Bruno Marchal wrote:Any potentially largest finite number n that I could name could be incremented by 1 so this finite number could not be the largest. The trick is not to name a particular number but to specify a method to reach the unreachable.Now I think I should train you with diagonalization. I give you an exercise: write a program which, if executed, will stop on the biggest possible natural number. Fairy tale version: you meet a fairy who propose you a wish. You ask to be immortal but the fairy replies that she has only finite power. So she can make you living as long as you wish, but she asks precisely how long. It is up too you to describe precisely how long you want to live by writing a program naming that big (but finite) number. You have a limited amount of paper to write your answer, but the fairy is kind enough to give you a little more if you ask. You can ask the question to very little children. The cutest answer I got was "7 + 7 + 7 + 7 + 7" (by a six year old). Why seven? It was the age of his elder brother! Method 1) Use the fairy power against her. She says she has "finite power". Ask for precisely the largest number of days she can provide with her "finite power." This method is similar to the robber's response when the victim asks him "how much money do you want?": "All the money in your pocket." Method 2) Use the concept of "limits" Ask for as many days it would take to obtain a sum of 2 as terms in the series 1+1/2 + 1/4 + 1/8 + 1/16..... If the fairies knows any math she may argue that the series never reaches 2. On the other hand I may argue that "in the limit" it does reach 2. Method 3) Come up with a unprovably non-halting problem: For
example ask for as many days as required digits in PI to prove that PI
has a single repetition of a form such that digits 1 to n match
digits n+1 to 2n. For example 2^0.5 = 1.4142135... has a single
repetition (1 4 match 1 4) in which digits 1 to 2 match digits 3 to 4.
Similarly 79^0.5=8.8881944 and 147^0.5= 12.12435565. Note that the
repetition must include all numbers 1 to n from the beginning and match
all number n+1 to 2n The problem with this approach is I don't know for
sure if PI is repeatable or non-repeatable (according to above
requirements.) I don't even know if this problem is unprovable. All I
know is that the probability for any irrational to have a single repeat
is about 0.1111. For PI the probability is much lower since I already
know PI to a large number of digits and as far as I can see it does not
repeat. However, with this approach I could be taking chances.Diagonalization clearly allows you to specify a number outside any given set of number, but I have not been able to weave it into this argument. George --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~--- |

- Re: Smullyan Shmullyan, give me a real example George Levy
- Re: Smullyan Shmullyan, give me a real example Bruno Marchal
- Re: Smullyan Shmullyan, give me a real example "Hal Finney"
- Re: Smullyan Shmullyan, give me a real exa... Bruno Marchal

- Re: Smullyan Shmullyan, give me a real example Tom Caylor
- Re: Smullyan Shmullyan, give me a real exa... Tom Caylor
- Re: Smullyan Shmullyan, give me a real exa... Bruno Marchal
- Re: Smullyan Shmullyan, give me a real... Tom Caylor
- Re: Smullyan Shmullyan, give me a ... Bruno Marchal

- Re: Smullyan Shmullyan, give me a real... George Levy
- Re: Smullyan Shmullyan, give me a ... Bruno Marchal