[Bruce Gregory 960318.1637 EST]
Phil Runkel 960315
Even if a teacher listens to you and begins to glow with enthusiasm, how
can you protect the teacher from the rest of society? Everybody else in
the school system knows that the whole purpose of schooling is to extract
the student's own goals as if they were infected teeth, throw them away,
and insert in their place the goals prescribed by the curriculum
committee, the state legislators, New Gingrich, and others.
You certainly know the problems. We have had the best success with
elementary school science and working with non-traditional courses such as
high-school astronomy, where there are no standards or thousand page
textbooks to overcome. As for transplanting goals, I am convinced that
Bill Powers hit the nail on the head when he said, "When all people
understand how control works, they will see that controlling other
people's goal-achievements is impossible, has always been impossible,
and will always lead to dangerous conflict when seriously attempted."
(LCS II p. 194.)
Bruce Abbott 960316.1910 EST
Thanks for the program. I will give it a workout.
Chris Kitzke 960315.1843
Just stuck me funny, because I had always thought chaos would be
unpredictable, and when I saw you call it exponential, I thought that
we know what an exponential curve looks like, so then how could it
really be chaos.
In the case of the solar system, choas with respect to orbital position
may simply amount to the fact that you can't predict where in its orbit
Pluto, for example will be after a few hundred million years because if
you calculate its future position from two positions in its orbit that
are initially quite close together, you wind up with completely different
orbital positions after some period. During those calculation you find
at some point that the positions are diverging exponentially. (The
positions do not keep diverging because the two "planets" can only
get so far apart and still be in the "same" orbit.
Bill Powers 960316.0300
Has anyone tried to explain why chaos occurs?
While I have made it clear that I am no expert, I can say that when
it comes to chaos associated with orbits in the solar system, resonances
seem to be be the culprits. Objects with twice or one-half the orbital
period of Jupiter succomb on relatively short time scales and are ejected
from the system.
This way of teaching doesn't teach procedures or facts; it teaches
goals. If you know what the goal is, and accept it as your own, you will
find some procedure to reach it. Half of the fun of learning is to find
your very own way to achieve a goal, whether or not it's of any basic
interest to you (has any higher-level usefulness). Of course the other
half (there are probably many halves) is seeing someone else come up
with a really neat way to reach a goal, and learning to do it the same
way. This kind of learning, I think, is called "playing games," because
the outcome is less important than how you get there.
Amen. I suspect that your description applies to everything we would be
happy calling "understanding". Working to get the right answers to physics
problems, for example, leads to a familiar technique called plugging and
chugging, where the goal is to find the right formula in the text and then
to plug in the numbers from the problem. What is then totally lost sight
of is "how you got there", i.e., the principles involved. I very much like
your phrase "teaching goals". I suspect that the best we can do is make
our goals explicit and let the students decide if they want to adopt them.
First, however, they must discover how their present goals differ from ours.
The Nature of Reality
The Nobel laureate Richard Feynman asked his biographer Jagdesh Mehra what
he, Mehra, thought of Feynman's contribution to physics. Mehra replied,
"My answer would be what Einstein wrote to Langevin about Louis de Broglie's
thesis when the former asked Einstein for his opinion of it. Einstein wrote:
'He has lifted a corner of the veil of Nature.' I believe that is what you
have done also." Feynman replied, "I have been trying to dance with and woo
her all my life, but she doesn't let you lift her veil."
Bruce Gregory