Shane wrote:
> 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.

Well, I think that's an interesting value judgment!

Basically, the question is whether physical or mathematical reality is more
fundamental.

Your vote is with  mathematical reality.  Not surprising ;-)

> I don't really mind you calling the latter "fundamental" so long
> as I know what you mean.

yeah, we understand each other OK

It's that Wang dude I'm worried about  ;-)

-- Ben

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