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 the
equivalent notion according to your chosen system). let us call
those 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 the
equality 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 both
In phi_u(B(x,y)) = phi_x(y), x is called the program, and y the
data. 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 the
functions and what bijection is used?
Any number. I am not sure, the enumeration has to be given by an
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
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
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