From: Ronald Wong (ronwong@inreach.com)
Date: Fri Dec 29 2000 - 13:24:13 PST
Message-Id: <l03102802b6641d5f820b@[209.209.20.22]> Date: Fri, 29 Dec 2000 13:24:13 -0800 From: Ronald Wong <ronwong@inreach.com> Subject: re: Not Knowing
A little while ago Steven Eiger replied to my comments on "Not Knowing by
saying:
>...However at the beginning he argued that some "why" statements were
>untestable. Using his arguments, one could have said the same thing about
>Aristotelean physics; one could argue that it is the spunk and defiance of
>individuals who question assumptions that end up moving those "why" statments
>one step deeper, witht he explanation of, and perhaps evidence for previously
>assumed "untestable" assumptions.
I'd like to comment on the two areas that Steven brought up:
A. Aristotelian physics
B. "...individuals who question assumptions that end up moving
those "why" statments one step deeper..."
======================================
Let's start with Aristotelian physics.
It's important to know that Aristotelian physics was based on three things:
a. Observations
b. Common Sense
c. Logic
The scientific truths of Aristotelian physics were the product of the
application of the rules of logic to the common sense notions arrived at
from observing the world we live in.
For instance, observations lead us to the common sense notion that there is
a natural order in the universe in the form of earth, water, and air - in
that order (there's more to this scheme but I am trying to keep things
simple).
Logically, objects made of earth will try to return to where they belong
because in doing so they will restore the natural order of things. The
greater the amount of earth possessed by the object, the greater the
propensity for restoring order. As a result, heavier objects fall to the
earth faster than lighter objects. This was consistent with common
observations in the past and is probably true even today (when people fall
out of trees, they hit the ground before the leaves and branches).
"Scientific truths" in Aristotelian physics were validated on the basis
that they logically followed from a set of initial conditions. The initial
conditions could be earlier "scientific truths" or common sense notions
based on extensive observations (i.e. "facts").
If this seems to have the flavor of Euclidean geometry, it's not by
accident. It was the power of logic in establishing what was mathematically
true that made it the tool of choice for establishing what was true in
Aristotelian physics.
Interestingly enough, Aristotle avoided mathematics in his scientific
studies at all cost. Most of his scientific work was in the area of biology
- not physics. Thus there was no attempt to quantify or mathematically
analyze things in his study of nature as there is today.
In a similar fashion, there was no need for experimentation. It would have
been redundant. If a "scientific principle" was found to be logically true,
what's the point of doing an experiment? It would only "prove" what we
already have shown to be true.
The bottom line is that in Aristotelian physics there are no "previously
assumed 'untestable' assumptions" to begin with. The nature of his physics
precludes testability.
This is one reason it was so successful for thousands of years. Everything
it had to say about nature was logically true. What more could you want?
The discipline was free of error to the extent that the rules of logic were
applied correctly.
======================================
Now on to item B:
>...it is the spunk and defiance of individuals who question assumptions that
>end up moving those "why" statments one step deeper, witht he explanation of,
>and perhaps evidence for previously assumed "untestable" assumptions.
When it comes to Aristotelian physics, there were no "why" statements for
individuals to move "... one step deeper, witht he explanation of, and
perhaps evidence for previously assumed 'untestable' assumptions."
Everyone with any education agreed on the assumptions. Common sense was all
that you needed in order to see that they were true and logic took care of
the rest.
So how did we move forward from the Aristotelian framework that had reigned
successfully for thousands of years to where we are now?
Some examples:
---------------------------------------
Copernicus was not thinking in terms of spunk or defiance when he looked at
Ptolemy's model of the motion in the heavens. He had studied it more than
most scholars of his day (he could read the original Greek manuscripts) and
what came out of his studies was the idea that Ptolemy used one too many
mathematical devices in making his model. For esthetic and religious
reasons, Copernicus thought that a model of the heavens could be made using
only the mathematical devices known as the epicycle and the eccentric.
After 40 years of work, he was able to show how one could indeed transpose
the Ptolemaic model into one that used only these two devices.
That the new model was heliocentric and not geocentric, like Ptolemy's, did
not trouble Copernicus. He made it quite clear that the new, Copernican
model was just a mathematical transformation of the geocentric model of
Ptolemy's.
Thus you could continue to believe in the geocentric world of Aristotelian
physics with it's geocentric universe if you wished but his mathematically
equivalent model was just as good for predicting the motions in the heavens
and could be used for this purpose just as well. He also felt that in
developing this "simpler" model he had brought mankind closer to an
understanding of the Divine Creator - an appropriate thing for him to have
done given his position in the church as a canon (and another reason for
choosing his model over it's predecessor).
Although he offered a number of reasons in support for his "new" model of
the universe, but they fell on deaf ears - for good reasons (that's another
story).
Copernicus probably did not see his work as revolutionary. The model was
just a mathematical transformation. If it was anything, it was an act of
piety that he had performed in the course of developing his model.
