🚀 go-pugleaf

In article <1992Nov16.065208.28725@murdoch.acc.Virginia.EDU>, crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass) writes...
>>
>>As one simple example consider the difference between a model based on
>>finite difference equations and one based on partial differential
>>equations. 
> 
>    Name a physical system in which the FDE is considered more fundamental
>    than the PDE?  For most of us, we take the 'true' PDE and muck it
>    up, introducing loads of spurious conservation laws and higher
>    order terms, by deriving a finite difference formulation of it. 
>    I'd be interested in a system in which we did the reverse.

How about your favorite and mine - the flexible string.  Since the string
is really atomic at the smallest scale, the "most" appropriate equation
is the FDE.  It is only in the approximation that the discrete nature of the
string is irrelevant (a damn good approximation, I admit) that the PDE
becomes a useful description.  

In older textbooks, like Morse and Feshbach, they put more of an emphasis
on these distinctions than modern books do, which tend to be more abstract. 
M&F go to some length to emphasize that the PDE's are not the "true"
models of many systems.  They make a clear distinction between physical
systems which are inseparable from their description in terms of fields
(i.e., PDE's), such as electromagnetic fields, and systems for which 
the fields *are* separable from the physical system, such as the string,
where it is really the finite number atomic positions which are fundamental,
the field being a useful characterization but not one that is intrinsic
to the system, which is properly a discrete system.

-Scott
--------------------
Scott I. Chase			"It is not a simple life to be a single cell,
SICHASE@CSA2.LBL.GOV		 although I have no right to say so, having
				 been a single cell so long ago myself that I 
				 have no memory at all of that stage of my 
				 life." - Lewis Thomas