Re: physics/pedagogy of coffee-mixing

[Tim Folkerts <tfolkert@FHSU.EDU>]

> 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)


I didn't quite follow the first time, and this didn't really clear it up.

I think your example is as follows:

Cup 1                       Cup 2
Red    Black             Red    Black
1000   0                 0      1000
         Transfer "a spoonful" = 500 red balls from 1 to 2
500    0                 500    1000
         Transfer "a spoonful" = 1 ball (happens to be red) from 2 to 1
501    0                 499    1000


I guess to me it was implied clearly that "a spoonful" was meant to me a
definite measure.  Perhaps part of that is that I've seen this problem
before and then is was stated as a specific amount, e.g 10 cc.

Do we agree that if "a spoonful" is a definite measure, then the amounts
must be equal.  Or perhaps more specifically, if the "spoonfuls" are the
same to within experimental resolution, then the concentrations will be the
same to within experimental resolution.  Clearly if different amounts are
transferred, then different concentrations will result.

Or is there some other point I am missing?


Tim Folkerts