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Re: physics/pedagogy of coffee-mixing



At 16:00 6/25/00 -0400, you wrote:
...
....John is providing an amusing illustration of the dangers of using
simplifying assumptions, another favorite device of physicists....

And that is how I show that his incisive qualititative analysis is wrong.
...
my solution holds to an arbitrarily high degree of approximation, and the
more carefully you follow the directions the more accurately it holds.



Let's try again.

For any partition of quantities into two vessels other than exact halves,
John's solution is wrong.

A numerical example again:
first cup 501 red balls, second cup 499 red balls, 1000 black balls.
This represents two different mix ratios.

This is not exactly hard to see. How could it happen?
If the 'spoonful' quantities into the first cup turn out to contain fewer
balls than the spoonfuls into the second cup. (This is inevitable in
physical partitioning at the molecular level)



In Ludwik's model of discrete balls, my solution holds exactly.

I used Ludwik's ball model again to show the error in John's assertion.

Sincerely