The Debunking Outer Space Challenge

According to John Loftus:

I've proposed reading one skeptical book a month in 2011 as the Debunking Christianity Challenge. Now I'm going to propose a Part 2. Both of these challenges are designed to help Christians test their faith as outsiders. Here's another way for Christians to take the Outsider Test for Faith. Do this...

First, if you are a conservative Christian (my target audience) then 1) Spend one month visiting and commenting at the Progressive Christianity Board. You will see quite clearly that your brand of Christianity isn't the only one. Try to deal with their arguments while you're at it (Hey, they're not coming from atheists). 

Then visit and comment on the following forums for one additional month each: 

2) Scientology Forum. 

3) Mormon Forum. 

4) Islam Forum. 

5) Hindu Forum. 

6) Orthodox Jewish Forum. 

My claim is you will see quite clearly that the basis for your faith is the same as the basis for each one of these other faiths. You will see why you should abandon it in favor of a science based reasoning.

http://debunkingchristianity.blogspot.com/2011/01/debunking-christianity-challenge-part-2.html

I have a counterproposal to help Loftus test his faith in science as an "outsider."

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Figure 3. A model for the hyperbolic plane. Heaven and Hell by M.C. Escher.

Not quite as well-known are Poincare's models of 3-d non-Euclidean space. Imagine space to be filled with small metal balls, whose size is proportional to the temperature T of space.  Euclidean space is represented by a constant temperature, so that the spheres are uniformly the same size throughout space. A model for infinite hyperbolic space can be constructed by taking a finite Euclidean sphere of radius R with a temperature variation of T = k (R2- r2), where k is a constant of proportionality and r is the distance of a ball from the center. The metal balls then shrink to nothing as they approach the edge (this is the 3-d version of Figure 3). For a moving object, its speed likewise diminishes as it approaches the edge, so it never quite reaches the edge.

 Similarly, we can model (finite) elliptical space of radius R in the same Euclidean sphere by letting the temperature vary as T = k/(R2- r 2). Now the spheres grow infinitely large as they approach the edge, thus re-appearing on the opposite side.

Such modeling of non-euclidean geometries within the more familiar euclidean space helps us to visualize the properties of such novel geometries. This illustrates a further function of mathematical models: to represent various aspects of reality that are otherwise hard to visualize. Mathematical models help to translate novel conceptual geometries into the more common Euclidean space of our everyday experiences.

Of Earths Inverted and Flattened

Closely related to these geometrical models are some unusual conceptions of the universe. For example, Fritz Braun (1973) asserts, based on his interpretation of biblical texts, that the Earth should be inverted. The Earth's surface is the inside of a hollow sphere enclosing the Sun, Moon, and stars. Heaven is at the center of the inverted universe, thus making this model literally theocentric (see Figure 4).

Figure 4. Braun’s Inverted Universe. Note that heaven is at the center, surrounded by the glassy sea, the planets, Sun and clouds.

         At first sight this model seems obviously false. One might think, for example, that this model entails that we should be able to see across the hollow sphere to the other side of the Earth. Indeed, in 1933 German promoters of the hollow Earth theory tried to prove their theory by means of rockets. They reasoned that a rocket, fired straight up, should hit the opposite side of the Earth. Various rockets were fired but, unfortunately, they all malfunctioned and the test was eventually abandoned.

However, this model is not that easily dispensed with. It can be devised so that disproof is impossible.        The above tests take for granted that the normal laws of physics hold. In particular, light is expected to travel in roughly straight lines and rockets, in the absence of forces, are expected to move at a constant velocity. But what if this is no longer the case?

     

The hollow Earth model can be derived from the more usual picture of the universe via a simple mathematical transformation called a "geometric inversion". The procedure is very simple. For each point in the universe, measure its distance r from the center of the Earth and move the point along the center-to-point line to a new distance 1/r. The result of this operation is that all objects originally outside the Earth (e.g., mountains, houses, clouds and stars) are now inside, and vice versa (see Figure 5). Inversion is a conformal transformation, which means that local shapes are preserved.

Figure 5. A Simple Model of the Universe and Its Inverse. The second figure is the result of inverting the first figure, taking the earth’s center as the center of inversion. For ease of comparison, the first figure has been flipped horizontally. Note the curved light rays and the diminishing size of the rocket as it recedes from the earth.

The laws of physics are also inverted, with consequences that may seem strange for those accustomed to thinking in terms of the more conventional universe. For example, light now travels in circular arcs. Also, a rocket launched from the Earth to outer - or, rather, now "inner" - space will shrink and slow down as it approaches the central heaven, never quite reaching it (see Figure 5).

     

Consequently, Braun's inverted universe is observationally indistinguishable from more conventional models of the universe. Yet, although the two models are empirically identical, they involve quite different ways of viewing reality. Braun's model reflects his theological beliefs. Again, the mathematical model functions here to connect a particular worldview with observations, thus making that worldview more viable.

Note that, if we were to take a point on the Earths’ surface as the center of inversion then we would get a flat Earth (i.e., this is the stereographic projection of geography). As you travel to the edge you become infinitely large at the edge, so that you re-appear at the right (see Figure 6). Again, this model is observationally undisprovable.

Figure 6. Inverting to a Flat Earth. An inverted picture of Figure 5, with the center of inversion on the earth’s surface. The other figure is an enlarged view.

http://www.reformation.edu/scripture-science-byl/pages/09-mathematical-models.htm