Leaving for Yue Today and Arriving Yesterday
Little is known about the ancient Chinese philosopher Huizi (or Hui Tzu, c. 300 BCE), but some of his paradoxes survive in the remoter chapters of the Zhuangzi. It's diverting to consider what reasoning might lie behind them. For example:
* I left for Yue today and arrived yesterday.
* I know the center of the world: It is north of Yen [in the north] and south of Yue [in the south].
* An egg has feathers.
* Wheels never touch the ground.
* No matter how swift the barbed arrow, there are times when it is neither moving nor at rest.
* Take a pole one foot long, cut away half of it every day, and at the end of ten thousand generations there will still be some left.
[Burton Watson, trans., except the first which is mine.]
The last two of these paradoxes are surprisingly close to Zero's famous paradoxes of motion in ancient Greece. (It is highly doubtful there was any influence.)
Consider the first of these: I left for Yue today and arrived yesterday. Is there any way to make sense of it?
Well, the following are plausible principles:
(a.) The last day you are in a locale is the day you left.
(b.) The first day you are in a locale is the day you arrived.
(c.) You are in a locale if at least 50% of your body is in that locale.
Now suppose I crossed over the border of Yue at exactly midnight, so that 50% of my body was in my home state at that instant and 50% was in Yue at that instant. It follows from (c) that:
(d.) I was in my home state both yesterday and today.
(e.) I was in Yue both yesterday and today.
By (a) and (d), I left for Yue today. However, by (b) and (e), I arrived yesterday.