Tom Caylor wrote: > OK. I noticed that you can get the Universal Machine (UM) to run for > ever even without the "+ 1". If I think of the program for G as a big > "case statement" with cases 1, 2, 3, to infinity, then the case for k > will contain the code for, or better yet a call to (hence the name > "recursive"?), Fk(k), but if we state by defining even G = Fn(n) (even > without the "+ 1") then this is equivalent to calling G(k)... But then > when we call G(k) we end up back in the "k case" again, calling G(k) > again,... forever. This will happen even if we add the "+ 1". > Personally I like this argument (running forever) better than the 0 = 1 > argument that somehow concludes that the UM will crash. A UM > "crashing" to me brings up pictures of physical machines that recognize > an unallowed operation, and then stop themselves. >
And on the surface, it seems that the "running forever because of self-reference" argument is better because you don't need the "+ 1". It seems that it isn't the "+ 1" that makes the UM run forever, and conversely the UM runs forever even without the contradiction of 0 = 1. Tom --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---
