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Re: Centrifuge (was: Just So Stories)

John Denker wrote:

Recommendation: Be modest and honest.

Yes, we should be modest and honest.

"small particles settle more slowly because of thermal
zig-zagging".

This is not a quotation from what I wrote. In the last message
I agreed with you that zig-zagging is not an explanation. It is
part of a qualitative model which can be used to understand
settling of mud particles in a stationary container. A smaller
particle subjected to Brownian kicks (during its fall) will
usually need more time to reach the bottom than a larger
particle for which kicks are relatively less important.
Thermal kicks have practically no effect on particles whose
masses exceed a certain limit, such as one gram.

What is wrong with this? What kind of misconception I am
going to implant by using this simple model. This is not my
model; I do not remember where I saw it for the first time.

Don't pollute your brain with false explanations. Don't
pollute your students' brains.

Where am I polluting?

Meanwhile, taking a higher-level view, what is the goal?
I thought it was to give students some exercise using the
centrifugal field formula.

The goal was to explain what happens in the centrifuge in
terms of what students already learned in seven chapters.
Explaining what happens in a stationary situation was
the first step. The next step was to introduce artificial gravity
which plays the essential role in rapid precipitation. The
model predicts (qualitatively) that precipitation is faster
when the angular velocity is larger. I hope that somebody
can go one step further and compose a qualitative problem
based on what happens in the centrifuge. Is this possible?
Is this desirable? Is it worth trying?

Good authors check their work!

Yes. And I sorry for some typing errors I noticed today.
So let me read this message again before sending it this
time. I did and I do not see anything wrong. But this is
a subjective opinion. I think that even good authors are
often blind to what is wrong in their compositions.
Ludwik Kowalski

John Denken wrote:

At 09:09 PM 11/3/00 -0500, Ludwik Kowalski wrote:
How do we decide what is and what is not an explanation?

By whether it makes correct predictions!!!!!!!!!!!

Yes.

But a qualitaltive explanation could not be expected to produce
a quantitative prediction. Why should it provide answers to
all possible questions?

A theory need not answer all possible questions... but it should either
make reasonably accurate predictions, or keep silent. If it makes a
prediction, the prediction should be correct.

As an illustration, consider the Just So Story that says a wing produces
lift because it is curved on top and flat on the bottom:
-- It makes incorrect predictions about the effect of increasing or
decreasing the curviness.
-- It makes incorrect predictions about the feasibility of upside-down
flight.
-- It makes incorrect predictions about numerous other relevant physical
phenomena.

So it is with the zig-zag theory. The problem is not its
non-predictions; the problem is its false predictions. As I wrote previously:
-- The zig-zag theory predicts the wrong dependence on temperature.
-- The zig-zag theory predicts the wrong dependence on viscosity.
-- The zig-zag theory predicts the wrong dependence on particle size.
-- The zig-zag theory predicts the wrong dependence on particle mass.

And contrary to what I wrote previously, I now doubt that the zig-zag
theory correctly predicts that large particles settle out faster. In
kinetic theory, vertical velocity is independent of horizontal
velocity. (It's not like a car with a 55-mph speed limit that can either
go horizontal or vertical.) There's a separation of variables.

Meanwhile, taking a higher-level view, what is the goal? I thought it was
to give students some exercise using the centrifugal field formula. If so,
the question arises of why bring up the size-dependence at all? Why not
just consider particles with some uniform size? Why not just assert that
there is a terminal velocity proportional to net force?
-- The assertion is plausible, consistent with everyday experience with
viscous liquids.
-- The assertion can be justified as a phenomenological observed fact.
-- Any discussion of the detailed submicroscopic theory can be deferred
to a later chapter.

======================

The world is already oversupplied with Just So Stories being passed off as
"scientific explanations". The last thing we need is another one.

Recommendation: Be modest and honest. It is much better to say "small
particles settle more slowly, and I don't know why" than to say "small
particles settle more slowly because of thermal zig-zagging". Don't
pollute your brain with false explanations. Don't pollute your students'
brains.

> authors nearly always like what they compose

Good authors check their work!

Recommendation to all physlers, and students, and everybody else: Check
your work! If you devise a theory, check its predictions. Check as many
of them as you can, and make sure they are all true. Any theory worthy of
the name can be subjected to numerous tests:
-- Do the dimensional analysis and check the scaling properties.
-- Check the limiting cases.
-- Check the order of magnitude for reasonability.
-- Check against whatever experimental data is available.
-- Check the sign and magnitude of the dependence on the independent
variables.
-- Et cetera.

Check your work!