Zeno of Elea“proved” in 9 paradoxes in support of the monism of Parmenides that motion is impossible, because it would require an infinity of steps to get anywhere. Math has dealt with that. But it is true about Truth and Buddhist training.
The Paradoxes
Several of the paradoxes, including Achilles and the Tortoise, argue that we cannot arrive anywhere. In chasing the tortoise, Achilles first has to run to where it started, then where it got to during that time, and so on to infinity. The paradox of Atalanta, a famed woman runner in Greek culture, argues that we cannot even begin to move. To get anywhere, you have to go half way. But that requires you to go a quarter of the way first, and an eighth, and again so on to infinity. The very first step, the very first twitch of a muscle, the very first nerve impulse as we would put it today, has to go through an infinity of points.
Math and Physics
In the 17th century math began to unravel Zeno’s Paradoxes through the ideas of calculus, which were formalized as continuity and limits and then the various sorts of infinity. Quantum mechanics, it turns out, agrees with Zeno, since objects do not follow paths in spacetime. An electron in an atom can be found in one approximate location at one moment, and elsewhere on the next observation, with no path between them. Quarks and gluons are worse. Richard Feynman was able to reformulate QM as a sum over all possible histories. It gives the right answers, but nobody should suppose that it is a description of reality, whatever that is.
The Koan
Do not be fooled by the appearances of Parmenides and Zeno, as they have come down to us in history. They were after something far different from the usual fussing about the opposites.
Here is a Zen take on the question of getting somewhere.
The journey is not hindered by non-arrival, but is definitely hindered by arrival.
Dogen Zenji
O sincere trainees, do not doubt the true dragon, do not spend so much time in rubbing only a part of the elephant;look inwards and advance directly along the road that leads to the Mind, respect those who have reached the goal ofgoallessness, become one with the wisdom of the Buddhas, Transmit the wisdom of the Ancestors.
Rules for Meditation, by Dogen Zenji
One must start in training with some sort of goal, such as dealing with suffering or asking why we train if we all have the Buddha nature. We call that Raising the Thought of Awakening. Then we must go through the koan and come out the other side, which turns out to be the same side we came in on. And then we go back to help others on the path. And then…Well, we’ll get to that.