[Computational Equivalence-Page 6] - A New Kind of Science: The NKS ForumA New Kind of Science: The NKS Forum
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Computational Equivalence-Page 6
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Posted by: Patrick A. Meuser
http://www.wolframscience.com/nksonline/page-6
Regarding computational equivalence, I see that there is no exception to the rule, rules must apply to the whole program and therefore must be completely traced in order to validate the rule.
In the context of NKS as read thus far, as an abstract framework this precludes exceptions, in other words a trace local to the exception is in some cases all that is required. Does the granularity of a rule truly apply to the whole program?
It is interesting to see that the level of abstraction implied by 'simple' programs is that there is no physical connection to the universe, only equivalence. This could not be farther from the truth!
In my research, I have found that the granularity of a computer program could be encoded within its physical operation as to state a connection in principle, of physical equivalence among words and wave functions, in other words a open sentential wave formula of free words that embody instructions within the wave function of their physical connection manifests a faster 'virtual' operation conserving the local ordering of more or less enegetic instructions through the connection, specific to all permutations of their operational occurence. Surely this concept of equivalence applies at a 'deeper' level than is described here.
To see my incomplete work of this principle: http://home.cogeco.ca/~pmeuser/dsinls.html
Best Regards
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