Re: [Phys-l] tutorial on scaling laws

[Ludwik Kowalski <kowalskil@mail.montclair.edu>]

On Jul 26, 2007, at 4:21 PM, John Denker wrote:

> I recently put together a tutorial on scaling laws:
>   http://www.av8n.com/physics/scaling.htm
>
> Comments and suggestions are always welcome.  Since this is still a 
> work in
> progress, now is a particularly timely time for comments.

1) Not only volume but anything proportional to volume, for example 
mass, scales cubically with distance.
2) On the other hand it is possible to think of a situation in which 
the mass of an object remains constant when its volume changes. In such 
case mass does not scale cubically with a linear dimension.
3) This observation makes me think that the concept of volume is 
somehow closer to the concept of distance than the concept of mass is. 
Yes, I know that the  idea of "closer" is not applicable because it 
implies distance in space populated with ideas rather than with 
material objects.
4) Does it make sense to discuss a space populated with ideas? I think 
so. That what we do when pedagogical issues are debated. Ideas form 
sequences in which some concepts are pedagogically closer to each other 
than other. A line of ideas? A surface of ideas? A volume of ideas? A 
space of ideas? Spiral pedagogy? Volume of knowledge?
5) Hmm, I was not thinking about all this when John's  essay prompted 
me compose the first sentence. The rest is instant improvisation.
_______________________________________________________
Ludwik Kowalski, a retired physicist
5 Horizon Road, apt. 2702, Fort Lee, NJ, 07024, USA
Also an amateur journalist at http://csam.montclair.edu/~kowalski/cf/