[Equivalence in theory more than practice] - A New Kind of Science: The NKS Forum

A New Kind of Science: The NKS Forum

Pages:1


Equivalence in theory more than practice

(Click here to view the original thread with full colors/images)


Posted by: Tony Smith

There is a strong methodological point in NKS and the Principle of Computational Equivalence (PCE) that many seem to be missing, which, if it were more widely recognised, might save a lot of talking at cross purposes.

We need to ask ourselves why Wolfram has gone to such lengths to describe so many clearly distinct kinds of simple programs if they are all computationally equivalent. Certainly there are some chains of dependency in his argument for computational equivalence, but it also seems clear that he has used appropriate practical tasks to showcase each kind, tasks which in practice one particular kind may be much better suited to than are others.

Yes, there are demonstrations that some tasks can be handled by more than one kind, and that is important to his case for the PCE. But it seems even more important to demonstrate the range of results that can be achived in practice across all those kinds and then rely on the PCE to make the case that each result can at least in theory be achived by any non trivial simple program.

Yet many seem to be reading NKS as claiming that CAs are all they should ever need to consider. While the PCE may suggest that in theory any of the examples shown in NKS could be achived by a CA, I see NKS making a strong case that in practice you should choose the most suitable simple program for the particular task.

If CAs are special, it is because they are relatively gentle on human perception processes, and easy to implement on computers, rather than because they are well suited to modeling real world tasks. The one thing they are particularly good for, and the reason they get the lead role in NKS, is because they provide accessible demonstrations of basic principles of the world of simple programs. We should not demand more of CAs than that.




Forum Sponsored by Wolfram Research

© 2004-2008 Wolfram Research, Inc. | Powered by vBulletin 2.3.0 © 2000-2002 Jelsoft Enterprises, Ltd. | Disclaimer
vB Easy Archive Final - Created by Xenon and modified/released by SkuZZy from the Job Openings