We had a discussion about this 2+2 != 4 idea in another thread:

What you have is MATH. What I have is empirical observation. Your math only works under the model it is intended for. If the assumptions of the underlying model changes, or is wrong, the math does not work.

2 + 2 = 4 relies on the underlying model, and is not a universal truth. Under some models 2 + 2 does not equal 4. See Two Plus Two Equals Four, But Not Always.

All math relies on the underlying model for it to have truth. You need to prove that your underlying model for perspective lines is valid.

the writer is a psychology PhD, explaining that 40 on a given test scale for, say, hydrophobia, is not necessarily twice as hydrophobic as a 20 is. ...

Here is an excellent paper on the universality of 2 + 2 = 4.

I admit, I cannot conceive of a "situation" that would make 2 + 2 = 4 false. (There are redefinitions, but those are not "situations", and then you're no longer talking about 2, 4, =, or +.) But that doesn't make my belief unconditional. I find it quite easy to imagine a situation which would convince me that 2 + 2 = 3.

Suppose I got up one morning, and took out two earplugs, and set them down next to two other earplugs on my nighttable, and noticed that there were now three earplugs, without any earplugs having appeared or disappeared—in contrast to my stored memory that 2 + 2 was supposed to equal 4. Moreover, when I visualized the process in my own mind, it seemed that making XX and XX come out to XXXX required an extra X to appear from nowhere, and was, moreover, inconsistent with other arithmetic I visualized, since subtracting XX from XXX left XX, but subtracting XX from XXXX left XXX. This would conflict with my stored memory that 3 - 2 = 1, but memory would be absurd in the face of physical and mental confirmation that XXX - XX = XX.

...

What would convince me that 2 + 2 = 3, in other words, is exactly the same kind of evidence that currently convinces me that 2 + 2 = 4: The evidential crossfire of physical observation, mental visualization, and social agreement.

...

It is observed from counting that 2 + 2 = 4. Whenever counting works, 2 + 2 = 4 is true; i.e., for anything you can count, 2 of the thing and 2 more of the thing is the same as 4 of the thing. If you can't count it, then the very terms of 2 + 2 = 4 don't make sense, but it doesn't somehow mean 2 + 2 doesn't equal 4.

Expanding on my previous example, you can't count hydrophobia. There is no quantifiable measure in nature of 'how much hydrophobia.' So when psychiatrists form a test to figure out how hydrophobic someone is, they contrive a scale based on some indicators that they can observe and measure, and it results in arbitrarily scaled numbers. Even though this results in a number, it is still not countable, so saying 20 hydrophobic + 20 hydrophobic = 40 hydrophobic doesn't make any sense; '20 hydrophobic' is literally not a thing that can exist. This is the whole point of the paper you keep linking to, and you are badly misrepresenting it by insisting that it supports an idea that 2 + 2 = 4 is not universally true.

ANYWAY the whole 2+2 thing is like, all the way off topic! I think there was something about new vs old proofs, right? Astronomers only use the same old proofs, we were told.

This is incorrect. I think this particular one is only a few years old:

http://www.ustream.tv/channel/iss-hdev-payload