The Process Heuristic is a bundle of problem solving ideas based upon the following scheme:
Look on the situation as a change from initial state A to final state B.
Invent some fictitious state C, for which changes from A to C
and from C to B can both be easily found.
In a "Process" analysis of the Dragon Milko. where one perceives this Dragon as
involving a transformation
State Aâ State B
where
State A: Homogenous milk in milk bottle. with base pressure p[A] = p
State B: Stratified milk in milk bottle. with base pressure p[B] = p'
One can't compute the alteration in base pressure - - i.e., p[A] - p[B] = p - p' directly - - after all, this is the problem of this Dragon. Yet if the neck of the milk bottle was rubber, or was hinged somehow, and the bottle transformed into a cylinder it would be easy, in fact trivial, to compute the base pressure change after stratification by reference to the states:
State X: Homogenous milk in cylinder with base pressure p[X]
State Y: Stratified milk in cylinder with base pressure p[Y]
In a cylinder the only vertical forces acting on the fluid contents (of total weight W) are gravity and the base pressure acting over the area A, so that as X â Y
p[X] = p[Y]
In detail, both pressures are equal to W/A.
The additional base pressure in State A compared to State X is due to an additional height D of milk so that under the transformation
Aâ X : p[A] - p[X] = p - W/A = Dg*density(milk)
Likewise
Y â B : p[Y] - p[B] = W/A - p' = Dg*density(cream)
Hence
p - p' = p[A] - p[B] = Dg*{density(milk) - density(cream)}
which is positive as cream density = density(cream) is less than the density(milk).
This "Process" argument is illustrated in the diagram:
p
p - D
p - D
p - D + d
Looking at this diagram -- one realises that one doesn't need to do any mathematics at all, to deduce that the pressure decreases.
At the first step, A â X, the height of milk drops, so that pressure decreases a lot, from p to p - D
Going from State X to Y, X â Y, the base pressure is not altered.
But at the final step, Y â B, there is a increase in pressure, as cream is pushed up --
of amount d,
but d < D
since cream is light.
So one deduces that the final pressure is
p - D + d less than the initial.
The discussion above is deliberately stylised. Its worth reading the transcript of the interview
where I first recorded a Process attack on Milko, which is included,
along with some related transcrips,
under the heading
"The Milk Game"
For other ways to snare Milko,
and for related pages, link to: