Life is a mountain whose summit we are always trying to reach. It is surmised by many climbers that the mountain is of infinite height, as it is composed of an infinite number of cliffs. Others, though, have surmised that a short-cut could be found to the top.*
If each cliff is climbed in half the time as the previous, then an infinite number of cliffs could be scaled in twice the time that it takes to climb the first one.
Maybe the first is climbed in one year.
The second is climbed in half a year.
The third in 1/4 of a year.
The fourth in 1/8 of a year.
The fifth in 1/16 of a year.
The sixth in 1/32 of a year.
And so on.
If you add up all of these infinite cliffs, 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64… 1/n = 2
Some have dismissed this as a mind game, with no bearing on the climbing of real cliffs.
Others, however, have taken up the game of paradox, and in fact argue that through extensive meditation on these paradoxes, one can begin to perceive the totality of the mountain, though in dim outline only. In fact, they argue that this mountain is not only infinitely large but infinitely small as well, and that it can be perceived in a sunflower, a bird flying south, or a drop of water falling into a tea cup.
Others have argued that anyone who perceived the mountain would always fail to perceive herself as well, and therefore taking in the whole at once would be impossible.
*Rudy Rucker, “Infinity and the Mind.”