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
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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