31 Jul 2007

The origins of Greco-Chinese apeirophobia

Let's say you have a swift runner and a lazy-going tortoise placed on a track with the intent of racing each other for the curious enjoyment of a classical audience. Do not ask why. This absurd scenario is purely theoretical for the sake of a point about dead philosophers. Now, the tortoise, being slow, is given a head start by the gracious Achilles. In order that Achilles even pass his reptilian competitor, he must first travel the distance from himself to the tortoise. Yet before, he gets to the tortoise, he must have travelled half of that distance. And before half that distance, he must have journeyed a quarter the distance, and before that, an eighth, and before that, a 16th, et cetera ad vomitum. As we can see then, he has to accomplish an infinite number of tasks to even get to that sluggish turtle. So we can conclude that Achilles will never win the race at all, no matter how fast he runs.

No, wait. Nevermind. Bad example. Let's just skip the Greek calculus exam and sum it all up by saying that, um... the dimensionless cannot be accumulated, yet its size is a thousand miles. Sound good? Excellent.

What am I carrying on about? Infinity, of course. And both the Ancient Chinese and the Classical Greeks are to blame for its discovery as well as the countless mathematicians on both sides of Eurasia tormented by its abstract purgatory of existential paradoxes during the following two millenia thereafter. Personally, I like to think that both Zeno of Elea and Hui Shi were fraternal twins seperated at birth on the open Indian sea by a freak storm. Strangely, they both covered similar topics involving the notions of infinity, motion and spacetime approximately 2500 years ago without the use of a telephone. Another coincidence is that little happens to be known of both of these people's lives.

Zeno of Elea, a Greek, was born in the town of Elea (hence the name) and was probably born around 490 BCE. Zeno was said to be a handsome man, at least according to Plato, and in his youth he had probably been the eromenos to an older philosopher named Parmenides (read Plato, Parmenides, 127b). He seems to especially have been devoted to the notion of paradoxes involving the divisibility of dimensions, the nature of motion and the illusion of plurality. He appears to have made a name for himself through his genius explorations taking advantage of logical proof by contradiction to undermine the very things we most take for granted in our daily lives. He is famous for the self-named Zeno's Paradox involving that mindnumbing turtle example above.

However, miles away, a contemporaneous fellow by the name of Hui Shi (惠施) wrote about surprisingly similar things concerning plurality and our notions of infinity. He was part of the "School of Names", a nebulous label we use for a group of recognized philosophers of the same time period as Zeno and his followers, who likewise delighted in paradoxes, mind twisters and an overall profound contemplation of logic in a way that wasn't done before (as far as we know). And of course, it can be attributed to Hui Shi who stated in Classical Chinese:

  • 无厚不可积也,其大千里。
    Wú-hòu bù kě jī yě, qí dà qiān lǐ. (Modern Mandarin pronunciation)
    Literally: Non-thickness not can accumulate also its size thousand miles.
    The dimensionless cannot be accumulated, yet its size is a thousand miles.
(Mar 27 2008) Updated thanks to a tipoff from an anonymous person. The Chinese character 也 is to be read yě, not tā whose character is quite similar: 他. Sorry, this is due to my carelessness.


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