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Re: [Phys-L] The Make-Believe World of Real-World Physics



Newton's First Law is a Concept rather than a Behavior - to my way of thinking.

Some will say that it is a 'Special Case' of the Second Law (a = 0) and hence should not be given the Status of a Distinct Law.

This position sadly points out how difficult it is to move beyond Aristotelian Thinking.

Does anyone here really think that getting beginning students to fully grasp the First Law is trivial?


On Jul 17, 2013, at 5:24 PM, John Denker <jsd@av8n.com> wrote:

The discussion in this thread seems to somewhat resemble the
proverbial situation where there are multiple views of the same
elephant, seemingly inconsistent, but not really so.

The central question is: Are physics concepts counterintuitive?
A closely-related question is: Are physics concepts scary?

As stated, these questions are seriously ill-posed. They are
underspecified.

For starters, we must recognize that the answer is a moving target.
There is a proverb that says:
Education is the process of cultivating your intuition.

That means that concepts that students would find counterintuitive
at the beginning of the course should be obvious and intuitive at
the end of the course.

To be blunt: If we cannot make the fundamental concepts intuitive,
we should quit and go home. We should stop wasting everybody's
time.

Secondly, when applying the fundamental concepts to particular
situations, we must recognize the distinction between ordinary
situations and exceptionally deceptive situations. The fact
that you can trick somebody into misapplying the concepts,
especially in a time-pressured situation, or when they're off
guard, does not demonstrate that the concepts are ill-understood
or intrinsically counterintuitive.

Thirdly, there are questions of teaching style. Long experience
has shown that good results can be obtained from any of several
different teaching styles. We don't want to get into a holy war
over matters of style ... but if we are careful, we should be
able to catalog the various styles and discuss some of the pros
and cons.

Let's proceed in that spirit. Given that the concepts start out
counterintuitive and end up intuitive, we are left with a question
of emphasis, a question of spin.

++ On the one hand, telling the students that physics is scary
and counterintuitive has the advantage of showing /sympathy/
for where they are coming from.

-- One disadvantage is that it may make them more scared than
they already were. "Wow, if the instructor thinks it's hard,
it must be worse than we ever imagined!"

-- As a related point, saying the subject is counterintuitive
and scary is a demotivator. It provides a convenient excuse for
giving up.

-- Another factor to consider: As I see it, telling students
that the subject is scary and counterintuitive is a subtle form
of bragging. "Hey, look at me, I'm so macho and so smart that
I can do this scary and counterintuitive thing!" I don't think
any teacher would intentionally build up his ego by scaring and
intimidating the students, but we're all human. Nobody is called
to be a teacher unless (a) they are driven to excel and (b) they
at least somewhat enjoy being in the spotlight, being the focus
of attention. These two factors pretty much guarantee that
feelings of insecurity are an occupational hazard.
http://en.wikipedia.org/wiki/Impostor_syndrome
I can't imagine any way of preventing this, so I reckon the
winning strategy is to recognize it for what it is, and then
try to channel it in to constructive directions.

IMHO, telling students the subject is scary and counterintuitive
is /not/ constructive.

-- Last but not least, it is a matter of relativity and perspective.
Relative to 8th-grade earth science, high-school physics is indeed
complicated and sophisticated. However, compared to living in the
real world, classroom physics is trivial. A huge part of the
teacher's job is to give the students some perspective.
"If you think the cost of education is high,
compare it to the cost of ignorance."

On 07/16/2013 02:53 PM, Anthony Lapinski provided some thought-
provoking examples.

The observation is that these examples are counterintuitive.
I don't mean to disagree with the observation, but I insist
that the answer is a moving target. I do not *want* these to
be counterintuitive. We have it in our power to make these
examples -- and many others -- become more intuitive.


MOTION: Throw a ball straight upward. What is its acceleration at the peak?

I don't see this as a physics problem, but rather as a trap for
the unwary, deceptive in two different ways. One of the oldest
booby-traps in the book arises when there are two different
concepts hiding behind a single name. Sometimes I think I spend
half of my life detecting situations like this, and searching
for ways to disambiguate them ... which I consider a reasonably
good use of my time.

In the present case, we have
a) The scalar acceleration, namely the rate-of-change of
speed. This is the opposite of deceleration.
b) The vector acceleration, namely the rate-of-change of
velocity. This has no corresponding notion of deceleration;
all you get is an acceleration in the other direction.

All students have a prior conception of scalar acceleration. The
concept of vector acceleration that is so heavily emphasized in
the textbook will never fully supplant this prior concept -- nor
should it! Every physicist I know routinely uses the concept of
scalar acceleration and deceleration in some situations.

We can make this situation easier to handle in two steps: First,
we should explicitly teach students to recognize and accept the
distinction between scalar acceleration and vector acceleration.
Neither supplants the other.

