(I’m starting a new thread because the discussion in “Some Perspective on Perspective” has drifted beyond the topic of perspective. I hope that’s OK.)
Here’s the problem for Flat-Earth Theory: By an unfortunate coincidence, the sun, Moon, planets, their moons, stars, and even the putative earth-orbiting satellites happen to look and move exactly like they would look if mainstream round-earth science were true. This is also true of the earth itself, with some disputed exceptions noted below, and of the purported photos of the earth from space. So the challenge for the FE camp is how to rationally persuade RE believers to hop on the FET bandwagon. The only way I can think of to do this is to demonstrate that FET explains the observations explained by mainstream RET science better than RET does. Here is where FET runs into some problems, for example in explaining how the sun appears to rise and set in a manner consistent with FET:
The math is very limited, and assumes that local effects hold true endlessly. Unless you have accurately experimented at all scales, it cannot be said that we know how things will look like at all scales based on math alone.
The universal laws and principles of the physical sciences are independent of scale or location, otherwise they would not be universal. It’s reasonable to assume, for example, that chemistry follows the same principles on Neptune as it does on the earth, because those principles have been found to hold wherever they have been tested, and they have been tested very extensively indeed, experimentally and by other forms of observation. Of course it's conceivable that chemistry works on different principles on Neptune or the Andromeda galaxy, but we have no evidence pointing in that direction and therefore no good reason to think so.
The same is true of the laws and principles of thermodynamics, optics, gravitation, etc. If, after a vast amount of testing by observation including experimentation, we always find that light follows Fermat’s principle, i.e., takes the least-time path (usually a virtually straight line), then it’s reasonable to assume that light follows the same rule in a new situation, absent evidence to the contrary. (I know the situation is more complicated from the point of view of quantum mechanics, but let’s stick with macroscopic physics for the time being.)
Thus if we want to predict how the sun would appear at a height of 3000 miles above a point 8000 miles distant from the observer on a flat earth, the principles of optics and our knowledge of the composition and structure of the earth’s atmosphere will give us a pretty exact answer. Inconveniently for FET, the answer is not that the sun will appear to be setting. Of course, it is possible that our theories of optics could be wrong in some respects, such that the sun would appear on the horizon. But at this point we have absolutely no experimental or theoretical evidence that this is the case, so the rational prediction is the one given by our thoroughly tested and understood principles of optics and well-understood composition of the atmosphere. The only remotely plausible way the sun could appear to be setting, consistent with mainstream physics, is that the light from the sun undergoes a huge amount of refraction, which is inconsistent with what we know about the atmosphere and would cause the sun to appear somewhat rotated upward when setting (this could be checked with sunspots). And if you think mainstream physics is wrong, let’s please see some actual evidence.
And here’s the thing: we already have a theory that explains, simply, with great accuracy, and consistently with the rest of our scientific knowledge, how the sun and other celestial objects appear and their positions and paths through the sky.
"Zeus and the other gods did it" is also a theory that explains everything. That's why experimentation is necessary, I am afraid.
“The gods did it” is not a scientific theory. In any case, scientists have already done a huge amount of experimentation and other types of observation, resulting in mainstream physics and astronomy, including a round earth. They’re quite amazingly successful in explaining what we observe. Virtually the only way in which flat-earthers claim mainstream physics and astronomy are unsuccessful is in explaining a relatively few supposed observations, such as the horizon remaining at eye level as you go up (no it doesn’t), water surfaces appearing to be flat, and ships’ hulls remaining visible many miles away. If you think these are real anomalies for RET (i.e., cannot be explained consistently with RET), then you should document them carefully and get them into a peer-reviewed scientific journal. You could just call them “unexplained anomalies” without mentioning the shape of the earth. Then we can talk; until then you just have unverified anecdotes.
And to be rationally persuaded to jump on the FET bandwagon, we need to see mutually consistent FET explanations of all the observations that mainstream physics and astronomy explain, and that explain some observations that the mainstream explanations cannot. We could start with the supposed spiral path of the sun above a flat earth: what is the FET explanation? Then we can move on to how the sun produces the energy it radiates, how starlight is produced, what explains the different spectra of stars, the different types of stars and their origins, galaxies and the red shift of their spectra, meteors, star clusters, binary stars, dust clouds in the Milky Way, Cepheid variable stars, the fact that the radar echo takes several minutes to return when a signal is bounced off Venus, the specific patterns of seismic waves, apparent volcanoes on planets and their satellites, and countless other observations, increasing by the day. Oh, and how the phases of the Moon appear simultaneously the same across the earth. The Wiki discussion of this topic (second half of
http://wiki.tfes.org/The_Phases_of_the_Moon) appears not to understand what “phase of the moon” means, to dictionaries as well as astronomers.