The role of space and time in the theory:


If we label the three spacial dimensions as red, yellow, blue and the time dimension as green then William Rowan Hamilton's (1805 - 1865) quaternion theory says:


red * yellow = blue


yellow * blue = red


blue * red = yellow


Red times yellow equals blue,
yellow times blue equals red
and blue times red equals yellow.


red * red = green


yellow * yellow = green


blue * blue = green


Red times red equals green,
yellow times yellow equals green
and blue times blue equals green.


red * yellow * blue = green


Red times yellow times blue equals green.


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 21.