To infinity...

and beyond.

One of the topics that has always fascinated me has got be infinity. Both things that are infinity small (like my desire to achieve), and those that are infinitely large (like my ego). But seriously, let's examine a famous philosophical example of infinite smallness.... I give you, Zeno's paradox.

Zeno (circa 450 BC) is credited with the proof that you can never reach your destination, or if taken to an extreme, that all movement is impossible. The argument is as follows:

• Zeno surmised that in order to reach a destination one would have to travel half of the distance first. One then would have to travel half of the remaining distance. Then half of that remaining distance, and so on, and so on. Because there will always be a half way point between the distance remaining and the goal, you can never reach the goal.
• Again, taken to the extreme, it proves that motion itself is impossible. Before I can cover any distance, I must cover half of that distance, and before I can do that, I must cover half of half of that distance, and so on, so that in reality I can never move any distance at all, because doing so involves moving an infinite number of small intermediate distances first.

Wow... I need a moment to ponder my existence.

The coolest thing is that this paradox was not fully resolved mathematically until the mid 1800's. You gotta love the ancient Philosophers!!