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Caledonian2 comments on Beyond the Reach of God - Less Wrong
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1) Consciousness exists. 2) There are no known examples of 'infinite' mathematics in the universe. 3) It is therefore more reasonable to say that consciousness can be constructed with non-infinite mathematics than to postulate that it can't.
Disagree? Give us an example of a phenomenon that cannot be represented by a Turing Machine, and we'll talk.
I may hold a different belief but this is certainly a working hypothesis and one that should be explored to the fullest extent possible. That is I am not inclined to believe that we are Turing machines but I could be wrong on this as I do not know it to be the case. The hypothesis that we are Turing machines is one that should be explored as fully as possible. If we are not Turing machines then exploring the hypothesis that we are is worth pursuing as it will get us closer to understanding what it is we are.
Turing machines rely on a tape of infinite length at least in conception. I imagine the theory has been looked at with tapes of finite length?