On 21 Mar 2013, at 02:32, Stephen P. King wrote:

Are physical computers truly "universal Turing Machines"? No! They do not have infinite tape, not precise read/write heads. They are subject to noise and error.

The infinite tape is not part of the universal machine. A universal machine is a number u such that phi_u(x, y) = phi_x(y).

Please concentrate to the thought experiments, the sum will be taken on the memories of those who get the continuations, and the extensions.

When a löbian universal number run out of memory, he asks for more memory space or write on the wall of the cave, soon or later. And if it does not get it it dies, but from the 1p, it will find itself in a situation extending the memory (by just 1p indeterminacy).

Universal machines are finite entities. Physical Computer are particular case of Turing machine, and can emulate all other possible universal number, and the same is true for each of them. All universal machine can imitate all universal machines. But no universal machines can be universal for the notion of a belief, knowledge, observation, feeling, etc. In those matter, they can differ a lot.

But they are all finite, and their ability is measured by abstracting from the time and space (in the number theoretical or computer theoretical sense) needed to accomplish the task.

That they have no precise read/write components, makes them harder to recognize among the phi_i, but this is not a problem, given that we know that we already cannot know which machine we are, and form the first person point of view, we are supported by all the relevant machines and computations.

And they are all subject to noise and error, (that follows from arithmetic). Those noise and errors are their best allies to build more stable realities, I guess.



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