[Phys-L] show the work +- movies +- conservation

[John Denker <jsd@av8n.com>]

On 01/29/2014 03:57 PM, Jeffrey Schnick wrote:

> Thanks John.  

:-)

> I want to be sold on the momentum flow method so I am
> trying to see what the advantage of it is.  The short version of the
> force method would be, "add the mass of a table-tennis ball to the
> left (the internal forces don't matter) and push down hard on the
> right--the right goes down."  I got the impression that a short movie
> with little down arrows flowing into and out of the beakers flashed
> into your mind and you immediately saw the little down arrows flowing
> into the beaker on the right faster.  I wanted to see that movie.

I'd like to see the movie, too ... but I've never seen it.  
Maybe some day I can make the movie, but the movie does not
make itself.

Here's a better metaphor for how the thought process
actually looks:  It's more like "ask the audience" on 
the millionaire show, but without the clickers;  it's 
just hundreds of people shouting.  About 600 people 
come up with the answer.  About 100 of them come up 
with a particular reason.  Another 75 come up with 
the same answer for a different reason.  Another 50 
come up with yet another reason.  And so on.

Movies are sequential.  Real human thought is not.  I don't 
get to watch those 600 guys in sequence.  All I get is 600 
guys waving their hands and shouting, all in parallel.

That's how I know the answer to the buoyancy problem.  Now, 
if you want me to /explain/ the answer, if you want me to 
show the work, that's a whole nother story.  It's a big 
archaeological dig, trying to find pieces of the story.
It's a big editing project, trying to serialize a bunch 
of snippets that didn't happen serially.  This is utterly 
nontrivial, because the various snippets are related to 
each other in nonlinear ways:  Idea A reinforces idea B 
and vice versa, so there's no obvious basis for deciding 
Who's on first.

A formal, logical proof is sequential.  Anybody who thinks
that real human thought is sequential is seriously deluded.
Especially when it comes to problem-solving or anything that
is the least bit creative.

Let's be clear:  If you ask me to show the work, the work
that I show is not the work that I originally did.  The
Way that can be spoken of is not the true Way.  The Name
that can be named is not the eternal Name.

When I'm writing a web page, the first step is to just
barf out the ideas, to get them on paper, without regard
to "logical" order.  Then I typically restructure it ten 
times before I push it to the web site for the first time.
Even then a lot of nonlinearity remains, in the form of 
hyperlinks to earlier as well as later material.

This has immediate relevance for teaching and testing:  If
it takes X amount of time for students to simply answer the 
question, you need to budget at least 2X time if you want
them to show the work, which you should.  Ditto for managing 
real-world R&D projects:  Figure out how long it "should" 
take, then multiply by 3 or 4.

I know there are people on this list who say there is no
such thing as multitasking.  Well, as H.E. Fosdick was
fond of saying, person saying cannot be done is liable
to be interrupted by persons doing it.  Sometimes I
assign homework requiring people to learn to /juggle/.
Let's juggle as we walk down the corridor and have a
discussion.  /Very/ early in the process of learning to
juggle you have to consciously attend to what you're
doing, but later on you don't.  The miracle of learning
is that somehow we can tell our subconscious what to do.
I have only 0.01% of a clue as to how this works, but I
know it happens, and it is super-important.

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

Last but not least:  The real objective shouldn't be just
learning about the momentum-flow idea.  The real issue is 
conservation laws in general.  There are a lot of 'em:
 -- Energy is conserved.
 -- Momentum is conserved.  In any chosen basis, px, py, 
  and pz are each separately conserved.
 -- Electric charge is conserved.
 -- Lepton number is conserved.
 -- In chemical reactions, to an excellent approximation,
  there are approximately 92 separate conservation laws,
  one for each element.
 -- Continuity is not synonymous with conservation, but it
  is related.  Electrical current is not conserved, but it
  has a continuity property.
 -- Electric field lines have a continuity property.
 -- Magnetic field lines have an even stronger continuity 
  property.
 -- et cetera.

As the saying goes:  If you see a fish in a barrel, you
might as well shoot it.  In the game of hearts, if you
get dealt nothing but the highest cards, you might as
well shoot the moon.

By that I mean, if you see a problem that is begging to
be solved by appeal to a conservation law, you might as
well solve it that way.

My father taught me about conservation of energy when I
was about 5 years old, and conservation of electric charge
not much later.  I just can't look at a problem without
seeing it in those terms.  It would be like looking at a
hand of cards and not noticing four aces.