rocketdodger
Philosopher
- Joined
- Jun 22, 2005
- Messages
- 6,946
I'm afraid you're misusing the word "isomorphic" here. Isomorphism is something that applies to algebraic structures. The contents of a hard drive is not an algebraic structure, it's simply a natural number, X.
If you meant to ask, "will there be anything else that represents the number X in some encoded form", the answer is, of course. Everything represents the number X in some encoded form. It's just a question of choosing a proper decoding function.
No, that is not quite the whole story. Thats why in my OP I was careful to stipulate "isomorphic under the same set of rules."
So for example, there are a number of rules stipulating how the data is organized on your hard drive. Lets just forget about everything else and suppose it is a string of binary digits. Suppose further that the distinction between the digits are location on the disc, and the value of each digit is represented by the polarity of a magnetic field measured from some location relative to each digit, say the center.
Now, it is quite clear how a finite number can be represented on this substrate given this set of rules -- if the field in a location is closer to one polarity than the other, that location is attributed either a 1 or 0.
Could we do the same with any old system? Not really, because the structure of most systems is not amenable to this set of rules. Where is the distinction between bits in a glass of water, for instance? Or the physical properties that correspond to value?
And given that P1 is that consciousness is information processing, or flow, the complexity of any isomorphism increases exponentially, because it is no longer just a static arrangement that must be accounted for but a dynamic system where each informational component has direction.