I have added a small figure to the MathPerfect article that displays two time angles and their associated "hydrogen" circles. The vertical leg is always the constant and the hypotenuse is essentially the time vector.
http://www.vip.ocsnet.net/~ancient/MathPerfect04.pdf
The radius of the outer hydrogen circle relates to the time unit defined by the SI second. The radius of the inner hydrogen circle represents a relationship to a mathematically defined unit of time. The following URL discusses the history of defining the earth second and the vagaries of the current SI second.
http://www.cl.cam.ac.uk/...25/time/metrologia-leapsecond.pdf
The SI second is not an absolute constant, it is a defined unit of "convenience", something that can be used as a reference until a better value is determined. The conclusions in the above article indicate that at some time the accumulating error will have to be addressed, and "Therefore, we should perhaps not be too hesistant in adapting to modern technology and modern needs."
A modern need could be the establishment of a unit of time that is not trying to emulate the 1/86,400th division of the revolution of an earth sized planet (with a perfect rotation), but create a mathematically defined unit of time. The geometric-mathematical relationships defined in Universal.pdf could provide the basis for the definition.