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 undefined.

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 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.



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