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A Greek Koan: Where Zeno Went Right [1]
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Date: 2023-08-20
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 of goallessness, 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.
Monism
Monism is a great way to tie yourself into knots much worse than the famous Gordian Knot or the less well-known Matthew Walker knot, both challenges that seemingly cannot be untied, though both, as material knots, can of course be cut. The knots of monism can neither be untied nor cut through, making some of them excellent koans.
To start with, monism is presented to us in opposition to dualism. But in monism, there can be no opposition, no dualism. So if Parmenides is right, what are the rest of us going on about? In fact, what was he going on about, if the question cannot even arise?
The astro-philosophers of Krull once succeeded in proving conclusively that all places are one place and that the distance between them is an illusion, and this news was an embarrassment to all thinking philosophers because it did not explain, among other things, signposts. After years of wrangling the whole thing was then turned over to Lyn Tin Wheedle, arguably the Disc’s greatest philosopher*, who after some thought proclaimed that although it was indeed true that all places were one place, that place was very large. *He always argued that he was.
Terry Pratchett
The mystics, Zen masters or otherwise, don’t worry about it. The trick is to neither try to put it aside nor get stuck.
The One is the Mother of the Ten Thousand Things.
Dao is the Mother of the One.
Laozi, Dao De Jing
All is one, and all is different.
Zen koan
In the beginning, rivers are rivers and mountains are mountains. Then rivers are not rivers and mountains are not mountains. Finally, rivers are again rivers and mountains are again mountains.
Also a Zen koan
We will examine this koan in more detail when we come to Tozan’s Five Ranks of the Ideal and the Actual, the second highest level of koans in the usual ordering, the highest level being the Precepts of the Buddhas.
There is a lot of talk about using a ship or raft to go to the other shore in Buddhist Skill in means, and then about leaving them behind when you get there. But there is much more.
Paramita [conventionally, perfection] means “arriving at the other shore.” Although the other shore does not have the appearance or trace from olden times, arriving is actualized. Arriving is the fundamental point. Do not think that practice leads to the other shore. Because there is practice on the other shore, when you practice, the other shore arrives. It is because this practice embodies the capacity to actualize all realms.
Also Dogen Zenji
If you find that confusing, you are doing well.
Parmenides
Link above.
The historical Parmenides is one of those shadowy figures who lived just outside the realm of documented history. We have parts of a poem he wrote, and a great many legends, including some invented for a Platonic dialogue.
Parmenides' sole work, which has only survived in fragments, is a poem in dactylic hexameter, later titled On Nature. Approximately 160 verses remain today from an original total that was probably near 800.[3] The poem was originally divided into three parts: an introductory proem that contains an allegorical narrative which explains the purpose of the work, a former section known as "The Way of Truth" (aletheia, ἀλήθεια), and a latter section known as "The Way of Appearance/Opinion" (doxa, δόξα). Despite the poem's fragmentary nature, the general plan of both the proem and the first part, "The Way of Truth" have been ascertained by modern scholars, thanks to large excerpts made by Sextus Empiricus[d] and Simplicius of Cilicia.[e][3] Unfortunately, the second part, "The Way of Opinion", which is supposed to have been much longer than the first, only survives in small fragments and prose paraphrases.[3]
Lots of people thought that his monism was the real deal and deserved all of our attention, but he put more effort into describing Opinion, and the fundamental binary nature of the Cosmos.
Other References
This has little to do with the Douglas Hofstadter version of Zen-O in Gödel, Escher, Bach, an Eternal Golden Braid, nor with Lewis Carroll’s What the Tortoise Said to Achilles.
"What the Tortoise Said to Achilles",[51] written in 1895 by Lewis Carroll, was an attempt to reveal an analogous paradox in the realm of pure logic. If Carroll's argument is valid, the implication is that Zeno's paradoxes of motion are not essentially problems of space and time, but go right to the heart of reasoning itself. Douglas Hofstadter made Carroll's article a centrepiece of his book Gödel, Escher, Bach: An Eternal Golden Braid, writing many more dialogues between Achilles and the Tortoise to elucidate his arguments. Hofstadter connects Zeno's paradoxes to Gödel's incompleteness theorem in an attempt to demonstrate that the problems raised by Zeno are pervasive and manifest in formal systems theory, computing and the philosophy of mind.
"The sixth patriarch is Zeno" (p. 30) Achilles claims that Zeno is a Zen master. The real ➟ Zeno of Elea, of course, couldn't have been a Zen master, because he was Greek and he lived about a millennium before Zen Buddhism existed. Achilles' confusion stems from a pun: he repeats "the sixth patriarch is Zeno" to himself. The sixth patriarch is Enō, at least when named in Japanese. (His Wikipedia article is under his Chinese name, ➟ Huineng.) Hofstadter playfully lets the dialogue proceed as if Zeno and Enō are the same person.
They discuss an impossible flag with holes in it, based on the Escher print at the top of this post.
Music
J.S. Bach Three Part Inventions BWV 787-801, Pieter Jan Belder
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