Operations using base 8 still follow real number rules of commutation and association. The other divisional algebras mentioned in the article do not. And that just dances right past the edge of my comprehension. There are hints of a more vast and deeper reality than we know.
Will have to look for more info on octonions.
Imagine the compass points in a plane, then add to the imagery ‘above’ and ‘below’ the plane, then select right or left of the perpendicular bisector of the plane ...