What the hell does this mean?

[cashierbex]

It's probably not a team at all. Baseball caps' designs aren't all about baseball. For example, I have one with the TrackIR logo on it - it's designed to have the trio of reflectors needed for 3D head-tracking fitted on top, but it could just as easily be substituted by another baseball cap.

That may be true. But NY is typically meant for New York baseball teams. Pending on the look of the lettering, its one of two teams as someone has posted. The more popular ones are the Yankees.

[AmbrosiaWriter]

Given the possibility of time travel and whatever in the book I still can't wrap my head around a possible series of events (regardless of how implausible) that could make that statement (I bolded) true. Any ideas?

Ok, so current person is Z1, his dad is Z2, his grand father is Z3, and his great grandfather is Z4?

Quite possibly, it could be that his dad, grandfather, and great grandfather are not only his ancestors, but also his descendants. It would mean the time machine getting liberal use, but it is certainly a mind fuck.

Z1 fathers Z2, who fathers Z3, who then fathers Z4.

Shenanigan happen (a lot) where Z4 ends up impregnating his grandmother with his own father (why? Perhaps because time screw where he HAD to impregnate his grandmother otherwise cause a PARADOX, and named him "Z3" in order to avoid the same paradox.)

For whatever reason, this happens a lot. To the point where Z2 had to (or just DID) impregnate Z1's mother.

Since time travel is known, it wouldn't be too far to think that the Z's would be aware of all of this. This would also cause the "both ancestor and descendant" line of thinking.
Z4 fathered Z3, who fathered Z2, who fathered Z1.

Because Z1 doesn't want to deal with having to explain all the mind-fuckery, he just says "the condom broke and there was a time machine involved."

Does that work?

[NecessaryCatharsis]

I think that solves it!

Of special note -- it's possible that ...

- The Infinite Improbability Drive is involved in some way. After all, the LESS likely something is to happen, the greater the chances that the ID will make it happen
).

Most likely!

Ok, so current person is Z1, his dad is Z2, his grand father is Z3, and his great grandfather is Z4?
snip
Z1 fathers Z2, who fathers Z3, who then fathers Z4.
snip
Perhaps because time screw where he HAD to impregnate his grandmother otherwise cause a PARADOX, and named him "Z3" in order to avoid the same paradox.)
For whatever reason, this happens a lot. To the point where Z2 had to (or just DID) impregnate Z1's mother.
snip
Z4 fathered Z3, who fathered Z2, who fathered Z1.
snip

Does that work?

I think that does work. The first three times I tried to work it through I got stuck but then - lightbulb moment - So the last seven generations would be, from first ancestor to final born, Z1, Z2, Z3, Z4, Z3, Z2, and ending in Z1