I think it's a matter of perception, not eyesight. Most people wouldn't know a straight line by simply looking at it, and conversely, a barely curved one. For example, a machinist who is quite familiar with working with perfectly straight lines would be able to spot minute defects that would escape most eyes.
Also, consider that you can not focus in on a very large area across your vision. The focus is at the center of your vision, and the peripheral is, well, not.
As a cool experiment, may I suggest that you line yourself up with something straight and horizontal, say a deck railing or perhaps a yardstick strung up at eye level. Use this as a reference to the horizon in the background and compare. Now, I won't speculate whether or not a curve can be seen, as I've never tried it personally, but if it is detectable, the straight line in front of it will surely bring it out.
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