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Re: what is understanding?



Hi!
Since this thread seems still alive and active, let me add my
2 cts. worth opinion. This particularly addresses Leigh's very
accurate observation that "understanding" can happen at different
levels and can mean different things. Here is my opinion:
The basic question is to distinguish "knowlkedge" - basically memo-
rization - from this less tangible (but very important)"understanding".
To know the names of kings and queens, of battles and their dates, is
obviously "memory". But to know, say, Kepler's laws of planetary
motion or Kirchhoff's law of circuits, involves much more: about
the solar system, about electricity and so on. Here some "understanding"
is essential.
In general and in physics in particular, whenever we learn
something new, we already know something "old". When students get
exposed to relativity, they should already know a lot of classical
physics and so on. When they learn about the Lorentz transformation,
they should of course memorize it, but the should also compare it
withe galilean counterpart. To recognize that for small beta both
give the practically same answers should be clear. It also should
become clear that for larger values of beta this changes. The difference
is investigated by the well known examples (dependence of the "time"
from the velocity of the observer, the shrinking of the length of an
object, etc. etc.). The "understanding" consists in precisely seeing
how the "new things" we learned fits into our previous, "old" knowledge.
There the degree of understanding depends crucially on all our "old"
knowledge. When this peripheral knowledge is expanded, our understanding n
deepens. The way a freshman understands the concept of force will be
different from a senior, after taking some good physics courses. And
this will be certainly different from a grad student going into the
defense of his/her dissertation.
Regards, Emilio