Tom, Steve,
I think it is important to conceive of "a state change in the line is action in the system". This is naturally a continuum, and perhaps the most easily envisioned definitive recognition of simple connectivity that is quintessential of the whole of real, physical Spacetime.
Time is treated in a variety of applications, both linear and nonlinear, specific to the task under analysis. But all those characteristic properties of action must also be naturally coexistent in a unified reality. "That dog don't hunt!" is an old saying generally referring to the keen sense of smell canines are famous for, and if a dog can't follow it's nose, it can't track down the source of the scent. So treating Time as only one dimension, or one operative property, is following only one characteristic of the scent. We can, and must, accept the bounded interval of light velocity as a universal constraint; but that Dog 'hunts' for what that velocity might physically, really might be across any theoretically expressed proper measured interval. And that Speed of Time can only be something, anywhere, between nil and light velocity. And physically operating as a continuous 'hunting' between those bounds. We can arbitrarily structure that hunt theoretically; and propose that Time searches for its operational rate as an exponential function, rising from nil to its upper limit and back again. So it also argues that anywhere along a line across a spatial distance, that 'hunt' for existential velocity of Time, is a continuous changing of state. best as I can express the idea at the moment :-) jrc