I've been thinking of Conway's "game of life" as a metaphor for human existence. (There are many descriptions of GoL online. See, for example, https://bitstorm.org/gameoflife/).
If the grid is finite, a given initial configuration will evolve over time in two possible ways: 1) everything dies; or 2) infinite repetition. (Actually, I guess "everything dies" is an infinite repetition of an empty board, as well.) If the board is infinite, however, there is a third possibility: endless growth.
Conway's rules preclude overpopulation -- cells that are too close to each other always "die" of overcrowding -- so the growth is always in a very sparse manner, generally in the form of small crawling creatures on an infinite plane. Endless growth, but with a low population density.
So it is with human existence. Humanity confined to a finite area will either die off, or cycle through an endless repetition of social structures. Of course, the rules for humanity are complex and chaotic, so the analogy breaks down. Even so, the prospects for humanity confined in a finite cage seem ultimately boring. Current human history goes back a few thousand years; imagine human society confined to Earth for a hundred times that long -- how many cycles of barbarism and civilization will that entail?
Thinking about human history extending say a quarter million years into the future isn't a usual pastime, but as the human race gets old it will surely become more common -- the knowledge of the previous hundreds of civilizations will sink into the zeitgeist until it becomes a dreary, barely conscious backdrop to every thought.