The earth is spherical in shape.

Overview I'll start by discussing the opponent's arguments, then I'll move on to my own. I will note that the opponent posted in excess of 70 minutes of Youtube video. I think it is reasonable to expect that I am going to skim the videos to absorb their content, but I won't be watching them through. The point of limiting each side to two arguments is so we have plenty of room to talk about each topic in depth. This goal could be harmed if it's expected that one responds to video that is nearly as long as a feature-length movie. That said, I will review it. Don't want to miss anything. The Opponent's Arguments 1. The Shape of Water The opponent argues that bodies of water are flat, whereas in the round earth model they should be curved. If they are flat, this implies that the world is also flat. The opponent is correct that, if water were flat, the round earth model (as well as much other science) would be in grave peril. Fortunately, a simple exercise in mathematics will explain that the opponent's evidence fits squarely into the round earth model. For his first example, he shows a video of a man standing at a body of water with his wife 6 miles away on the other side. He has a camera, which he has set up about 4 ft off the ground and his wife has a 4 ft mirror. If one does some plug-and-play with some math regarding arc length and chords [1], you find that one expects a "bulge" of 6 ft in between the man and his wife. He should not be able to see the mirror at all, and yet he does. How is this possible? The answer here is the answer for all of the videos and it has to do with how one thinks about "drop off" and how one measures "bulge". In the [1] source, you see a picture with a chord connecting two points along the edge of a circle. Think of these two points as the "viewer" and "object", the chord being the "direct line of sight" and the bulge in between being the bulge of the water. When I refer to bulge height, I am referring to the largest distance from the line of sight to the edge of the circle. In other words, in the picture provided it is a directly vertical line segment connecting the chord to the edge of the circle, such that this segment is as long as possible. (This height is called "h" in the image. ) Note that this model will not tell you anything of use when used alone. We do not observe things from the exact surface of the earth; we stand taller than that. For example, in the first video the man"s camera and the top of the mirror are both about 4 ft off the ground. In the "30 mile" video, the man is about 20 ft from the water line. (It is difficult to tell, though. ) To correct this, we draw another circle around the one already there, such that it has a radius "f" ft. longer, where f is the distance the viewer and object are off the ground. (We assume they are the same to ease calculation. ) We then subtract the radius of the earth (which corresponds to the "top" of the bulge from the distance from the origin to the chord of the second circle (the line of sight) in order to get a new bulge value -- one which describes the height of the bulge from the viewer"s actual perspective. Formulas: If R is the radius of the earth, f is the distance from the surface to the viewer and object, and s is the distance along the ground between view and object: Then the height of the bulge when seen from the surface is: R * (1 - cos( s / 2R ) ), and the height of the bulge when seen from the viewer is: (R + f) * cos( s / 2R ) - R. Finally, note that once we have the bulge height when seen from viewer, we have to multiply that number by 2 to get the final height being obstructed. This is because one has to look "over" the bulge, which is exactly halfway between the viewer and the object. Since a line of sight is an actual line, when we double the run we must double the rise. Ok, let"s look at each example. In the 6 mile example, we calculate the bulge-from-ground as about 6 ft. The bulge-from-viewer, however, is 2 ft (assuming the viewer and object are 4 ft off the ground). Double this, and we get our final obstruction of 4 ft. That"s exactly the height of the mirror, so shouldn"t it be covered? Not enough evidence to tell. Given the choppy conditions, refractive effects and the inability to tell how much of the mirror is revealed -- this is well within the margin of error. In the 12 mile example, things are more clear. The 12 mile bulge-from-viewer is 24 feet, so 48 ft obstruction. We do note some obstruction in the video and it is not clear if it is 48 ft. We shouldn"t expect it to be exactly that, either, again due to refraction. [2] The effects of refraction are not large at short distances, but one would expect to see tens of feet of difference in the evening time when looking across