Hi Ben,
In short yes, I am using the term in this conventional way.If two computational models can solve radically different problems *under realistic space and time constraints*, then are they "fundamentally different" or not??You seem to want call two models "fundamentally the same" if they can solve the same problems under infinite time and space constraints.
Two systems are fundamentally equivalent if it's possible for them to
simulate each other given any finite amount of resources. They are
fundamentally different if this is impossible no matter how much
resource is made available. Clearly this is a very deep and
fundamental difference between two classes of systems as they can
never be equivalent in either theory or practice.
A finer distinction is the one you raise: can two systems ever be
equivalent given only realistic resources?
Clearly the former concept is more fundamental than the second one
as the former is an absolute while the latter is a more refined
matter of degree. Though it's probably going to be the latter
concept that is more useful in many situations.
I don't really mind you calling the latter "fundamental" so long
as I know what you mean.
Cheers
Shane
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