Wiktionary
noncommutative
a. (context of an algebraic structure English) Not having commutativity of all elements under its operation.
Wikipedia
Usage examples of "noncommutative".
Perhaps in a different universe arithmetic would be noncommutative and there would be no law of inverse squares.
It is likely that the framework of noncommutative geometry is still some significant steps away from the blank-slate state anticipated above, but it does give us a hint of what the more complete framework for incorporating space and time may involve.