I’ve seen a lot of confused discussion of perspective on this forum as well as on the Wiki. I think some of this confusion arises because “perspective” has at least two distinct meanings in the context of scientific discussions:
(1) A branch of geometry that considers where straight lines drawn between a specified point P and a set of other points in three dimensions will intersect with a plane placed between P and the other points. Perspective in this sense was pioneered by ancient Greeks such as Euclid and was further developed during the Renaissance to assist artists, on the assumption that light travels in straight lines, in producing paintings and drawings with a more realistic 3-D look. To my knowledge no one has found any logical flaws in the proofs of the theorems of perspective in this sense, so it still stands as an established field of geometry. Let’s call this kind of perspective “perspectiveG” for purposes of this discussion.
(2) A branch of optics, which in turn is a branch of physics, that studies what happens to light when it passes through air. This is sometimes called “aerial perspective,” so let’s call it “perspectiveA.”
Let’s further distinguish both of these senses of “perspective” from the study of how the human eye perceives light and how the brain interprets the messages it receives from the eye. That is
vision science, which overlaps with neuroscience, psychology, ophthalmology, and other sciences.
Bearing these distinctions in mind, I want to look at some comments from Tom Bishop, not to pick on Tom (whose courtesy and apparent sincerity I appreciate) but because he seems to post frequently on perspective. I hope I am not distorting his meaning by taking his quotes out of context:
Tom Bishop:
I'm asking for some sort of evidence that perspective works the way the Ancient Greek math says it works. Will two parallel lines really recede forever into the distance and never appear to touch? That seems extraordinary.
Why should we believe that just because an ancient greek philosopher said that a perfect world would be that way?
To begin with, ancient Greek math, in this case Euclid,
defined parallel straight lines as “straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.” You can’t refute a definition, and you can’t refute math without showing a logical flaw in the reasoning. What Tom seems to be talking about here is how distant objects will actually appear to the human eye and brain. The science of optics covers what happens to light as it travels from the objects to the eye, and vision science studies how our brains interpret the light received by the eye (for instance, whether we perceive one object or two when they are separated by 1 second of arc), so this is a question of optics and vision science.
Tom Bishop:
How do we "know" what happens to perspective tens or hundreds of miles away? Who studied that?
Perspective hasn't been tested at any large distance at all. At what distances has it been tested? Who studied it? Please name names and cite studies rather than claiming that it has been proven.
Here Tom is apparently talking about perspectiveA, not perspectiveG – he’s asking how objects actually appear to us when viewed through hundreds of miles of air. But we actually know, beyond reasonable doubt, a great deal about this. The science of optics is well developed and extremely successful at explaining the behavior of light, including what happens to it as it passes through air containing moisture and dust and with temperature and pressure gradients. We can’t directly test what happens to light when it passes through 6000 miles of air because no one has been able to find 6000 miles of the earth’s atmosphere in a straight line. In any case, modern optics provides absolutely no grounds for supposing that light performs the acrobatics posited by FET to explain how the moon displays the same phase simultaneously to all viewers, or how the sun and moon appear to set, or how they maintain the same angular diameter, all while remaining above a flat earth.
Of course, you can argue that mainstream optics is wrong about this – but then you need to come up with better theories that do a better job of explanation and prediction than the currently accepted ones. This is just one instance of what we may call The Big Problem with Flat Earth Theory, namely the fact that FET tosses out large chunks of mainstream science without offering any mutually consistent alternative theories that do at least as good a job of explanation and prediction as the mainstream theories, which include Round Earth Theory. Since what we want from scientific theories is to explain and predict what we observe, we are left with no rational reason to switch to the FE side.