If x is the world, and Ax=b is what someone can see, then the null space of A is invisibile! I never really thought about it like this before. As John pointed out, every failed inverse problem is an opportunity in disguise, (for instance if you're interested in making Harry Potter cloaks or stealth airplanes).

Swiming was difficult for me the first time because I was forgetting to breath. I was only getting fresh air from ridiculously short gasps every couple of strokes- no wonder I felt like passing out.