He probably would have agreed wholeheartedly with the idea
>...that a pure description of what happens (a model), devoid of a
>deeper understanding, can be quite useful, and therfore worthwile
>accepting.
----------------------------------------
In a similar vein, Kepler spent a number years simply trying to improve the
existing models of the heaven. After almost seventy models he had come to a
model that achieved the highest level of precision for his time. Although a
higher level of precision would not seem to have yielded any benefits,
given the needs of his time, Kepler was not satisfied. His instruments
could measure the position of heavenly bodies to a higher level of
precision than the model (the importance of accuracy and precision was just
becoming an issue at the time).
He made an assumption that was to determine the direction his work for the
rest of his life. Kepler decided that any model of nature should enable us
to predict events to a level of precision that matches that of our
instruments (it's a belief that we continue to endorse to this day, but it
is important to realize that it IS an assumption).
>From this comes his famous three laws (which showed that neither Copernicus
nor any of his predecessors were exactly correct when it came to heavenly
motion).
----------------------------------------
As a scholar brought up with a thorough knowledge of Aristotelian physics,
Galileo was less interested in looking at the assumptions of the early
Greeks than in looking at their conclusions.
One of the things that he was able to do was show that Aristotelian physics
leads logically to the principle that all bodies fall to the earth at the
same rate - no matter what their weight. This is one reason why the story
that he dropped spheres of different weights off the Tower of Pisa remains
just that - a story.
There is no reason why he would have engaged in such an activity since he
had already demonstrated, as any good Aristotelian would, that his
conclusion was logically true. There was no reason for him to perform an
experiment (why he should be the father of experimental science when there
was seemingly no reason for him to engage in an experiment is a totally
different thread from this one). True, Galileo's conclusion was contrary to
what Aristotle said almost two thousand years earlier, but logic was logic.
This, plus many more activities that he was to engage in, lead him to
question the Aristotelian world view. In the process of establishing a new
way of studying nature, Galileo went on to make his own set of discoveries.
---------------------------------------
Following Galileo, more and more of the world's phenomena was subjected to
experimental investigations that led to a mathematical models which, when
tested and found to be valid, became laws.
Newton, of course, started with a series of observations - his three laws -
and took it from there. No issue here regarding previous, untested
assumptions.
---------------------------------------
In a similar vein, Maxwell summarized in a very succinct, mathematical way
all that we had learned about light, electricity, magnetism (and later, all
the other forms of electromagnetic radiation). It was a major synthesis
comparable to that of Newton's when he brought together heaven and earth in
the course of establishing the concept of universal gravitation.
---------------------------------------
By the time Einstein arrived on the scene, there were a number of puzzling
issues. One was the fact that a simple Galilean transformation of Maxwell's
equations led to false predictions. Another was the unexpected results of
the Michelson-Moreley experiment. A third was the Lorentz's handy, dandy
transformation equations that resolved the issues brought up by the first
two facts without explaining anything in the process (including itself).
All of these were resolved when Einstein took the imaginative step of
adding time as a fourth dimension to the three of space - blending time
with space. In the process, he created a whole new frame of reference from
which to look at our universe.
---------------------------------------
What you will find missing in all of the examples above is any attempt to
look back at past assumptions in order to find "testable" assumptions to
validate.
Like the students in our classrooms, scientists find themselves inundated
with enough questions posed from their present knowledge and experience of
nature to keep them busy for a lifetime.
Prior to Galileo, they would look at what was known and, based on their own
experiences, make some fundamental assumptions which were undeniably true.
Based on these assumptions and well known facts, they used the mathematical
tools of logic and geometry to develop models of nature that they felt were
more pleasing, useful, or complete than their predecessors.
After Galileo came the current trend where we craft testable hypothesis
stemming from our observations of nature which we then test - creating
laws, or principles when the tests prove successful. Not all scientific
developments followed this trend. A common alternative was simply to
quantify the relationship between different elements in nature (The laws of
Coulomb, Ohm, Faraday, etc.). In time, enough successfully developed laws
would come into being that would allow someone like Maxwell to bring about
a major synthesis - the Electromagnetic Wave Theory in this case. In other
cases, unexplained results and fanciful solutions floated around until
someone came along with a more imaginative approach to the situation that
would resolve the puzzle and send us off into another whole new area of
inquiry (Planck and Einstein come to mind).
In short, scientists don't tend to look back to the past. It's very rare
when they do. They concentrate on the present as they work towards the
future. The last thing they would consider is
>..previously assumed "untestable" assumptions.
It's this aspect of science - the positive, forward-looking movement filled
with the fun of discovery and the exhilaration that comes of success - that
we should be conveying to our students.
That's the best thing about being a SCIENCE teacher. It's easy for us to
create an environment in our classrooms that will allow our students to
actually have such experiences.
Best wishes to all for a Happy New Year.
ron
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