I posted earlier on the subject of Being Here, and so today I want to look at moving on. My starting point is the paradox of Zeno’s Arrow. It is closely related to his paradox about Achilles racing a tortoise – quite apt given my current pre-occupation with all things running (did I mention I’m training for the 2017 Brighton Marathon, so in keeping with my Greek philosophical leanings?!). The latter paradox states that if a tortoise was given a head-start, then theoretically Achilles would not be able to catch up with it. Achilles first has to reach the place where the tortoise is at the start. By the time he gets there, the tortoise has moved on, so he then has to reach that place, by which time it has moved on further…and so on.
The arrow paradox follows a similar line of argument. In order to reach its target, it has to travel half the distance. From that point, it again has to travel half of the remaining distance. And so forth. Mathematically, the summation of these halves, quarters, eighths, sixteenths and so forth approach 1 but never actually reach it.
The paradoxes work on a misunderstanding of time and motion, and obviously they are shown to be untrue in daily life. I would not volunteer to be a target for one of his arrows! However, they contain some interesting messages. Firstly, what is theoretically impossible can be shown to be possible in reality. The great progress made in science and technology would not have been possible if people stayed only with the theoretically possible. And the corollary – just because something is theoretically possible does not mean it is actually achievable.
There are some practical applications of the paradox. In martial arts, the focus for the strike is located behind (or beyond) the target. The practitioner aims for a point behind the breaking board, not on the board. And a runner aims for beyond the finishing line, not the line itself. The message is to aim beyond the target.
The next time I travel to Edinburgh, I will aim for Inverness.
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