Re: [Phys-l] analogies

[John Denker <jsd@av8n.com>]

On 11/30/2007 02:02 PM, Dan MacIsaac wrote:

> Actually, I think we only learn new concepts by approximate
> similarities or analogy.  

Agreed.

> I think a perfect analogy would be a
> tautology, and I see NO pedagogical power in tautology;
> therefore learning by analogy may be inescapable :^)

That's an interesting point.  I'm not sure I've ever heard
it made quite so pointedly.

RPF wasn't shy about using analogies.  He even had an analogy
for knowledge itself.  He said it was like a grand tapestry,
and if you didn't know something, it was like a hole in the
tapestry.  He emphasized that there were always multiple
ways of figuring something out:  You could repair the hole 
by weaving your way down from the top, or up from the bottom, 
or in from the sides.

My twist on this idea is that more often than not, you wind
up weaving your way in vertically *and* horizontally.  I even
have a picture of this:

The goal is to explain the idea of a _blue triangle_ to 
someone who has never seen one.  We do that by calling 
attention to the space in the middle of this figure:
  http://www.av8n.com/physics/img48/blue-triangle.png

You can see there is a big role for imperfect analogies.

The middle is where the blue triangle lives.  It is not
perfectly analogous to the other blue things, and it is
not perfectly analogous to the other triangular things,
but if you weave multiple analogies together you can 
create quite a strong fabric.

> Getting excited about the fact that analogies aren't identical
> seems a waste of time to me. Knowing the domain and range of
> analogies, where they work and where they do not seems
> to the the important idea.

Yes indeed.