This post is a continuation of my arguent (started here) that it is engineering that leads the way in the growth of real knowledge, and that science at best follows engineering. Science is awash with idle speculations, most of which, historically, have proven false over time. As I wrote in that essay, science is the attempt to parse out the underlying structure and causes of the universe. Engineering is the attempt to get things done. Academic science, when it is without a pragmatic purpose, is unmoored from reality, adrift in random speculation having no measure of success other than the good opinion of other scientists. Engineering is firmly moored to reality because everyone can see whether or not it works.
One of the earliest scientific thinkers was Parmenides of Elea (c. 475 BC) who taught that there can be no change because any change involves something coming from nothing, and that was impossible. This idea gained a following despite being completely at odds with experience. The attractiveness of Parmenides's teaching may be related to the competitive nature of scholarship in this period. A philosopher would be admired for being able to “prove” something that everyone thought was impossible. To a large extent, a philosopher gained points for cleverness rather than for truth.
Zeno of Elea was a friend of Parmenides who was famous for a set of paradoxes intended to support Parmenides by showing contradictions in the idea of movement. There are only a few of Zeno’s paradoxes still known today of which one is this: in order to walk 100 feet you first half to walk half way, then you have to walk half of the remaining distance then half of the remaining distance. You are making a series of walks of 50 feet, then 25 feet, then 12.5 feet, etc. There are an infinite number of these half walks so to walk the whole 100 feet you have to do an infinite number of actions. According to Zeno, you cannot do an infinite number of actions in a finite time, so motion is logically impossible.
Your approach to these paradoxes is a good indicator of whether you think like a scientist or like an engineer. If you take the reasoning as a given and try to come up with some way to show that an infinite sequence can sum to a finite number, then you are thinking like a scientist. A solution of this sort was invented in the 19th century, which means that this paradox left the poor scientists in a state of confusion and bafflement for about 2,400 years.
If you think like an engineer then you reject the premise that the argument is describing any actual process. The process of going halfway, then halfway again, is just a description, a way of thinking about the process. The very notion of halfway is an idea, not a real physical thing. To an engineer, the paradox shows, not a problem of motion, but a problem with the way the motion is being analyzed.
Both the engineer and the scientist agree on what the solution is, but not on what the solution means. They both agree that the solution is a mathematical theory that can properly handle the sum of an infinite series, but to the engineer, this is just a fix to the mathematics. To the scientist, there is a real infinite process and he needs to understand how this real infinite process can complete in a finite time.
Parmenides's theory and Zeno's paradoxes give an example of the sort of nonsense that you can come up with when you think like a scientist. The theory was obviously false. Zeno's proofs were obviously nonsense. There was no serious question but that motion was possible because it was experienced all the time. But scientists viewed this as a serious problem to be addressed.
Flat-earth theory is the same kind of thing. They rely on complex and superficially reasonable arguments to defend a point that experience shows to be false. There is a difference though: anyone could clearly see that Parmenides's theory was false; to see that the flat-earth theory is false, you need to look at engineering.
Contrary to common accounts, the earth was not proven to be round by the ancient Greeks. There were various inconclusive scientific arguments that the earth was round, but these arguments were scientific in the sense that there was no practical result of the theory: nothing would be done different, no outcomes would be predicted differently--except for one thing. The only place where there was a practical difference was astronomy. Astronomy proved that the earth was curved from north to south by the differing angles between the earth and the sky at different latitudes. They were even able to measure the north/south curvature by measuring the angle of the sun.
However, there were still lots of theories about the shape of the earth. In the Middle Ages, people believed that the sphere of water and the sphere of earth were essentially separate things (this was a consequence of Aristotle's primitive theory of gravity) so they though that the oceans bulged out on the Western Hemisphere. In fact, the amount of water was often assumed to be 10 times the amount of earth, so it would be a big bulge. The spherical nature of the earth was not really proved by practical methods until In 1522 when one ship from Magellan’s expedition arrived back in Spain, having completed the first circumnavigation of the earth.
According to flat earthers, Magellan's ship would have sailed in a large circle on a flat earth with the center at the North Pole, but this explanation goes against the engineering--that is, against the stellar navigation and the cartography. Stellar navigation and cartography are pragmatic disciplines--engineering disciplines--with practical results. Anyone can see if your course leads to the right place in the right amount of time, and stellar navigation does take the curvature of the earth into account. Cartography also takes the curvature of the earth into account because distances cannot be properly represented on a flat surface. To draw a map of the entire earth with all distances to one scale, you have to draw it on a globe. This is a simple fact of engineering.
Subsequent engineering efforts in other areas have also had to take the curvature of the earth into account. Long-range ballistics assumes a spherical earth. Space travel, satellites and GPS have to take the curvature of the earth into account. Prediction of weather and ocean currents assume a spherical earth. The routes of jet planes take into account the curvature of the earth.
This is all engineering, not science. By contrast, flat-earth theory is science. They can play around with their theories and speculations all they want, but when any scientific theory comes into conflict with practical engineering, the science is wrong. It's that simple. The engineer is right and the scientist is wrong. That's what the whole "scientific revolution" was about. Modern anti-religious historians like to describe it as a battle between religion and science, but the Catholic Church was on the side of science in that revolution, and it was the practical astronomers, mathematicians, and military engineers who showed that the scientists and the Catholic Church were wrong.
But some people can never be convinced by practical experience. In ancient Greece, there were philosophers who refused to admit that anything actually moves, and today there are those who think that the earth is flat and all of the engineering is wrong. You can't argue with people who put their philosophy above practical experience, because you can always, always, twist things around to save a scientific theory if you try hard enough. And if the twisting gets too hard, you can just deny the evidence. Just claim it is a conspiracy. Because a pointless conspiracy by tens of thousands of people providing real and valuable services is more plausible than the idea that you might be wrong about something.