[FOM] The boundary of objective mathematics

[Steve Stevenson]

On Mar 24, 2009, at 5:16 PM, Steven Ericsson-Zenith wrote:
>
> .... Ultimately the fundamental questions here relate to a deeper  
> consideration of our apprehension of the world as it applies in both  
> these cases (mathematical and physical)....

The "scientific method" now recognizes "modeling and simulation" as a  
third leg. The reliance on models and simulations to conduct science  
leads to and 'mathematical' and 'physical' problems discussed in  
Steven's note. The process for dealing with these problems is called  
verification and validation (V&V). This might be interesting to FOM  
members because many "theorems" are only "approximately true"  
computational. How much can we rely on these "facts" and how much can  
the scientist rely on computation in judging the veracity of models?
	* (Verification) Models set logical conditions for the simulations.  
Did the simulation get constructed correctly?
	* (Validation) Models predict the observable world. Does the model  
presented so represent the 'real world'?
Validation is, for all intents and purposes, a judgment/decision  
problem about the models and establishes the ontology of the model.  
Science in the modeling and validation world claim-evidence-inference- 
warrant and at best 'just' a statistics problem.

Steve
--------
D. E. Stevenson, Department of Computer Science
Director, Institute for Modeling and Simulation Applications
Clemson University, Clemson, SC 29634-0974