Secondly, we should teach students to recognize that this question
poses a pathological situation. In this special case, the scalar
acceleration is discontinuous at the peak. This conflicts with
students' entirely reasonable intuition that the physics should
be continuous. Fortunately, the conflict arises only on a set of
measure zero, for a /perfectly/ vertical trajectory. It does not
mean that the laws of physics are discontinuous. It only means
that thinking in terms of the scalar acceleration is not the
optimal way to model the physics.

In the elementary course, the best strategy is to encourage
students to use the vector acceleration, and to focus attention
on velocity rather than speed.

OTOH, a master of the subject should be able to see things both
ways. If you insist on asking about the scalar acceleration,
there are ways of handling it. An experienced physicist would
immediately add a /regularizer/ to the problem, in this case
something like an infinitesimal horizontal velocity. That
suffices to ensure that the scalar acceleration goes smoothly
through zero at the peak. This is probably beyond the scope
of the introductory course, but it is nice to know that physics
has ways of handling even seemingly-pathological cases.

FORCES: Helium balloon in car. When the car decelerates, which way does
the balloon move?

This is another situation where the concepts are simple, but the
situation is deceptive.

The situation involves fluid dynamics, and such situations are very
commonly deceptive. Almost everybody thinks they understand fluids,
but they're fooling themselves.

There is a two-step process for teaching students to handle the
balloon-in-car situation. As a first step, they should recognize
that the situation is tricky, so even if they cannot fully figure
out the right answer, they can at least put their guard up. They
should learn never to allow themselves to be put in a situation
where they are forced to answer deceptive questions, or to rely
on the answer to deceptive questions.

As always, it pays to think about the question in more than one way.
a) I insist that the concept of inertia is simple! It tells us
that if the car stops suddenly, everything including the air and
the balloon *must* be thrown forward relative to the car.
b) I insist that Einstein's principle of equivalence is simple!
It tells us that a car undergoing steady deceleration corresponds
to a gravitational field in a slightly unusual direction, such that
the air settles to the front of the car and the balloon floats to
the back.

The right answer is that both (a) and (b) are true. The question is
ill-posed, because it does not specify the deceleration profile or
the timescale(s) of interest. It is quite possible that one will
observe (a) followed by (b).

I insist that the principles involved are simple. When the principles
are applied to a deceptive, ill-posed problem, wackiness ensues, but
that does not mean the principles are counterintuitive or in any way
ill-understood. Most likely, it just means that the students have
not been trained to cope with ill-posed problems.

This leads us to an idea that is more important than any particular
concept:
Any problem worth doing is worth doing twice.
Especially if the problem seems hard, counterintuitive, scary, or
deceptive, it really pays to analyze it in two different ways. Even
if you get it wrong both times, you are likely to get it wrong in
two different ways, and the inconsistency should raise all sorts
of red flags.

The problem is, this way of doing business runs completely counter
to the usual classroom atmosphere, where everything is a mile wide
and an inch deep, everything revolves around hit-and-run multiple-
guess tests, everything is rushed.

Personally I would prefer to really understand a small number of
things, rather than to misunderstand a large number of things.

As always, motivation is a big factor. The previous proverb has a
mirror image:
If it's not worth doing, it's not worth doing right.


GRAVITATION: Orbiting astronauts in the ISS. They float, but is gravity
acting on them?

Again, this seems like distilled essence of deception. There is nothing
wrong with the physics as I understand it. The problem is that all the
textbooks I've seen screw this up. They define gravity and "g" one way
in the early chapters ... and then use a dramatically different definition
in later chapters ... and seem blissfully unaware of the inconsistency.

Specifically:
a) We have the gravitational field g@f, defined relative to some
specified frame f. This is frame-dependent, as it must be, in
accordance with Einstein's principle of equivalence.
b) We have the barogenic contribution δg_M which is _independent_ of
the choice of reference frame. we can calculate it in accordance
with Newton's law of universal gravitation:

- G M r
δg_M(r) = -------- -----
r^2 |r|

So once again we have two very different concepts running around under
the same name.
++ I say concept (a) is not confusing.
++ I say concept (b) is not confusing.
-- However, if you blur the distinction between (a) and (b), calling
them both "gravity", then you get an unholy monstrosity, guaranteed
to cause confusion, for reasons having nothing to do with physics.

Anyone have other "counterintuitive" questions?

I have collected a handful of amusing ill-posed and/or deceptive
questions at
http://www.av8n.com/physics/ill-posed.htm

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

Bottom line: If for some reason you want physics to be scary and
confusing, then yeah, sure, you have it within your power to make
it scary and confusing. But why would you want to?

I see it as my job to make it not scary and not confusing.


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