The notation exists because it can be applied to the field, because the field can be applied to reality. It's not solely invention.
Engineers love ruining physics but at very least they can still be ugly rather than bloated.
Engineers love ruining physics but at very least they can still be ugly rather than bloated.
Non-Euclidean geometry has applications to reality, but before these applications were known, how did they determine that the notation would appropriately apply to the field?