For the second installment of the TSOS series, I'll be discussing the freakiness of space itself, as opposed to the stuff in space.
Most people know that the universe is expanding. What people might not realize is that the universe is not expanding into empty space. Rather, space itself is expanding. The universe is like the two-dimesional surface of a bubble being inflated -- one minute there's X amount of surface; the next minute there's X + Y amount of surface. Space works the same way -- just expand the two-dimensional surface to a three-dimensional surface.
This has several important ramifications. First off, cosmic objects are generally moving away from each other. The movement of galaxies relevant to each other is a function not only of the peculiar velocity of each galaxy relative to space, but also of the rate at which space itself is expanding between the galaxies. It's like two bugs standing on a bubble, moving away from each other because the bubble is getting bigger.
This also means that the universe has a shape. And depending on that shape, space could be non-Euclidean, meaning that parallel lines actually diverge or converge. In a closed universe, in which parallel lines converge, light also travels in a circle. This means that, theoretically, if you observe an extremely old object in one direction, you should be able to turn around and see the exact same thing in the opposite direction. I believe (and someone may correct me), that the most current observations indicate that we actually live in a flat (Euclidean) universe, where cool stuff like this doesn't happen. But still.
Finally, it means that there's nothing "outside" the universe. Or at least nothing accessible by our current understanding of things. Time and space exist within the universe, not outside it. This, of course, brings up all kinds of unanswerable questions about what happened before the Big Bang, the existence of multiple universes, and so on, but for now this is a fun thing to toss out at cocktail parties.