For those who want to measure learning, the question was whether or not
(as for measuring length-- where to be able to measure length, we must
also be able to observe length) measuring learning requires that we be
able to observe learning.
Dale's discussion of measuring the coast of Maine illustrated that the
meaning of any particular number acquired is determined by a situation
constituted of actions and individuals. To be meaningful to an audience,
the situation that supports the acquisition of the number must be of a
type to which the audience is attuned.
This relates to the subject of "competition" now being discussed on
another thread.
The meaning of "competition" is, for us, determined by the types of
situations to which we're attuned. That someone could justify, by
social-scientific studies, that competition means badness, while at the
same time, their default connotation of "competition" also associates
competition to badness, simply implies (to me, given Dale's example) that
most of us have never seen a completely fair and just game, under which
competition could develop a meaningful and alternative connotation of
"goodness."
So both the social-scientific results and the default connotation may well
be issues in Design (of the required game).
Put another way, can anyone who performed these studies rigorously argue
that these studies establishing that competition means badness prove,
beyond all doubt, that no game can ever be designed that will wring
goodness from competition?
Once again, we seem to be bound by the types of situations (i.e., games)
to which we're attuned.
So, for example, any system of learning that is claimed to involve
competition may be measured-- due a limited attunement to types of
situations (types of games)-- on the binary scale of "good or bad" as
"bad."
A very basic model for understanding both 1) measurement, as discussed in
Dale's example, and 2) competition may be Zeno's paradox about Achilles.
As the story goes, Achilles is the fastest of the gods, and the tortoise
is the slowest of the animals. So we give the tortoise a head start. But
before Achilles can catch up with the tortoise, he must reach a point half
way between himself and the tortoise.
And so on.
And so on.
With the rules of the game written this way, we can never deduce (even in
an infinite number of statements) that Achilles overtakes the tortoise,
which, as we all know, he does accomplish.
Similarly, with a view of competition based upon the types of games to
which we are attuned, we may never be able to deduce (in a finite number
of statements) that competition can be "good."
With no feeling to the contrary, we may simply support the deduction that
competition is bad.
But maybe it's the game, and not the competition, that produces what is
felt to be bad.
We could entertain at least two hypotheses:
1) that the badness observed is due to the competition, not the game; and
2) that the badness observed is due to the game, not the competition.
To resolve which hypothesis is supported means, to me, that maybe we
should try to measure learning.
But what if our observations of learning are just as constrained as our
view of Achilles in Zeno's paradox (that in his catching up to the
tortoise, Achilles must be observed at a point half way between himself
and the tortoise, and so on-- i.e., we are constrained just to Observing
states and Imagining events)?
>From what I read, Zeno created these mathematical paradoxes to defend
Parmenides, his teacher. Parmenides taught him about knowledge, that is,
true learning.
Hmmm...
Zeno left mathematical paradoxes.
Parmenides left folk poetry.
...Mathematical paradoxes created to defend folk poetry about
learning?
>From reading some of this poetry and using Chu spaces (from mathematics)
to think about Zeno's mathematical paradoxes, here's what I suspect
Parmenides was saying--
***
These measurements of learning what he had to teach, these races,
these competitive games to learn what he had to teach, may exist or
they may not.
Put another way, we can certainly imagine things which do not
necessarily exist.
...Such as the observations of Achilles at half-way points.
...Such as games.
Then if the hypothesis is mostly supported that the badness usually
comes from the games, and not necessarily from the competition,
then how many of the games we play are imaginary?
And which game-- which way of playing, which way of running, which
way of measuring or observing-- is real?
Badness can be due to imagined games which do not actually exist.
On the other hand, if a game is real, how can we observe it, not
simply imagine it?
(This reminds me of what David Hume began with... thoughts and
feelings.)
Moreover... for choices we might make, do thoughts and feelings
compete? In any choice situation, can learning result from going
with one instead of the other?
Obviously, thinking can go off track-- by positing things which
don't exist but which can be imagined.
And we know Achilles wins the race because we Feel it.
So in this case, feelings win.
Competition bad?
Without it, thoughts in this case would not be defeated by
feelings.
The real game is inside.
***
So much for this interpretation of Greek poetry based on Chu
spaces!
But if today, with all the new and exciting advances in mathematics, we
can't get a clear picture of what Parmenides and Zeno were saying about
learning-- way back then at the very beginnings of Western mathematics--
then I think we're fooling ourselves.
Or at the very least, we've giving up on new methods of literary
interpretation.
; )
Lee Bloomquist
--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>