A Parallel Universe?

Natasha1

Has anyone got the answers to the questions on the attached document? With some explanations.

This is something a friend came up with... I'm a little clueless on this on...

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HallsofIvy

Since the problem specifically asks about "visual field"- that's easy. The two "lines" are curved because the "visual field" itself is a two-dimensional curved space.

Natasha1

Consider the following:

Take any 2 points on that straight line - which can be at any angle and any distance from your eye or from each other. Now, imagine a triangle made with those 2 points and your eye. The 3 points you have are now all on a plane. Therefore, whatever point your eye is at, it will see the straight line between the other 2 points as straight, because they are all sharing a flat plane and so is the line between the points you are looking at.

However, if it is true that every straight line you see is not seen as curved, but as a straight line, why do we also have the argument that we see parallel lines as curved in relation to each other?

Hurkyl

This is probably much better as a psychology question than a math question. Our brains do a tremendous amount of processing on the raw imagery our eyes detect!

In the modern world, we are constantly inundated with straight lines -- especially horizontal or vertical straight lines. So, we learn at a very early age to recognize straight lines as straight... at least the horizontal and vertical ones. Diagonal ones, I believe, are generally harder simply because we aren't as often exposed to them.

I'm told that African tribesman, etc, will not see any illusion of depth in pictures such as:

and certainly won't see a 3-dimensional "corner" -- and that's because they aren't exposed to such things in their daily routines. (e.g. round buildings, not square!)