Please comment on the Atlantean Conspiracy's page "200 Proofs Earth is Not a Spinning Ball".
A video on the same subject was posted here almost a year ago with little comment.
My comments so far appear here. I'm very interested in the mathematical aspects but would rather if the exploration was a joint effort.
Ok, let's start with the first one "1) The horizon always appears perfectly flat 360 degrees around the observer regardless of altitude."
According to the "spinning ball" theory if you are 6 feet tall you can see at most about 35,000 feet in any direction over water. That's an angle of curve about 0.01 degrees or about 0.02%. A good lens has a distortion about 0.50%. Thus the lens has 25 times more error than what he is claiming he measured.
Now you can calibrate with some sort of photo target. That's not an easy task. You need a good target, software and with a 12MP camera you are at about 8 feet per pixel. So to see curve you need to need to calibrate out the 15 pixel error (0.5% of 3000) and measure the 1 pixel curve. Or you could possibly find a low distortion lens. One that good would cost six figures.
I am going to say that the yoga instructor who made this claim has probably not done these things. So there is no evidence for his first presumably most important claim. Thus, there is little reason to look at the other 199.
Did you mean 0.02% is actually 0.1 degrees?
I'm not familiar enough with lens calibration mechanics. It seems like from high altitude where you could see dozens of miles, the curvature would be more pronounced and could be more easily measured. But because the camera is focused at a certain point (is that what you mean by target?) then everything else is warped because equidistant objects would form a curved line in space but it must be transferred onto a flat picture. So if the point of focus is on a visible circle (like a horizon) then the curvature of the circle could be warped in different ways by different calibration methods converting the equidistant circle points onto planar points. So I'd first need to know what is the mechanic by which this warping is measured so that we don't result in fisheye. I affirm the general point that the effect is too negligible to be dogmatic about at sea level, which also applies to point 2, but I'd have to work it out at 20-mile altitudes.
Obviously the article counts items as independent proofs that are closely connected, so point 2 follows close on point 1. It seems that at 20 miles altitude you couldn't make the claim that the horizon was still at eye level any more than you could claim it's perfectly horizontal, since the horizon is said to be finite in the flat model. If one lived on an infinite plane then the horizon would always be literally at eye level no matter how high you went, but that's not the model. (In fact if you were close to Antarctica and highly elevated the alleged flat-earth Antarctic "wall" should present a tilted horizon because some wall is so close and some so far.) But this is one of those subtleties where I might tell myself the difference between a circular horizon, a "level" one, and a tilted one should be obvious, but when the math is done the measurements are hard to verify empirically, partly due to the calibration effects of the measuring device. So I don't have the immediate answer, and am speaking from my experience of observation at beaches, on mountains, and in planes, that it just "seems" curved, but I don't have the quantification right at hand.
The best way to do it would probably be to use a fixed lens and use C spacers to make the focal length short enough to image a calibration pattern. A 3" pattern is about $600 and is accurate to less than a micron. Then once the lens is calibrated remove the spacers so you can image the curve. You can't use a zoom lens because changing the zoom changes the error mapping of the lens.
Like you said a high altitude is better because more curve increases your measurement to error ratio. Anyway there's only a handful of people who know how to do all that but someone could probably research it and figure it out using something like OpenCV.
Also, after all that some model for atmosphere refraction should also be considered.
So in the end you cannot just look with your eyes and think something is flat. Imagine printing out 10 lines on paper and one has a 1% curve. You could never see the difference.