Re: Why assume?

[paul o johnson <pojhome@FLASH.NET>]

> Don -- I have learned more from your messages than
> from most others on this list, but sometimes you leave me scratching my
> head.

> You stated: "Maybe we ought more often to question
> those assumptions, not to make a huge deal about it, but just to remind
> ourselves, and students, that such assumptions, if taken seriously, could
> lead to absurd results. Other such assumptions:
> Frictionless surfaces and bearings.
> Rigid (incompressible) bodies. Leads to absurdities when you examine
> a collision in detail.
> Thin lenses, and their equation."
It has always been clear to me that these are not assumptions but are descriptions
of admittedly ideal situations, never to be realized in the real world.
We employ such ideal situations because we're not smart enough to explain
the messier real-world situations.

Then you said:

"There are other questions which stump some teachers:

Why does warm air rise, rather than hotter molecules simply diffusing
outward and, through collisions, transmitting energy to other molecules
outward from a hot object in all directions equally? I.e., why do more
of the faster molecules choose to move upward, and more of the slower ones
choose to move downward. A kinetic model answer is wanted. To simply say
"Warm air is less dense and therefore rises because of Archimedes
principle" is evading the question. Details, please."

Of course the hotter molecules diffuse outward and transfer energy. And
they do it in all directions, not just upward. Neither do the colder molecules
move preferentially downward.

How is it evading the question to state, with Archimedes, that it is not individual molecules but the (ill-defined) region of hotter air, consisting of gazillions of molecules, that is buoyed upward because it is displacing an equal volume of air consisting of even more but colder molecules?

What am I missing?

poj