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*From*: Derek Padilla <derekpadilla@gmail.com>*Date*: Mon, 2 Jun 2014 10:01:48 -0700

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

Are they pedagogically different than the Faraday paradox?

It seems only in that they are presented along with the new tools required

to resolve the paradoxes while the Faraday paradox would perhaps be

presented within classical EM leaving the student without the context or

tools to properly (simply?) resolve the issue.

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.

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.

This drives home the fact that they are already comfortable with the

concept of a "system" that is defined based on our choice of where to draw

the boundary; problems can sometimes be analyzed differently based on

different choices for the system -- a point students can easily get tangled

up in when first learning thermo.

Perhaps the problem is with the word "paradox." Instead, it may make more

sent to present the situation as "This happens," and ask the students to

explain how it happens. It seems paradoxes are only paradoxes when

presented along with an improper way of thinking about the problem.

Or, maybe that is, itself, a learning tool. 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 (or be able recognize

that it was wrong in the first place).

All fun things to think about!

Derek

On Sat, May 31, 2014 at 4:19 PM, John Denker <jsd@av8n.com> wrote:

Hi Folks --

The question for today is how and when to teach people

to handle ill-posed problems in general, and paradoxes

in particular.

I like to say that physics isn't hard. We do problems

because they are important, not because they are hard.

Sometimes we do things that /would have been hard/ if

you didn't know the tricks ... which is why it is worth

learning the tricks.

Also: Different games are played by different rules.

You don't play baseball by football rules or vice versa.

In teaching, the introduction to a subject is different

from mastery of the subject.

In an introductory situation, it is best to emphasize

correct ideas. Later on it becomes appropriate to delve

into ill-posed questions and paradoxes.

Usually on this list we look at topics that arise in

introductory situations, topics that arise on the first

turn around the spiral. That's fine as a starting point,

but it's not enough. Where you start out is not where

you want to end up.

At some point, people need to learn to handle ill-posed

problems. In the real world, most decent jobs involve

lots of problem-solving. Unless your job consists of

asking "would you like fries with that", most of the

problems are ill-posed. Otherwise they would have been

solved long ago.

Problem-solving skills can be used for lots of things,

not just physics. However, all too often, the physics

teacher gets stuck teaching remedial problem-solving,

along with remedial math and everything else.

Suggestion: Start with Fermi problems that do not

require very much physics domain knowledge, e.g.

-- how many hairs on your head?

-- how much water in the Atlantic ocean?

Another suggestion: Start with underspecified problems

(such as the examples above). Later move on to wrongly

specified problems (as we now discuss).

If you want to see what it looks like when things go

horribly wrong, look at the Wikipedia article on the

"Faraday paradox"

https://en.wikipedia.org/wiki/Faraday_paradox

The only part of the article that makes sense to me

is the banner at the top that points out that the

rest of the article is incomprehensible and self-

contradictory. I find it encouraging that somebody

noticed the problem. OTOH I find it discouraging that

AFAICT nobody bothered to write a clear, correct, modern

explanation.

I cobbled together a few words and diagrams here:

http://www.av8n.com/physics/faraday-puzzle.htm

There is practically zero overlap between my explanation

and the wikipedia article.

I put the Faraday rotor squarely in the category of

problems that /would have been hard/ if you didn't

know the tricks. Michael Faraday couldn't figure it

out. James Clerk Maxwell couldn't figure it out.

In general, a frontal assault on this problem using

19th-century techniques is going to be a disaster.

So don't do that.

On the other hand, this does /not/ mean this is a

hard problem. It is a would-be-hard problem. It

would be hard if you tried to do it without the

proper tools.

MF and JCM died long before there was any such thing

as vectors, long before there was any such thing as

spacetime, and long before there was a Drude model.

This gets back to the pedagogical question: How should

we teach people to deal with problems like this? I don't

have all the answers, but here are some ideas, to get the

discussion started: IMHO it does not make sense to assign

this problem to naïve students. We can talk about guided

inquiry, with the emphasis on guidance, but if you start

with this problem, AFAICT there is not much guidance you

can give, short of giving away the answer, which defeats

the purpose. Therefore it seems to me that good guidance

requires teaching people to recognize when they are in

over their head. They should put problems like this on

the back burner. Do not attempt a frontal attack on this

problem using 19th-century techniques. Wait until you

have a deeper understanding of the physics, whereupon

this problem becomes a gazillion times easier.

Also, good guidance means starting out with a succession

of easier problems, rather than tossing non-swimmers into

the deep end of the pool.

At some point people need to learn to survive with less

guidance, and indeed to survive a certain amount of

wrong guidance. Sometimes it is important to /not/ follow

directions. If the question is whether the magnetic field

lines rotate along with the magnet, the only reasonable

way to proceed starts by pointing out that magnetic field

lines don't actually exist.

This is the skill that a lot of otherwise-smart people

seem to lack. Even though they nominally have all the

tools needed to solve this problem, if it is presented

to them as a paradox they take the bait and start thinking

about it in all the wrong ways. They get wrapped around

the axle. They have a hard time disengaging from the

wrong approach. They misapply some tools, and leave

other tools completely unapplied.

I guess this gets back to the connectionist theory of

learning. It doesn't matter whether you nominally

"learned" something. What matters is whether you can

recall it when needed. This requires hard work in

advance. By the time you need to recall it, it's

(mostly) too late. It doesn't matter how much you

currently "want" to recall it. What matters is how

hard you thought about it in previous weeks and months

and years, figuring out what it's good for, figuring

out what it's connected to. This is not a new theory.

William James was big on this, back in the 1890s.

More generally, there are lots of people running around

trying to figure out how to teach students to handle

FCI problems. That's fine as far as it goes, but it

doesn't go nearly far enough. At some point we need

to figure out how to teach people to handle problems

that are orders of magnitude harder than FCI problems.

Surely the folks on this list have thought about this.

Any suggestions? Anecdotes?

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**Follow-Ups**:**Re: [Phys-L] Faraday paradox +- pedagogy +- critical thinking***From:*John Denker <jsd@av8n.com>

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