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Re: [Phys-L] Faraday paradox +- pedagogy +- critical thinking

Teaching is more of an art than a science. Each person's
style of teaching is largely a matter of taste, and we
should not dispute matters of taste.

HOWEVER ... it may be within bounds to point out and
discuss the various possibilities.

I mention this because on 06/02/2014 10:01 AM, Derek Padilla wrote:

All fun things to think about!


In life, students will
encounter problematic explanations and logic, and they need to be able to
cut through the reasoning to find where it went wrong

Agreed! However, it doesn't pay to throw non-swimmers
into the deep end of the pool. Most students have no
clue how to solve under-specified problems, let alone
wrongly-specified problems. By the time they arrive in
the physics class, they have been trained for 10 years
to follow instructions, period. Conformity and obedience
are rewarded. Creativity, originality, and initiative
are not tolerated on school grounds.

When I'm talking with school-board members and I mention
"creativity", they assume I'm talking about art and music
(which they got rid of years ago). The idea that there
could be any creativity or originality in physics is
quite beyond their comprehension.

In life, students will
encounter problematic explanations and logic, and they need to be able to
cut through the reasoning to find where it went wrong

Again, agreed. This is a crucial problem-solving skill.

My main point is, there are better ways and worse ways
of teaching this skill. I see this as almost entirely
separate from physics domain knowledge, at least at
first. I'm a big believer in the _building block_
approach to teaching. That is, given a complex task,
break it down into simpler tasks. Introduce each one
separately, then gradually combine them. As applied to
the present topic:
-- Introduce ill-posed problems in a context where the
students already have plenty of solid domain knowledge.
Example: how much water in the Atlantic ocean?
-- Introduce new physics concepts in a paradox-free way.
-- After the physics concepts are well established,
/then/ it becomes OK to play with physics paradoxes.

I find that "paradoxes" are very useful pedagogical tools when introducing
new material as they elucidate shortcomings of prior knowledge, or pull out
a fine, detailed point students perhaps missed when covering material the
first time through.

That mixes two different levels. There is a crucial
distinction between "introducing" the subject and "pulling
out a fine, detailed point". A so-called paradox that is
useful in a master class would be wildly inappropriate in
the introductory class.

One example: introducing the word "system" in regards to thermodynamics. To
begin, I have them think about how, "paradoxically," my momentum is not
conserved when I jump off the ground. To "resolve" this, they needed to
define the system (Is it me alone, or me+Earth?) to work through the
impulse+momentum interaction of my jumping.

Setting aside the pedagogical issues, I disagree with
the physics there. No matter how you define the "system",
momentum is /conserved/. It is not constant, during the
jump, but it is /conserved/. The distinction between
constancy and conservation is crucial, even at the most
introductory level. This issue is discussed at:

The case of /momentum/ in particular, including momentum
conservation and momentum flow, is discussed at:

Bottom line: Momentum is conserved, at every place, at
every time, no matter what. This is one of the bedrock
principles of physics.

This physics issue is related to the pedagogical issue in
the following way: As far as we can tell, there are no
paradoxes in the laws of physics, if the laws are properly
stated. Certainly there are not any paradoxes that affect
basic mechanics.

Exposing naïve students to mis-stated laws is very unhelpful.
Talking about a paradox in front of naïve students is more
likely to consolidate misconceptions than to dispel them.
There are many arguments leading to the same conclusion:

Save the paradoxes for the master class, *after* the students
have fully consolidated their understanding of the correct
physics ... and (!) after they have been trained to deal
with ill-posed questions.

How should the typical SR paradoxes (train+tunnel, twins, etc.) be used?

IMHO they shouldn't be used at all. The goal should
be to get everybody to the point where they cannot even
/state/ a paradox of that sort, because the statement
so obviously depends on mis-stating the basic laws of

More generally, I am appalled by the /attitude/ that
suggests relativity is paradoxical. I don't consider
SR paradoxical, or even weird. The basic principle of
relativity is not weird at all; it has been around
since 1632, which is ten years before Newton was born.
As for special relativity, it is just the geometry and
trigonometry of spacetime. The timelike dimension is
not exactly the same as the others, but it is more
similar than most people realize. It is as similar
as it possibly could be without being identical.

Mostly special relativity provides us with a /unified/
view of stuff that we already knew, prosaic non-weird
stuff like
-- space and time;
-- mass, momentum, and kinetic energy;
-- electricity and magnetism;
-- boosts and rotations;
-- et cetera.

Some teachers have admit that they enjoy emphasizing
the weirdness of special relativity because it makes
them seem like tough guys: "Hey, I'm so smart that I
can say all kinds of weird and paradoxical things."
IMHO that's a sign of pathological insecurity. Those
guys need to find more appropriate sources of self-
esteem. There's a difference between attracting
attention and attracting /favorable/ attention. My
advice: Do a good job with the teaching, and you'll
get all the esteem and all the attention you could
possibly want.

I know of hundreds of "paradoxes" at the level of basic
mechanics ... but I would never use them to introduce
the subject.

Example: When I was about 12 years old, my father
asked me the following question. He didn't know the
answer; he was genuinely mystified:

Suppose I throw a piece of chewing gum in the
west-to-east direction. It hits a brick wall.
It comes to a sudden stop (in the lab frame) and
sticks. The kinetic energy of the gum is converted
to thermal energy, leaving the gum slightly warmer.
Now repeat the analysis, using a nonrotating frame
comoving with the /center/ of the earth, not the
surface of the earth. At the equator, the brick
wall is moving 1000 miles per hour. In this frame,
the change in KE is vastly larger, more than enough
to boil the water in the chewing gum.

There's another version where I'm inside an airliner,
flying at mach 0.85. I throw the gum toward the front.
It hits the front bulkhead, stops, and sticks. Analyze
it in the frame of the aircraft, and again in the
frame of the ambient airmass.

It took me several years to figure out what's wrong
with the statement of the problem.


Just to maintain some balance here:

1) There are /some/ misconceptions that are so prevalent
and so pernicious that they must be confronted at the
first opportunity. The classic example is a washed-out
bridge. People would normally assume that the bridge is
OK, and would be in grave peril, so we put up barricades
and signs and flashing lights.

This however remains the exception, not the rule. In
physics, most so-called "paradoxes" involve questions
that (a) students would never ask on their own, and
(b) are not life-threatening. So we don't need to
confront them, not until we are good and ready.

2) As I said yesterday, different games are played by
different rules. The master class is different from
the introductory class.

Skilled physicists can have a lot of fun puzzling over
perpetual motion machines and other clever paradoxes.
However, what's fun for us is not necessarily fun for
students. If you take a bunch of non-experts and ask
them to think about a so-called "paradox", usually
all you get is a pile of self-contradictory nonsense.
For example:


A paradox, by definition, is an example of /misguided/
inquiry. The statement of the paradox leads people to
think about the problem the wrong way.

Wikipedia is representative of the community. The fact
that the community /as a whole/ cannot handle something
as simple as the Faraday "paradox" tells me that the
educational system needs to do a better job. I'm not
even worried about the physics, because not everybody
needs to understand electromagnetism. The point is,
everybody needs to know how to cope with ill-posed

Where are they supposed to learn that? In English
class? In math class? Sometimes I think there is more
strategic thinking taught in PE class than anywhere else.
Especially at the advanced levels, this includes dreaming
up trick plays, and preparing for the whole range of things
the opponents might try. OTOH they've been cutting way
back on PE, so what's left? Gaaaaack!