The role of space and time in the theory:


If we label the three spacial dimensions as Red, Green, Blue and the time dimension as White then William Rowan Hamilton's (1805 - 1865) quaternion theory says:


Red * Green = Blue


Green * Blue = Red


Blue * Red = Green


Red times Green equals Blue, Green times Blue equals Red and Blue times Red equals Green.


Red * Red = White


Green * Green = White


Blue * Blue = White


Red times Red equals White, Green times Green equals White and Blue times Blue equals White.


Red * Green * Blue = White


Red times Green times Blue equals White.


Hamilton believed that the three dimensions were that of space and the one dimension that of time.


Consequently the three spacial dimensions and the time dimension can exist independently of anything else.


The Complex Plane has rotations, since rotations require three spacial  dimensions (the plane of rotation and the rotation axis (gyration axis, G)) and a time dimension. This explains our everyday experience (the best example being a traditional analogue clock).


Since rotations are required, the minimum number of dimensions is four (three space and one time).


That concludes the role of space and time in the theory.


End of page 23.