Why is there always something new?

Let's use Deleuze's own method, and back up from the abstraction a bit so that we can see the concrete problem.  The problem lurking beneath this whole chapter is: how there can be anything new?  How can a new thing come to exist?  Since the chapter is titled "Repetition for Itself", it was not immediately clear that the real problem is novelty.  But as soon as we started thinking about repetition we were already on the road to thinking about novelty. 

First, we asked: how can some element could be repeated exactly if time passes?  Isn't it technically something different the second time around?  Second, we asked: is it rather the whole trajectory of an element that is repeated, and not the element itself?  Can we say that what is repeated is a memory or model, perhaps a timeless law that governs the apparent repetition of an element though time?  Either of these could serve as a definition of repetition, a concept that we know is somehow at the base of our understanding of time.  

But then we realized that either definition of repetition would not bring us to understanding repetition for-itself.  Because either way, we were discussing the repetition of something, something whose identity we had already taken for granted.  In the first case, we needed the identity of the element we were using to count off repetitions every time it popped up.  In the second case, we needed the identity of the Whole of time -- the immemorial model, the realm of Forms, or the timeless universal law.  This more abstract identity was repeated in the sense that every concrete incarnation was just another instance of it, every universe was just another solution to one and the same equation.  

So finally we asked: how can we think of repetition for-itself, prior to a repeated identity?  How can we think about repetition without simply counting off the number of times we circle past the identical point?  All the paradoxical abstraction of the third synthesis is aimed at addressing this problem.  It does this by kicking the whole discussion up a level and focusing on the form of repetition, rather than the content.  This is why it's the 'transcendental' synthesis.  The only 'thing' repeated exactly is the form of repetition, which is nothing less than the passage of time, the way it always unfolds a before and after separated by a qualitative transformation.  What's repeated is change.  Which is to say that repetition for-itself is precisely continuous novelty.  

So the whole complicated apparatus of the third synthesis, with the fractured I, the order of time, the split symbol and the caesura, is all meant to be a theory of the new.

I'm sure this all still sounds either ridiculously abstract, or completely vapid and new-age (or perhaps both).  I mean -- "the only constant is change?" -- deep thoughts dude.  All I can say is that they call them truisms for a reason.  You've heard all the profound things before.  You just haven't repeated them yet in your own words.