Re: physics/pedagogy of coffee-mixing

[brian whatcott <inet@INTELLISYS.NET>]

At 16:32 6/25/00 -0500, you wrote:
> > ...
> > A numerical example again:
> > first cup 501 red balls,  second cup 499 red balls, 1000 black balls.
> > This represents two different mix ratios.

> 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


First Tim, I must ask you to excuse my disputative posts at times.
It is quite possibly the mischievous work of my evil twin brother.
 Your description would clearly satisfy most physicists subscribing
 to this list.   But I am being a little more critical than that.

 We can all agree that there is a case of division into two parts where
it is certain that the mixing ratios are identical: that is the case
where each portion is identical in terms of quantity of identifiable
component parts. However, there is no compelling reason why repeated
 interchanges of experimentally measured identical value should maintain
the two portions at experimentally measured identical sizes.

Given that in a real world lab, repeated interchanges of precisely measured
aliquots can give an increasing error term in the size of the dividends,
 it is an interesting observation (at least to me!) that the mixing ratios
of each part need not be identical.

 Now I would expect these ratios to be rather similar - tea and coffee
for example  are usually quite miscible - so that besides the mechanical
 mixing effect, there is a diffusion of the parts tending to homogenize
the contents.
   But what if I chose frothy coffee (is that 'spresso or latte?
I never remember which...) and suppose I arranged a decent density
differential between the liquids - I assert I could unbalance the mix
ratios, and keep them off balance. It is another facet of this malicious,
 or misdirective magician's ploy that I am referring to....

 The personal characteristic in question is an imaginative
deconstructionism - I understand the propensity can be a valuable aid in
planning high risk projects (where anything that could go wrong, often
 does go wrong), as well as seeing through magicians' tricks.

Does this help?

Sincerely


brian whatcott <inet@intellisys.net>
Altus OK