There is a way of mapping the allegedly round globe onto a flat piece of paper which is the stereographic azimuthal projection. To do this we make the line which joins each point on earth with its corresponding point on the map begin at the south pole.(The south pole actually needs to be mapped onto an extra point.) (Wilhelmy, ch. 1, p. 43. A similar mathematical construction is often called "The one point compactification of the plane" )
When we use this projection to make a map we generally confine ourselves to only one hemisphere.
If we didn't, we'd get a map that looked something like this.
We've not included more of Antarctica (which would appear as a giant ring surrounding the whole world) because then we'd have had to shrink the northern hemisphere to a dot in order to fit everything onto the screen. And to show the whole of Antarctica the screen would have to be infinitely large.
Can we claim that our flat, distorted map represents reality, that the world isn't, in fact, spherical at all and that Tierra de Fuego is really larger than North America and Eurasia put together? There always a few skeptics. What would happen if some of these doubters tried to disprove our flat earth theory? They would set off on an expedition to the south, brandishing their yardsticks, to take measurements which would expose our theory. But our theory predicts that on their journey both they and their yardsticks will become steadily longer. So if they report that according to their measurements Tierra de Fuego is actually smaller than Iceland we can rightly say "Well, that's exactly what stereographic-azimuthal-flat-earth theory predicted!"
One might think that because physics happens in three dimensional space, one could find a contradiction to our flat earth theory by making use of this. But, in fact, the distortions caused by the stereographic azimuthal projection extend into three-dimensional space, so that all the evidence the skeptics thought would prove the earth to be round we can now interpret as justifying our flat-earth theory. The doubters may claim that we can still see the top of a ship which is far away and not its bottom, because light goes in straight rays and so the light from the bottom would have to go through the earth to reach our eyes.
But the stereographic azimuthal projection can be applied not only to the surface of the earth but simultaneously to every sphere which has the middle of the earth as its centre. To reduce the complexity of the following picture, the nested spheres have been simplified into circles. One of Wilhelmy's spheres then reduces to the following.
We can now imagine that the whole of space is divided into an infinite number of concentric spheres which are then transformed into planes so that they can be piled up one on top of another like a stack of infinitely thin sheets of paper and to form again a three-dimensional space. Together with the space we automatically transform the laws of physics.
Thus the stereographic azimutal projection permits a mapping of the total three-dimensional space onto itself. All physical phenomena are transformed accordingly. Let us look at what happens to a ray of light.
The path of the light ray over the flat earth can be plotted by transforming all the points where the light ray penetrates the (imaginary) spheres, (which are here shown as circles).
This shows us that our stereographic-azimuthal-flat-earth theory is in accordance with the evidence of our senses: the light which is reflected from the bottom of the ship cannot reach our eyes because the rays of light are curved and are therefore blocked by the flat earth.
The moral of it all is that we can not decide whether the earth is flat by purely physical means, that is, by observation.
Even so, our stereographic-azimuthal-flat-earth theory with its location-dependent yardsticks and variously curving light rays is not accepted by real scientists. They reject our theory solely on grounds of parsimony, and not because any experiment would disprove it.
Gardner, Martin. "Occam's Razor and the Nutshell Earth." Skeptical Inquirer 12 (4) (1988): 355-58.
Russell, Jeffrey Burton. Inventing the flat earth: Columbus and the modern historians. New York, Praeger, 1997
Schadewald, Robert. J. "The Flat-Earth Bible." The Bulletin of the Tychonian Society No. 44 (July 1987):
Schadewald, Robert. J. "Scientific Creationism, Geocentricity, and the Flat Earth." Skeptical Inquirer Winter 1981-82
Shermer, Michael. "The Heretic-Personality. Alfred Russell Wallace and the Nature of Heretical Science. " The Skeptic 4 (3) 1997: 84-93.
Straughen, Kirk. "Biblical Cosmography." the skeptic 17 (3) (19997): 28-31
Swindler, Adrian. "The Flat-Earth Belief of Bible Writers" The Skeptical Review winter (1990): 9-11
Wilhelmy, Herbert. Kartographie in Stichworten. Kiel: Ferdinand Hirt, 1972.
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Last update: 15. July 2007