imagining it as a circular section (as would result from a sphere getting squashed straight down to two dimensions). Metaphorically, the fact that the sphere has greater surface area than the disc seems totally appropriate.
Anyway, that was my thinking. Thanks for the input!

By: Ari

Ari — Mon, 19 Dec 2005 13:49:45 +0000

Hey Greg,
One immediate problem comes to mind: your sphere has 4 times the surface area of your disc with the same radius. To get the same area, you should double the radius of the disc.
Cheers,
Ari