Re: physics/pedagogy of coffee-mixing

[Stefan Jeglinski <jeglin@4PI.COM>]

> so the amount of tea in the first cup (t_1) is equal to the amount of
> coffee in the second cup (c_2).  No information about the transfer is
> needed.
>
> There must be a good way to show that in English, but I don't see it at
> the moment.

Perhaps this description: Say we instead poured the entire cup of
coffee into the tea and then poured half of it back into the empty
cup. By symmetry, we would expect there to be equal proportions of
coffee and tea in each cup (equal amounts in this specific case). It
is then reasonable to expect that a similar effect would occur for
smaller transfers, although this is still not obvious. Conservation
arguments are indeed powerful, but the problem is that to the 'common
man,' conservation arguments can be confusing and suspicious.

I think implicit in John's original questions about the pitfalls of
this sort of problem is something like "how do we communicate
approaches to this intriguing question and its solution to the
'common man?'" (ignoring the teaching of science students for now).

To be sure, concise statements in English that apparently "solve the
problem" are very powerful, but how many of us can create them except
for relatively simple concepts? Wasn't it one of the famous
physicists from early in the century who said something to the effect
of "you should know the answer before writing down the solution"? I
find this quite hard to do, but in the few times I have been able to
do it, I admit that I feel like I have gained great insight. And the
best teachers I've had have been successful to one degree or another
in doing the same.

When it comes to communicating science to the 'common man' though, I
believe this "power of English" is almost mandatory, which is why so
much of the public is ill-informed. That is, it is often easier for
us to resort to pencil and paper and light the mathematics rocket
engine. And instead of trying to follow along, the 'common man' would
much rather just get out of the flaming exhaust.


Stefan Jeglinski