a lake, when the land temperatures would be cooler than water temperatures (since water holds heat better than the ground. ) At 30 miles, we have a 120" bulge-from-view, giving 240" of obstruction. This is in line with what we see, given that there are at least 49 building in Toronto which are over 500 feet tall. [3] At 57 miles, we should expect about 1000" of obstruction from the viewer"s perspective. The big tower in the video, Willis Tower, is 1700" tall. Note that it appears we can see more than half of it, so we are missing about 400" of obstruction. This is, again, well explained by atmospheric refraction. [4] The effects of refraction become greater at longer distances, especially over bodies of water and at times of day when the temperature change is greatest. (This creates varying air density across the line of sight, which is exactly the conditions under which refraction is observed. ) Note that [4] includes other videos which show the same skyline at varying degrees of visibility. Sometimes, it can"t be seen at all (usually mid-day, when refractive effects should be minimal) and sometimes it can. If the Earth were flat, we would expect to *always* be able to see the skyline, and more so we should be able to see *all* of the buildings. If anything, this video demonstrates that Earth isn"t flat. The same is the case for the mountains in the last video. As we"ve seen, the behaviors viewed in the video are what would be predicted on a spherical earth. I think the confusion mostly arises here because people thinking about the flat earth tend to consider "drop off" in curvature rather than "bulge height". The former doesn"t speak to what can be seen while the latter does. Incidentally, the latter produces less extreme amounts of obstruction at small distances. 2. Gyroscopes Respectfully, this is less of an argument and more a critique that the Flat Earth community doesn"t have enough cash to perform experiments using expensive equipment, which is a requirement here. You see, a gyroscope does try and resist changes in motion when it is rotating. This is most usually noticed in a top"s ability to stay upright while spinning. However, one cannot compare the expectations of a theoretically perfect gyroscope to one you can buy at a store. A perfect gyroscope would rotate as the earth does, provided its axis of rotation is not inline with Earth"s. A cheap gyroscope has to deal with friction from bearing resistance, physical changes due to minute temperature differences, and varying local atmosphere behavior. This is why gyroscopes capable of demonstrating this effect often have magnetic components, are vacuum sealed and cost a fortune. Also, this experiment has been done with such expensive equipment. [5] That"s all that really needs to be said about gyroscopes. It should be noted that the easiest way to see that the earth is spinning is to measure the location of the sun and then measure its location two hours later. My Arguments 1. A flat earth is incongruous with current technology. This argument is simple -- so much of the technology we have would not work or would not be necessary on a flat earth. To start, satellites. One notes that in all of his videos, the people use google maps or an actual GPS, both of which rely upon satellite technology. If the earth were flat, it"s not clear how satellites would work. In a flat earth scenario, gravity as we know it cannot exist. Instead of everything attracting everything else, there would just be one, "global" down direction. And if "down" can ever only point one way, satellites cannot stay in the air. They would fall to the ground or into the abyss. The space station is one such satellite, and you can literally see it when it passes over at night. Given that we see the space station and that we use GPS, we must conclude that satellites exist. For them to exist, gravity must exist -- and if gravity exists then the world is most certainly round, as no other shape could form naturally form. Abrupt Cutoff I"m out of room. I"ll finish this argument and present my next immediately in the following round. For the purposes of being fair, my next argument will be probabilistic. I will argue that either all engineers even remotely related to aerospace, most government officials of most countries, all pilots, all flight control crews, etc. are lying to us, or there is no conspiracy and the Earth is indeed round. I"ll be discussing the likelihood of each scenario and concluding that the former scenario is so unlikely it can be disregarded. Sources: [1] - . http://mathworld.wolfram.com... [2] - . http://ww2010.atmos.uiuc.edu...(Gh)/guides/rs/rad/basics/crv.rxml [3] - . https://en.wikipedia.org... [4] - . https://flatearthinsanity.blogspot.com... [5] - . http://www.elsevierscitech.com...