The higher a mountain over its’ surroundings, the further the view, since you are looking “over the horizon” et. al. If you had an infinitly tall mountain, how far around Earth could you see? Just your half, or could you see the other side?
Well, “infinitely” tall doesn’t actually make sense–it’s gotta stop somewhere if you’re gonna be able to stand on it. But we’ll say “incredibly tall” instead. In fact, that’s really the situation we have when we look at, for example, the moon–when we look at the moon from the earth, we’re basically looking down at it from 260,000 miles from above the moon’s surface (or however far away from the moon we are, I forget). No matter how far we pull back, the other side of the moon can’t pop into view, it’s hidden by the side we’re actually viewing.
So no matter how tall the mountain is, you’ll never be able to see more than half the earth’s surface–just like, as another example, if we pull away from a wall, we’ll never be able to see the side of the wall opposite from us because it’s simply hidden from view.
The bear that went over the mountain knows !
I guess I was thinking a little bit more cosmically. Doesn’t light bend around objects because of gravity? Doesn’t light bend in the atmosphere (causing a blue sky)? Wouldn’t this allow you to peek around the corners?
The bending of light as it passes through a medium is called refraction. Refraction works to your benefit, even when you’re standing on the ground. We can see the Sun after it has “set”–when it’s geometrically below the horizon, its rays are bent so that you can still see it. However, refraction at the surface is only 34 arcminutes (an arcminute is 1/60 of a degree) and as you go up your hypothetical mountain, the atmosphere will get thinner, and the refraction isn’t going to get any better!
General relativity is an even smaller effect than refraction for a puny little thing like the Earth.
*Cabbage is quite right: you can’t do better than standing on the Moon.