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[Phys-l] explanatory and response variables (was calibration )



On Aug 7, 2007, at 11:30 AM, John Denker wrote:

On 08/07/2007 09:14 AM, Folkerts, Timothy J wrote:

You took a page or two in give an brief
explanation to practicing PhDs. Perhaps a more basic approach is
appropriate to a more basic audience.

Simplification is good. There are various reasonable ways of
simplifying the topic for the benefit of naive students. OTOH
teachers need to be /overqualified/ in the subject, so that they
can appreciate the consequences of the simplifications they are
introducing ... as opposed to just spouting something that is
only approximately true, without even realizing that it is an
approximation.

While I agree you give a wonderfully sophisticated view of treating
relationships as P(x,y), getting an upper-level science student (let
alone a typical high-school student) to appreciate the subtleties
would be a tall order.

They don't need to appreciate the "subtleties". They do
need to make a scatter plot so that they have some hint of
a glimmer of a clue as to the /meaning/ of what they are
being asked to do.

This article seems to be aimed at an audience
somewhere in between. In such a case, I think "dependent" and
"independent" are reasonable ways to think of the situation.

If the objective is simplification, then let's simplify things,
as follows:

Simplification #1 is to simply not mention "independent" or
"dependent" at all. The incoming students (and I dare say
most of the outgoing students) have no idea what those words
mean. How much time are you going to spend attempting to
define those terms? Why???????

Let's
get the students to master the idea of p = f(rho) (and many will have
a hard time makiing the jump from y =f(x) to p=f(rho) ) before
takeing your next step.

That sounds fine. Again: There are various reasonable ways of
simplifying things.

Simplification #2 is to consider the case where the uncertainty
in y is vastly more significant than the uncertainty in x.

My point remains that simplification #2 has, AFAICT, no connection
to calling one variable "independent" and another "dependent".
If there is any connection here, I'm not seeing it; please explain.
I would treat x and y on an equal footing. I would say x has error
bars and y has error bars, but the x error bars are smaller in the
appropriate units. (The slope of the trend line enters into the
"appropriateness" of the units.)

I see no harm in using well established mathematical terms -- dependent and independent variable -- in particular contexts. Yes, objects do not explain objects and variables do not explain variables. Explanations are logical chains of cause-and-effect created by humans. A statement like "too much fat in what you eat explains your overweight" is a shortcut. A doctor is saying that an acceptable cause-and-effect chain can be established between the diet and the overweight. The same is true for a statement "more rapid loss of potential difference, between two initially-charged plates, is caused by humidity." In this case humidity is the cause (in an explanation) while the time after which one half of the charge is lost is the effect. What kind of harm might result from saying that, in this context, humidity is the independent, or explanatory, variable while the half-discharge time is dependent, or response, variable? One may argue about validity of some explanations. But it would be difficult to argue that attempts to explain reality are not useful. That is the essence of what we do physics.

_______________________________________________________
Ludwik Kowalski, a retired physicist
5 Horizon Road, apt. 2702, Fort Lee, NJ, 07024, USA
Also an amateur journalist at http://csam.montclair.edu/~kowalski/cf/