I would firstly like to point out that it is 'XENO' in the title, not 'XENA, (the warrior princess); she of the immense cleavage and armoured breasts! I have often wondered what thirteen year old, pumped up with testosterone, came up with the idea that developing the biceps with the capacity to wield a two-handed 'medieval' sword would also develop the female mammary glands to similar staggering proportions; I would have thought that it would hinder sword-play rather than enhance it. I blame Brigitte Nielson and the infamous 'Red Sonja' for starting that particular stereotype, although I suspect that it is older. However, Amazons were reputed to have the right breast cut off, or cauterised as babies, so that they could better wield a sword or draw a bow.
To return to Xeno, the life of a philosopher must surely be a happy and contented one. Nowadays, income is usually provided by the universities in return for certain teaching duties for the benefit of those of the young who wish to carry on the time-honoured tradition of sitting on your arse and writing the odd incomprehensible book or two. In the past, it could only be carried out in the main by those of independent means; you surely would not get much philosophising done if you were working from dawn until dusk ploughing the fields or baking bread. Of course, once you had acquired a reputation for philosophising, you could earn extra copper the same way the university professors do now, by teaching, but you had to get your 'head start', so to speak.
Physical inactivity has a way of leading the brain along uncharted, and to be fair, incomprehensible routes. While much physical activity has a certain mindless quality about it, you still have to concentrate on getting your oxen to plough a straight furrow to make harvesting easier or adding just the right amount of yeast in order to make sure that your bread does not rise beyond the confines of your modest oven. However it still seems to me to be slightly beyond the bounds of your natural, 'thinking man' (or woman) to think of exploring the concept of the impossibility of motion; after all, how do get from one place to another if motion is impossible. The ancient Greeks would have found the Battle of Marathon* a little difficult to win if they could not get from Athens to Marathon in time and, even worse, could not even get started!
What has this to do with Achilles, hero of the Trojan War, and a tortoise, I hear you cry! Well, Xeno used the fictional tale of the race between Achilles and a tortoise to illustate the impossibility of motion. It was, in its own way, an extension of Parmenides ideas, which also influenced Plato. (And we have all seen where that got us; up a gum tree without a paddle.) Both Xeno and Parmenides came from the Italian town of Elea. The Romans had yet to embark on their quest for world domination at the time and Italy was dotted with Greek settlements around the coast. Ancient history can sometimes be confusing; a bit like the Irish are Scots who were originally Irish!
The rules of the race were simple; Achilles, because he was faster by far, would give the tortoise one hundred yards start over the course; the course was, to all extents and purposes, infinite. Achilles starts off and runs ten yards in a given time frame, the toroise travels one yard. In the next time frame, one half of the previous one, Achilles travels five yards, the tortoise eighteen inches. In the next time frame, one quarter of the original, Achilles travels two and a half yards, the tortoise nine inches. No matter how fast Achilles runs, he always has to pass through that place where the tortoise has just been. He can never overtake the reptile and thus will always lose. This is patently nonsense of course but it is difficult to get out of the paradox logically and 'logos' was what was inportant to Xeno (and Parmenides and for that matter Plato). There were two kinds of reality; perceptual reality, which was not real and 'logos', reasoned discourse, logic, which was. Hence the dilemma and the paradox.
It is possible to get around the conundrum with mathematics, specifically calculus and modern quantum physicists rely on the Planck length and the Planck time, ie that time and length are not infinitely divisible; there is a lower, observable limit to their divisibility. Strict logicians may deny this; after all, on a line of finite length, there are an infinite number of points and on a line between two points on that line of finite length, there is also an infinite number of points. Quantum mechanics denies that kind of infinity as being essentially 'unobservable' and, ergo, unknowable.
* Incidentally, the Marathon race, named after the Battle, actually conflates two historical (or pseudo-historical) events, depending on how much credence you give Heroditus; Pheidippdes' run to declare the victory to the waiting Athenians and his subsequent demise from exhaustion..
The first is Pheidippides' jog to Sparta to request aid; he completed the 150 mile run in two days, which is actually not beyond the bounds of possibility. MG used to be able to manage 30 miles per day with a back-pack for six weeks just at a sauntering, walking pace. Needless to say the Spartans were not too interested in turning up for a battle during their 'Festival of Peace' and so declined, at least for a week or so, which was just as well for the Persians because if the Spartans had turned up, what became a rout would have turned into a massacre on an epic scale. As it was, Xenophon was quoted 90 years later as writing that a goat was sacrificed every year, to a maximum of 500 per year, for every Persian killed at the battle and, after 90 years, still the Greeks were not done with the goat-sacrificing.
The second event was the march, jog, run of the remaining victorious Athenian hoplites, in full armour/kit, over the 25 or so miles from Marathon to Athens in order to head off the other half of the Persian army which had sailed, without landing, from Marathon. Athens had probably sent out all, or the vast majority, of its hoplites to Marathon and would have been largely defenceless. The Athenians arrived before the Persians could gain a toehold on the beachhead and the Persians turned tail and headed back off to Asia Minor. No surprise there then! One rout was costly, two would have been unthinkable!
Oh, the arrow. A similar paradox to Achilles and the tortoise but relating to time not distance. Planck time deals with that paradox!
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