ftg does an experiment:
I close my left eye and look down and to the left. I can clearly see a good part of my nose. Vice versa for closing my right eye.
With both eyes open and looking down and to the left I see …, well, it’s hard to describe. I see a “fringe” of my nose but just barely. Most of my nose is “not there”. I see what my left eye sees in it’s place.
Repeat the latter with my a pen pressed against the side of my nose. Now I can clearly see the pen. No fringe effect, no substitution with what the other eye sees.
Conclusion: my brain processes out almost all of my nose when it can. It can clearly see in that direction, but it has learned to ignore it for the most part.