The world IS flat. Space is curved.
(Just kidding. Though it's not an impossible view, but don't put that down as an answer on a science test unless you want a low score)
Depending on the current social/democratic consensus one view can be popularly consider non-sense while the other viewed as common sense. Times change and so do views and definitions.
I agree that there are many interesting examples of lines of thought that occured thousands of years ago that seemed to be more insightful than people typically recognize.
There truly are few, if any, viewpoints that don't have other possibly equally valid viewpoints. For example, someone might prefer working with binary numbers and say 1+1=10, instead of 2. There's nothing wrong with this as long as it's clear and proves useful. There's a principle called Computational Equivalence that basically says there are many ways of doing the same thing. Someone could create 100 different programming languages that could all be capable of writing a program though they would look different and likely use different methods, but all the while accomplishing the same thing.
Given that there can multiple ways of accomplishing the same thing, one might choose to optimize some value. Generally, having views that are compatible with others allows you to easily communicate them as well as benefit from the interchange, though if it's too clumsy or inefficient to do this, there's little reason you should have to stick with conventions if striking out on your own seems likely to have a better pay off. If there's benefits to this, other people gradually follow and what appeared as uncommon sense becomes common.