I’ve been reading " The unparalleled adventures of one Hans Pfaall" and was confused by the part when he describes the ocean (and the rest of Earth’s surface for that matter) as appearing concave.
He was viewing them from in his hot air ballon about 17 miles up at the time and gives a very confusing explanation involving an imaginary right angle triangle drawn between the balloon, the horizon and the ocean directly below him whereby the hypotenuse and the base were almost parallel.
Would the ocean really have this appearance and if so can anyone explain why?
It’s an optical illusion. I’ve been in a plane over open ocean and you get the same effect. I think your depth perception gets skewed because the ocean is a pretty uniform color, and the horizon doesn’t appear to be much below your eye level because of the distance.
If you stand on a beach and look out over the sea at the horizon it appears as if the sea level slopes up towards it, and the sky slopes down. This is presumably an optical illusion caused by your brain attempting to make sense of what appears to happen, ie the sea and sky meeting.
If you then sit in a small boat and look around you, the surface appears to slope up in every direction away from you, ie it appears as if the surface is concave with you at the bottom. I imagine the same effect is visible from the balloon as it is not that high above the surface, although this is just a guess. It surprises me somewhat, because the above effect seems to be diminished the larger the boat you are in, ie the higher above the surface.
You’re justified in being confused, since Poe’s argument is (probably knowingly) nonsensical.
It’s a pretty classic example of a type of geometrical trickery and trap that circle-squarers and the like fall into: the two lines are indeed almost parallel, but it’s the fact that they’re not quite parallel that’s actually most important. Poe’s explanation doesn’t work as geometry.
There’s a convincing argument - see Harold Beaver’s notes to The Science Fiction of Edgar Allen Poe (Penguin Classics, 1976) - that the whole story is a burlesque about credulity and the Great Moon Hoax of 1835. Poe cleverly threads a lot of plausible looking scientific references and the names of real scientists through the story, but virtually all the science in the story is deliberately nonsense.
The complication is that there are occasions when the surface of the ocean can appear concave. Minneart (in his classic The Nature of Light and Color in the Open Air) claims that this is usually because of the refraction of light in the atmosphere. In particular, if the air above it is warmer than the sea, rays of light can bend over the curve of the earth, so that you see past the “real” horizon. What you perceive as the horizon looks to be slightly above you.
Now I don’t think this entirely explains cases like sturmhauke’s from an aeroplane. There I suspect it’s more related to phenomena like the Moon Illusion or the way we perceive a blue sky as a shallow inverted bowl. Our brains just seem to slightly wonky when it comes to judging very large expanses.
Beaver notes that there’s a passage in Twain’s Roughing It where he sees the ocean as concave from the top of a volcano in Hawaii and explicitly links this to Poe’s story. Twain confesses that he’d always thought Poe simply made up the effect and was surprised to see it for real. Given that there were balloon flights to high altitudes before Poe was writing, it’s possible that he’d seen some reference in an account - and then made up the nonsensical geometrical explanation to fit the tone of the story.
Up to a considerable height the horizon appears to be at eye level. That makes everything look to us as if we were in a bowl or an inverted cone with us at the apex.
For example for a person 5’ 10" tall the horizon is about 3.43 miles away. A line drawn horizontally from the eye is only about 1’ of arc (1/60 degree) above a line drawn to the horizon.
For a person in a plane at 20000 ft. the horizon is at 200 miles and a line drawn horizontally from the eye is only 1[sup]o[/sup] of arc above a line drawn to the horizon.
For a person 17 miles above the surface the horizon is at 424 miles and a line drawn horizontally from the eye is just a tad over 2[sup]o[/sup] above a line drawn to the horizon which would still put the horizon close to eye level. However, I’m pretty sure that from 17 miles high you can see the curvature of the earth which I think would sort of spoil the bowl appearance.
For pilots the rule is that if the thing in your airspace is level with the horizon it is at your altitude.
From 17 miles, up, thats almost 90,000 feet. My guess is that he was oxygen deprived and imagined the whole thing.
Really, you can’t survive up there. It’s a wee bit cold and a wee bit not enough air. I don’t think your run-of-the-mill hot air balloon will take you there.