At 12:07 PM 6/24/00 -0500, Charley Myles wrote:
> What has happened to the PHYS in PHYS-L?
OK, here's widely-known little riddle that contains real physics and is
tangentially related to the recent "coffee" thread.
Suppose you have a cup of coffee and a cup of tea. In step 1, you transfer
one spoonful of liquid from the coffee-cup to the tea-cup. In step 2, you
transfer one spoonful of liquid from the tea-cup back to the
coffee-cup. Question: Is there more tea in the coffee, or more coffee in
the tea?
I know of several ways of analyzing this problem, some of which lead to the
right answer, and some of which don't. I my experience, there are quite a
few kids at the high-school level who
-- are strongly attracted to the wrong analysis,
-- are not convinced by the correct qualitative argument, and
-- are not even convinced by a detailed mathematical analysis.
So the questions for today are
*) Why do people have a hard time with this riddle?
*) What can be learned from this family of mistakes?
*) In what other circumstances might people be tempted to
make similar mistakes? What are the warning signs?