Comments on: Pragmatic Quincuncial Cartography

By: Cosmic Variance: Physics, postmodernism, and Richard Rorty « Identity Unknown

Wed, 13 Jun 2007 02:01:08 +0000

[...] pin down; while he was most closely identified with the American pragmatist tradition of Dewey and Peirce, he was trained as a hard-core analytic philosopher, and later became heavily influenced both by [...]

By: Richard Rorty | Cosmic Variance

Richard Rorty | Cosmic Variance — Sun, 10 Jun 2007 20:15:00 +0000

By: Plato

Plato — Thu, 15 Sep 2005 20:03:09 +0000

Conformal maps of the Earth are a great introduction to complex analysis. If you identify the Earth with the Riemann sphere, then the Mercator map is exp(i*z), while the quincuncial projection is a Weierstrass elliptic function. Or you could view it as a 2-to-1 conformal projection from a torus to a sphere with four ramified points. I imagine that it is relevant to one-loop calculations in string theory in that guise. While I like to see this movement, I wanted to develope it into a modern view. Not only this, but how perception is dependant when seeing tessellations. Sort of like using a line of a shadow or light, depending on your point of view to support the line?:) What mathematics would describe this?

By: Greg Kuperberg

Greg Kuperberg — Thu, 15 Sep 2005 17:11:12 +0000

It would be fun to use a modular form to make an Escher-like repeating conformal map of the earth in the hyperbolic plane. Escher himself veered towards similar possibilities. In addition to the famous hyperbolic tiling, Circle Limit IV or “Angels and Devils”, he used the same angels and devils to tile the sphere, as a wood carving. The real starting point is a smaller sphere tiled by one angel and one devil, with both of the Escher works as branched conformal lifts. (Indeed if you look carefully, the angels and devils are both just decorated triangles, rendering angels and devils equivalent to each other by reflection. So you could start with a disk with three marked points for the two wingtips and the joined feet of either creature.)

By: Alejandro Rivero

Alejandro Rivero — Thu, 15 Sep 2005 13:28:40 +0000

AKAIK, every islamic map has the south in the top. I am in doubt about islamic globes. Are they inverted when shown in museums? A related issue is constelation naming.

By: Clark Goble

Clark Goble — Thu, 15 Sep 2005 03:04:07 +0000

People I know who are Peirce scholars don't like Menand's book. I think it was less free love than wanting a divorce in a society that didn't condone such things. It also led to pretty much the end of his formal academic career. But he definitely is an amazing philosopher. There's a scholarly site for papers on him that has many of his main papers.

By: Matt McIrvin

Matt McIrvin — Thu, 15 Sep 2005 02:01:20 +0000

Equal-area projections are good for countering Northern Hemisphere ethnocentrism, but there are better ones out there than the Peters, such as the Mollweide or this particularly nice flat polar quartic one, or the interrupted equal-area projections. They're often used for statistical maps where equal area is particularly important.

By: Clifford

Clifford — Thu, 15 Sep 2005 00:27:41 +0000

I guess I misspoke and/or was not clear. Sorry. I meant that it was not the issue that I was emphasizing in my previous comments concerning liking equal area (despite its shortcomings). I did not mean to imply that “rediscovery” of an idea is not an issue in general.

-cvj

By: Sean

Sean — Thu, 15 Sep 2005 00:22:36 +0000

Well, the fact that Peters gained notoriety for his maps by emphasizing political concerns and ignoring centuries of cartographical research is an issue, and an interesting one. There are lots of equal-area projections out there, going back quite some time. My personal preference is not for strict equal-area projections, since they distort shapes so badly. Better to compromise between shape/size issues, as Peirce's map does pretty well. As Wolfgang points out, putting the South Pole at the top makes an interesting political statement. Although you still have to defend your equatorial-centrism.

By: Clifford

Clifford — Wed, 14 Sep 2005 23:58:03 +0000

Matt, the issue here is not who thought of it first, or whether Peters was a charlatan or not…. The issue is the idea of emphasizing the area over other political concerns. There will always be distortions, right? You have to make some sacrifices. So whether you call it Peters or Gall, or Rumpelstiltskin’s projection, there are some merits to choosing to emphasise area over other things. I for one like to be reminded that North America and Western Europe are not quite as huge and important as they think they are….

Cheers,

-cvj