Achilles and the tortoise walk into a bar

Remember (Pre-Socratic) Zeno's story about the race between Achilles, the fastest of the ancient Greek heroes, and the tortoise, the slowest of all the land animals? 

(Ancient Greeks didn't know about sloths.)

To be fair, the gods are giving the tortoise a head start in the race. 

However, according to the pre-race betting, Achilles will never be able to recover because of a logical paradox!

At this point I need to introduce Parmenides, who 'd accepted Zeno (the teller of this tale) as his student.

Specifically, Parmenides had accepted Zeno as his student in those techniques which he knew for practicing self knowledge-- of which techniques Parmenides was a master. 

Here the hypothesis:

1. That this is what it means to be a true master-- i.e. to have mastered practical techniques of self knowledge.

2. That a reflection of this mastery can be seen uniquely in Zeno. Why? Because nobody else who writes about Parmenides from those days (Aristotle, Plato, etc.) had been accepted as such a student by Parmenides.

Of all these classical stars, only Zeno was an actual student of Parmenides.

So to illustrate this usage of "master," I analyze Zeno's story about the race between Achilles and the tortoise.

Can I see reflections of Parmenides in this story?

And what evidence in the story can I find of Zeno's having learned something from Parmenides--perhaps some technique of thinking.

Having introduced the question, I now end with the simplest possible answer.

Depending on the translator (none of whom was a student of Parmenides like Zeno was a student of Parmenides) Parmenides had said in one of his poems:

"The same is for thinking and being."

Enter here: Zeno's paradox.

Logically Achilles can't catch up with the tortoise because by the time Achilles will have reached the tortoise's head start, the tortoise will have by that time moved on to a new "head start."

And so on. Again and again. No end in sight.

QED: Achilles can never catch up with the tortoise.

That is the "thinking" side of Parmenides' fragment.

On the “being” side:

Achilles has memories of running and memories of tortoises walking. 

So the same is for thinking and being.

Who wins?

Thinking says one thing.

But for Achilles-- being Achilles says another.

1. thinking-- Achilles can never catch up with the tortoise.

2. being-- Achilles knows by experience, by knowing himself, by being himself, that he can overtake the tortoise.

The same is for thinking and being.

Questions for next time: 

How does one without the other cause imbalance?

How does one with the other cause balance?