The theory is that to make a cut "work" (i.e. not be noticed), you need to change two of the three dimensions significantly. I've found that if you change one enough, the cut works just fine.
Change At Least One Dimension Significantly
But there is more to making a cut work than just moving the camera so many degrees, or pushing in so many feet. What the audience is looking at, and what they expect/want to look at next, can make cuts invisible as well.
For instance, in "Flowers", our girl comes out of the gate and notices the guy. We, as the audience, naturally want to know what she's thinking, so we cut in (changing the Z-axis).
Wide Shot of the Gate
CU on Her Face
I could keep going (I prepared more images), but I think that's enough of that. The point is this: There are many ways to make a cut "invisible". For a fascinating discussion of a few of these "tricks", check out Norman Hollyn's post on his blog (a very excellent read): Awareness Test. In his post he links to this video, and then comments on how it works.
One more example of just how amazing editing/filmmaking can be.
Your Media Production Mentor