The infinite vastness of space.

Finiteness and infinity kind of don't mesh well. If it is truly boundless out there, however much one travels should not matter.
In our perception, getting from Earth to Mars was a success, and we were proud of it. But going from Zeno's paradoxes, we really haven't gotten anywhere.

 refresher

Consider: In order to travel x distance, one has to cover x/2 distance first. It branches into two here:

1/ In order to travel that x/2 distance, one has to cover x/4 distance first, so on and so forth. The conclusion is that one never actually starts moving at all.

2/ Supposing one somehow does manage to cover the x/2 distance, he then has to move from x/2 to x (the distance of which is x/2) and, again, cover half the distance before even thinking about reaching his goal. The conclusion is that one should never reach a destination.

While those paradoxes seem silly if you consider the "factual" observations (you can actually start moving and actually GET to some point in space), plug in the role of infinity and things start to look similar.
From Earth to Mars may be a big distance for us, but somewhere out there, it's tiny. How tiny? Tiny tiny. So the distance from us to that somewhere out there must be big? Yes, for now. Once we've conceptualized the distance, it, in turn, becomes arbitrarily small compared to some "infinity" out there.

Infinity is however big you can imagine plus 1. To conquer infinity with a finite method seems even more silly than Zeno himself. But of course, we can't just sit here and do nothing so people always try to get out there, but are we actually getting anywhere? We think we're walking, are we? We think we're looking far out into space, what with the Hubble and all those observatories, but are we?