I think Srinath's first inference in his last note (that "we *feel* that
the minute hand overtakes the hour hand, and here is precisely that
feeling which is articulated mathematically") does map to the relationship
between Achilles and the tortoise in Zeno's paradox.
And since Zeno was apparently supporting his teacher, Parmenides, in
laying down this paradox, here are some possibly relevant lines from
Parmenides' poem about learning.
First...
***
"Come, I shall tell you, and do you listen and convey the story
What routes of inquiry alone there are for knowing--
The one-- "this exists," and "that cannot possibly exist"
is the compelling path, for it attends upon truth.
The other-- "this does not exist," and "that necessarily will never
exist"
I point out to you as a path wholly unlearnable,
For you could not know what does not exist, by any feasible means,
Nor could you point it out."
***
Second...
***
"The same thing is for thinking and feeling"
***
Taken together and applied to Srinath's analysis, "this exists" and "that
cannot possibly exist" may arise from feeling or experiencing (or "being"
as some translations have it)-- just as in Srinath's analysis, the
coincidence of the hands of the clock arises from feeling based on
experience.
Srinath's analysis seems to be an illustration of the first path described
by Parmenides.
But imagination-- thinking potentially not grounded in feeling, or
thinking not taking account of experiencing and being-- would include
imagining that the process of Achilles' running would be to aim for and
achieve one goal after another-- the never-ending half way points.
But the halfway points are in this case not felt, but imagined.
So in this sense of feeling, they "do not exist," as discussed for the
second path described by Parmenides.
>From this, as the paradox goes, we conclude that the event of
>Achilles overtaking the tortoise will "necessarily never exist.
This seems to be an illustration of the second path described by
Parmenides.
Parmenides does begin his poem with some lines that potentially
convey a lot of feeling...
***
"The mares that carry me, as far as impulse might reach,
Were taking me, when they brought and placed me upon the much-
speaking route
Of the goddess, that carries everywhere unscathed the man who
knows..."
***
To make the potential feeling here totally explicit for modern ears, I'll
paraphrase in an attempt to make explicit all of the potential context for
feeling that an ancient Greek like Zeno might have experienced.
***
The gentle mares,
who in their steadfast nurturing strength
carry me
as far as my longing heart might reach,
were in their careful, surely footed strength
carrying me
when in their protection
they brought me toward
and secured my journey
into the deeply telling route
of love
and knowledge.
Meaning after meaning
arose and held clear,
as by the grace of a
protecting
and powerful
spirit
of clarity
incumbent to respect,
beauty,
and awe...
***
Apparently, Parmenides himself was for both "thinking and feeling," and
from his poem, it looks as if restricting one's learning from Parmenides
just to thinking would have missed the feeling.
But to be fair...
Do any analyses exist to say that feeling and thinking would not be
simultaneously involved in the kind of learning we're looking for?
--Lee Bloomquist <LBLOOMQUIST/0005099717@MCIMAIL.COM>
Learning-org -- Hosted by Rick Karash <rkarash@karash.com> Public Dialog on Learning Organizations -- <http://www.learning-org.com>