On Mon, Jun 20, 2016 at 6:14 AM, Peter Sas <[email protected]> wrote:
> Hi guys and girls, > > I have a question about the concept of the universal dovetailer. I > understand that the necessity to postulate the UD follows from the Halting > Problem (HP): since there are uncomputable functions from N to N, and since > because of the HP there is no algorithm for deciding which functions are > computable, we need a UD to dovetail all possible functions zigzag-style. > > Now my question is: Does this mean that the UD dovetails all possible > functions, including the uncomputable ones? > > Interesting question. I suppose it comes down to the meaning of all possible. There are logically impossible functions, such as those that output a proof that 7 is even. There is also the issue that there are more possible functions than there are descriptions of Turing computable functions. The UDA never happens upon either of these types of functions, which we might say are functions with non-existent descriptions (that can be mapped to the integers). https://en.wikipedia.org/wiki/Dovetailing_(computer_science) https://en.wikipedia.org/wiki/Computable_function#Uncomputable_functions_and_unsolvable_problems There is a chapter from Fabric of Reality which talks about this to some extent, but is framed in terms of possible experiences: https://books.google.com/books?id=Z7uFxViR19oC&pg=PT94&lpg=PT94&dq=fabric+of+reality+impossible+experience&source=bl&ots=s4plmFznD6&sig=5qFxx8hwf89QZvPN84ORSogN1JM&hl=en&sa=X&ved=0ahUKEwi_3cem6bbNAhUPDlIKHdDBD6cQ6AEIHDAA#v=onepage&q=fabric%20of%20reality%20impossible%20experience&f=false Jason -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
