Perhaps you've seen a map where Greenland appeared to be as large as Africa, or the island of Madagascar stretched into a sliver as long as South America. We'll talk with a mathematician about the trouble with map making - after this on Earth and Sky.
JB: This is Earth and Sky, on the challenge of making maps. We spoke with Dr. Robert Osserman of Berkeley's Mathematical Sciences Research Institute:
(Tape 0:12:30-0:12:47) People keep inventing new maps and hope always that they will find in some sense the perfect map, but it is a mathematical theorem that there is no perfect map -- not only of the whole Earth, but of any part of the Earth on to a flat piece of paper.
JB: You can see for yourself the challenge that faces map-makers if you eat a half a grapefruit and then try to flatten the peel without tearing it. You can't do it. This is basically what the great nineteenth-century mathematician Carl Friedrich Gauss proved. Again, Dr. Osserman:
(Tape 0:13:19-0:13:54) You can't have an exact scale map, so that if on the earth two points are a certain distance apart, then the corresponding points on your map will be at a fixed scale. And because of that fact, map-making remains a very alive subject because you are always compromising one way or another and you've tried to minimize the effects of the distortion in order to get the most desirable effects that you're looking for in a given map.
JB: Thanks to Dr. Osserman for speaking with us. And with thanks to the National Science Foundation, I'm Joel Block, for Deborah Byrd, for Earth and Sky.
Author: Beverly Wachtel
Thanks to the following individual for aiding in the preparation of this script:
Dr. Robert Osserman
Mathematical Sciences Research Institute
If you enjoyed this program, you may be interested in the following:
Poetry of the Universe, by Robert Osserman. NY: Anchor/Doubleday, 1996.
Mathematical Sciences Research Institute website:
Dr. John Polking's Cartography website: