Re: [Phys-L] proportional reasoning, scaling laws, et cetera

[John Denker <jsd@av8n.com>]

On 05/16/2012 01:17 PM, Robert Cohen wrote:
> In fact, one analogy I use is one of trying to find your way to a
> particular destination.  You are faced with two choices: memorize
> each individual route or learn how to read a map.  I then make the
> analogy that in physics we are learning to use the same map over and
> over again to reach lots of different destinations.
>
> Unfortunately, I'm not so sure it is making the point as well as I
> had hoped.

We agree that this "marketing" issue is important.  I don't
know any perfect solutions.

We agree that the "map" example is the right general idea 
but has some imperfections.  The obvious weakness is that the
penalty for driving a sub-optimal route is usually rather small.


Here are a couple other imperfect possibilities to consider:

  a) The game of "Clue".  Maybe the butler did it in the library
   with the candlestick ,,, or may another of the 342 possibilities.
   If you try to eliminate the possibilities one by one, you will
   lose the game for sure ... so a deductive approach is mandatory.
   There are combinatorially many possibilities.

   One disadvantage is that it's only a game, not a life-critical
   real-world situation.  Also, 342 is not an overwhelmingly large 
   number.  OTOH students should be able to take a leap and /imagine/
   similar real-world situations with even more factors (and vastly 
   more possibilities).

   Note that supposedly-scientific "crime scene investigation" is 
   part of popular culture nowadays.

   Chess, checkers, go, and many other board games offer examples
   of rather few principles leading to combinatorially many cases.


  b) As a flight instructor, I have it easy.  Imagine trying to
   land an airplane.  Factors include:
      -- X position
      -- Y position
      -- Z position
      -- X momentum
      -- Y momentum
      -- Z momentum
      -- yaw orientation
      -- pitch orientation
      -- roll orientation
      -- yaw-wise momentum
      -- pitch-wise momentum
      -- roll-wise momentum
      -- headwind
      -- crosswind
      -- gusty wind
      -- updrafts and downdrafts
      -- flaps configuration
      -- landing gear configuration
      -- other configuration variables
      -- throttle setting
      -- density altitude
      -- runway width
      -- runway length
      -- runway markings or lack thereof
      -- day or night
      -- conflicting traffic
      -- air traffic control instructions
      ++ et cetera

   Multiplying all those together gives us millions upon millions of
   possibilities.  Do you really think you are going to see the same 
   situation twice?  Do you really think you are going see all the
   relevant situations during training so you can learn them by rote, 
   one by one?  I don't think so.

   Taking care of 30 different things is hard enough ... but if you
   factor things properly and take a principled approach, it's only 
   30 principles, not 2^30 separate cases.

   The obvious limitation of this "marketing scheme" is that it does
   not work nearly so well in the physics classroom.  Some students 
   will just decide that they are never going to be called upon to 
   land an airplane, and tune out at that point.

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

There have *got* to be better examples.  Suggestions, anyone?