On 01 Nov 2012, at 06:19, meekerdb wrote:

On 10/31/2012 6:58 PM, Stephen P. King wrote: (actually it was Bruno)Enumerate the programs computing functions fro N to N, (or theequivalent notion according to your chosen system). let us callthose functions: phi_0, phi_1, phi_2, ... (the phi_i)Let B be a fixed bijection from N x N to N. So B(x,y) is a number.The number u is universal if phi_u(B(x,y)) = phi_x(y). And theequality means really that either both phi_u(B(x,y)) and phi_x(y)are defined (number) and that they are equal, OR they are bothundefined.In phi_u(B(x,y)) = phi_x(y), x is called the program, and y thedata. u is the computer. u i said to emulate the program(machine, ...) x on the input y.So u could be any number, depending on how you enumerated thefunctions and what bijection is used?

`Any number. I am not sure, the enumeration has to be given by an`

`algorithm.`

`But yes, the notion of computation, universality, etc. are intensional`

`notion, and makes sense only relatively to the other number. That is`

`why a often add "relative" before number.`

`This should be obvious. The doctor who scan your brain will also have`

`some flexibility in the encoding of your current local and relative`

`state.`

I doubt it can encode it with the number 4, though.

`You might say, that 4 is for the fourth compact disk on the shell`

`doctor, but then 4 is no more an encoding, but only a pointer to an`

`encoding.`

Bruno http://iridia.ulb.ac.be/~marchal/ -- 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 everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.