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Re: vortex: defining properties

On Sun, 31 Jan 1999, John S. Denker wrote:

Really? Then I'm all screwed up.

I am quite confident about my vortex-velocity claim as quoted above. Take
a look at _The Feynman Lectures on Physics_ volume II, equation 40.20 (at
the top of page 40-10). Equivalently, take a look at von Mises, _Theory of
Flight_, equation 23 (at the top of page 40).

velocity = (circulation) / (2 pi R)

I have no problems with this. But it is a type of non-dynamical special
case, I think. My suspicion is that the pattern of a DRIVEN circulatory
flow is critically dependant upon viscosity, and has an abnormal
distribution of vorticity. If the driving action is removed, it collapses
into the form you describe above: a volume-filling pattern of zero-curl
flows which surround line-like "defects" of vorticity (like cosmic string
torsional defects in the spacetime of the early universe.) I've yet to
see this explained non-mathematically in depth anywhere, except Feynman's
referring to a stirred bucket on page 40-10, "Although you put in some 'w'
at the beginning, it soon dies down because of viscosity and the flow
becomes irrotational."

If my gut-feelings about aircraft are right, then the mechanism which
causes the lifting force is identical to the mechanism which ejects a
"smoke ring" from your standard oatmeal-box ring vortex generator. If so,
then the process is impossible to describe if we eliminate viscosity from
our mental imagry. Eliminating viscosity might make the mathematics very
simple, but there is a chance that it will distort our internal conceptual
networks to such an extent that they fracture. I believe this about 2D vs
3D descriptions of airfoils. I also believe this about nonviscious
descriptions (although until you led me to review Feynman's chapter 40, I
only understood this in a vauge way and did not know how to state it.)


Question: How strong is your mathematical background?

Undergrad engineering at U of Rochester, partial diff-equs, linear
algebra, nothing higher. And this all mostly unused after twenty years.

It seems you read a
lot and write a lot, but you seem to give short shrift to the equations.

Oh, most definitely. In part, this is from a longstanding dose of Math
Anxiety which I've never entirely defeated. But this just provided the
seed. My avoidance of symbological reasoning is also an intentional
philosophy: If I want to communicate with people who speak Latin, then I
must speak in Latin and finally THINK exclusively in Latin.

To REALLY EXPLAIN physics to the general public, I cannot rely on anything
resembling symbolic mathematical reasoning. It would cause me to tell
people "YOU CANNOT UNDERSTAND THIS, YOU DON'T HAVE ENOUGH MATH". The
truth actually would be that "I CANNOT EXPLAIN THIS, I AM HOBBLED BY A
CRUTCH COMPOSED OF MATHEMATICAL LANGUAGE." After "descending" from the
symbological heights and learning to talk physics with the unwashed
masses, I perceived the significant power in such an approach. Currently
I commit a massive physics-heresy by taking mathematics down from its high
pedestal, and instead elevating something else, a thing which is very
close to Pure Thought. Maybe describe it as "self-constructing conceptual
nets." Picture puzzles which, after being constructed manually in part,
can automatically attract the rest of the pieces and assemble themselves.

There are plenty of math-based physics experts about. Why should I pursue
what everyone else pursues, when there might be alternate paths which lead
to extremely useful viewpoints? "Everyone knows" that math is the only
route to physics. Study the misconceptions of textbook authors, and
you'll rapidly find that the greatest enemy of any educator is the phrase
"everyone knows."


I think we really should be discussing this on PHYS-L. Those people are
sharp. If I've made a glaring error, they will find it quick.

Well, most of my friends are embarrassed when they make a mistake. They
*really* hate screwing up in public, and they find it painful to back down
in public.

I originally was just like that. In my longrunning observations of
popular misconceptions, and also because of my fascination with the
history and sociology of science, I've come to the conclusion that
avoidance of public embarassment is a widespread mental disease among
scientists, and I constantly fight to eliminate it from myself. The
"disease" is based upon dishonesty and a need to sheild our egos from
embarassment-damage. Shielding ourselves from embarassment has nothing
to do with Scientific Integrity (see RF's CARGO CULT SCIENCE.)

Rather than courting dishonesty in order to avoid embarassment, we should
constantly be pursuing embarassment in order to avoid dishonesty. Even
stronger: we should strive to burn every trace of dishonesty and
ass-covering from our thinking process. Trial and error is vastly
accelerated if we think aloud, while simultaneously a group of people
points out our embarassing blunders. It can short out a large number of
common subconscious psychological ploys which we constantly use to flee
from embarassment. And it can almost instantly destroy our own cherished
misconceptions, as long as we can avoid the normal response of retreating
into defensiveness and reinforcement of our desire to always be correct.
If trial and error is to be pursued, we should be, in a sense,
intentionally pursuing error.

Don't get me wrong, I'm not saying that these things are EASY to do, or
that I am all that successful in doing them myself. I'm saying that we
would all benefit greatly if we could constantly strive to do them.

Therefore (applying the golden rule) I try to avoid telling
people "you screwed up" in public. If this discussion *had* been on the
list, I would have tried to take it off-line, so as to reduce the chance of
hurt feelings.

I request that you hurt my feelings, at least in regards to my falling
into physics errors and misconceptions. I want to know why I'm wrong,
and don't spare any bit of the gruesome details.


If you wish to avoid the embarassment of suddenly perceiving serious
mistakes while several hundred physics experts look on, then we can keep
this private. Me, I recommend that everyone in the Sciences make a habit
of pursuing this sort of embarassment, of developing a taste for it.
Become embarassment-gourmets, doing the equivalent of pursuing the type of
rare and exotic libation which inexperienced children described as "rancid
grape juice." The habit has rewards which the inexperienced children
don't reaize.

I am convinced that this "pursuit of embarassment" was major component of
Richard Feynman's genius. He really, truely, didn't care what other
people thought. Most people just don't get it. They give lip-service to
Scientific Integrity, but when it comes down to employing it, they'd
rather keep silent in order to maintain their self-image as experts. We
(amateur) scientists should be like little kids who poke at things without
a thought to looking like idiots: the very opposite of self-declared
experts with exhalted and carefully defended images of our own perfection.
Little kids can see the mysteries. Little kids have a chance to defeat
their misconceptions by themselves, and to see very obvious things that
the highly trained experts are blind to. In addition, the highly trained
experts have a chance of aquiring massive misconceptions which they will
fiercely defend against all attack, because relenquishing their
misconceptions will damage their expertise in the eyes of their collegues
and in the eyes of themselves.

(Yes, this is yet another Physics Sermon. Please put your donations in
the tray as it passes among the pews!) :)

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William J. Beaty SCIENCE HOBBYIST website
billb@eskimo.com http://www.amasci.com
EE/programmer/sci-exhibits science projects, tesla, weird science
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