Time seems to arise from the fact that subatomic particles undergo changes of state (observable events) through the time dimension. We cannot stop that, or choose it — it just happens. But that universal law also seems arbitrary: what if there were another dimension through which they underwent state changes?
With two time dimensions, one still might not be able to “loop back” — it might be that one could only go toward increasing values of time (in either dimension).
But two dimensions also seems arbitrary — as arbitrary as 10. Then again, many numbers in the universe seem arbitrary, such as the fact that there are only four division algebras — but that arises from a mathematical constraint, so if there are but 10 (or 12) dimensions, I would expect that to arise from a mathematical constraint and not be arbitrary — I would expect that no other number would work.
Here’s a wild thought: perhaps the Fermi Paradox is explained by the fact that advanced intelligences figure out how to live outside of the time that we know.
Then again, given the seemingly inextricable link between observable events, our awareness or consciousness, and time, perhaps it is not so wild an idea. Perhaps it is only our “observations” that are tied to time. There is clearly a big missing piece that we do not understand.