How as an individual can I know if the Earth is a sphere or a flat disc? What experiment can I do that doesn't involve trusting information from a 3rd party that would prove what the geometry really is?
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Slightly off-topic, as it sort of involves you trusting a third party, but Vsauce did a video about whether the Earth is flat, late last year:
https://www.youtube.com/watch?v=VNqNnUJVcVs (10m30s) - it's pretty good, and informative. Also, he included a large amount of links in the video description, where you can get additional information.
Consider that when you view things as they move away from you, perhaps they are really NOT moving away from you. Perhaps what is happening is that you and the object are actually exchanging some form of energy that causes you to actually become larger, and the object become smaller with relation to you.
When you throw a ball at the object that has moved away from you, all that you are really doing is transferring a certain kind of energy between you, the object, and the ball. As the ball moves away from you, it loses size even though we interpret it as gaining distance. With relation to the object, the ball gains size, even though to the object, the ball seems to have lost distance.
With a few twists to the concept of warp theory (yes, like Star Trek, but the real thing that Einstein and others formulated), things might be that there is virtually no distance between us and anything else. Wormholes that connect things that seem to be distant, might simply be energy transference "equations" that change the size relationships between various objects. Wormholes might be around us all the time, numbering in the millions, depending on the variety and numbers of "places" that we individually observe or are otherwise aware of.
We interpret distance. We interpret how we change distance between ourselves and other things. We calculate the amount of energy that it takes to "move things across such distances." But maybe it is all a trick of the mind, designed by God or nature to maintain order in the universe. Maybe with a little bit of the right kind of quantum math and mechanics, combined with a little change in the way that we think about things, we might be able to move between the earth, and planets that revolve around other stars, with just as much ease as we walk across the street.
Perhaps the ancients tapped into this "state of mind." Perhaps the piling up of the blocks of the Great Pyramid was accomplished through mental control of "short distance" wormholes. Perhaps the movie,
Jumper, is not that far off after all.
If things are getting bigger/smaller instead of closer/farther, then explain why mass doesn't change. Also, explain why, if Person B stands between Persons B and C, and then walks towards A, he wouldn't get both larger and smaller at the time time.
Also, when you move, do you see yourself get bigger or smaller?
Wow dude.