Millions, perhaps billions of humans have put food on the table and built machines with 100s of times the power or calculational ability of human individuals without ever needing to concern themselves with the breakdown of euclidean geometry.

Try sailing an ocean, as millions of humans have had to do (even just the ones doing so involuntarily like the Africa->America slave trade) with plain Euclidean geometry and then tell me how practical alternative forms of mapmaking, direction-setting, and locations are.

As it happens, Nick Szabo is slowly blogging how exactly one does that: http://unenumerated.blogspot.com/2012/10/dead-reckoning-and-exploration-explosion.html and http://unenumerated.blogspot.com/2012/10/dead-reckoning-maps-and-errors.html

Just because many millions of people don't need to concern themselves with that doesn't mean there aren't many other millions who don't.