A Journey to the Southern Cone

17 May 2010


Mathematical Cone

In geopolitical terms the southernmost portion of South America is sometimes called the “southern cone.” Truly enough, southernmost South America does look like a cone, although an inverted cone. In almost all mathematics textbooks you will see that a cone is represented as standing on its broad base and with its vertex pointing toward the sky. The exception to this includes illustrations of conic sections, which are sometime shown with two cones joined tangentially at the vertex, so that one cone appears in its usual posture while another appears inverted.

Conic Sections

This resemblance of the southern cone to an inverted cone, however, is entirely due to a convention of mapping that places the North Pole at the top of a map and the South Pole at the bottom of a map. While is this the most familiar orientation of maps today, there is nothing necessary about it. In fact, many “inverted” maps have been produced in order to challenge our perceptions about the orientation of the world. Australians and New Zealanders have a certain interest in such maps and have produced many of them.

On an inverted map, the “southern cone” appears as a cone in its ordinary orientation, though I should point out that the “ordinary” orientation of a cone, as familiar as it is, is no more necessary or even desirable than the “ordinary” orientation of a map. Both the cone that we know and love and the maps that we know and love are conventions, and part of our love for them is like our love for our family: we don’t know anything different. However, familiarity is as likely (if not more likely) to beget contempt as to beget love, so if one experiences a bout of Weltschmerz (or even mathematikschmerz, if we are speaking of pure cones rather than applied cones) it may simply be a weariness with the familiar aspect of the world, and if we would but make an effort to see the world from a new perspective it might appear fresh and exciting and our world-weariness would vanish without a trace.

Which is as much to say that I am about to embark upon another attempt to see the world from a new (or, at least, somewhat new) perspective. As I write this I am waiting in the Portland aiport to catch a flight that will ultimately (if all goes well) deposit me in Cordoba, Argentina sometime tomorrow. So I have about twenty-two hours of travel ahead of me. I have my travel reading mentioned yesterday packed with me in my carry-on baggage, and look forward to expanding and amending my perspective on the world for the next couple of weeks.

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2 Responses to “A Journey to the Southern Cone”

  1. Very good points!! I was planning to get a tattoo on my back, a map of the world, and the countries and highlight the ones I’d traveled to, then I decided not to include the borders and make it just geographical, naked, how it was meant… Now I’ve decided it was meant to be inverted! 🙂

    thanks! 😀

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