Quote:So there would be essentially nigh infinite time lines that the Dr could travel down upon?
Quote:That every version of the Dr could be living in one of those lines?
Quote:Thought Dr can history his history, but cannot change "fixed points" in time?
Paradox isn't something that can occur in science. If come across an apparent paradox, it just means you're getting it wrong and there's a solution somewhere you've missed.
But travelling into the past and changing it would create a paradox, and a domino effect of paradox that would ripple on into the future. There are only three solutions to this problem:
1) You're prevented from going into the past. Time travel can't happen.
2) You can travel to the past, but you'd be prevented from interacting with that past and thus couldn't change it.
3) The instant you appear in the 'past', you create a divergent timeline. An alternate universe. You can interact freely there, but your original timeline would remain unaltered.
Given the nature of Doctor Who, we can safely draw a line through the first two, which only leaves Solution #3.
The idea of 'fixed points' is a ridiculous one. ALL of spacetime in a given universe must be 'fixed'. If not, that would mean the vast majority of it is changeable, and that leads us back to paradox. And physics abhors a paradox.