(Image Source: gopixpic.com)
The fable of the Tortoise and the Hare derived from writings of the Ancient Greek storyteller ‘Aesop, is one of great reverance and meaning, and one which I remember having recited to me as a child, with the intention of delivering the message:
“Slow and steady, wins the race…”
What is meant by this was ambiguous to me in my younger years, however now I understand, that it aims to deliver the notion that consistent and effective effort will enevitably lead to success.
What I find most interesting about the fable however, is the powerful philosophical paradox which uses the story as a theoretical underpinning. The Paradox, known as one of Greek Philosopher, Zeno of Elea’s nine surviving paradoxes, which he formulated to support the idea that one’s senses were not to be trusted, and in particular, that the phenomena of motion, was nothing but an illusion.
Of course, the paradox which I wish to draw on, is that of ‘Achilles and the tortiose’, the point of which is to establish that:
“In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.” – as recounted by Aristotle, Physics VI:9, 239b15
That is to say that, assuming that the Tortoise is consistently moving at half the speed of Achilles, that although the measured gap between the two will indeed decrease, by the time Achilles has reached the point that the Tortoise began, the tortoise will have continued to cover a further distance, thus Achilles would then proceed to reach that point, and the Tortiose would have also moved further and so forth.
This very closely links with Zeno’s ‘Dichotomy Paradox’ which explains that:
“That which is in locomotion must arrive at the half-way stage before it arrives at the goal.”– as recounted by Aristotle, Physics VI:9, 239b10
Zeno maintains that in order to travel any distance, one must first cover an infinite regression of smaller distances, which is in essence, impossible. This is to say that in order to cross a road, say, it is a logical necessity that you must reach the half way point before you reach the other side, and before you reach the half way point, you must reach the quarter way point, and the eighth way point and so on… For this reason, one should never reach the other side of the road (Poor Chicken).
Further, it logically ensues that no object should ever complete a journey from one fixed point to another, you should never be able to walk to the shops, to cross the road, and by extention, my fingers should be logically incapable of touching the keys of my keyboard in order to make these words appear in front of you.
Just something to get your head round…
TemporalThinktank 