[whatshisface]

That's like choosing whether +x is a rightward or leftward facing coordinate axis. You can still use negative numbers, but you have to indicate whether positive means left or right. See also: positive and negative longitudes vs. east or west longitudes.

[kojim]

Oh completely. The "agreeing on what's left or right" in every context is the tough part, and already a solved problem with debits and credits.