Steve Pulsford asks how can he have 1073741824 great-...-great
grandparents if he goes back 30 generations, when there wouldn't
have been so many people alive. Of course, he has this many gaps
to fill in his family tree, but they are not all distinct people
or all alive simultaneously.

For example, if your parents were brother and sister then you still
have paternal grandparents and maternal grandparents, but they
are only 2 distinct people, rather than 4. The marriage of siblings
is not that common, but the marriage of cousins is, and more distant
relatives even more common.

I've often wondered who is my closest ancestor that appears twice
in my family tree. My mother thinks she may have identified two
cousins who turn up in different parts of my family tree around the
1850s, and so their grandparents will fill two roles in my family
tree.