On 14 Mar 2012, at 17:30, meekerdb wrote:
On 3/14/2012 7:12 AM, Bruno Marchal wrote:
On 12 Mar 2012, at 21:21, meekerdb wrote (to Stepehen King):
Stephen King:
One thing that I have found in the last few days is that it is
impossible to define the computational operations of deleting,
copying and pasting onto/into topological manifolds unless one is
willing to give up the invariance of genus and Betti numbering.
Cutting and pasting seem to be absolutely necessary operations of
computation
Why do you say that? Quantum computers don't duplicate and don't
erase.
Well, quantum computer can still duplicate classical information.
Since the world in quantum classical information is only a
statistical approximation.
I don't think so. I think a quantum reality has the potential to
manipulate relative classical data, basically when the quantum state
is known relatively to the choice of some base. If not quantum
computer would not been Turing universal. This has been shown by
Benioff. The quantum computer is authentically turing universal.
I could say more if your remember the combinators. They can be used
to show that without duplication and erasing you lost Turing
universality. You can recover it by allowing a minimal amount of
duplication, which does not mean that you can duplicate anything.
Hmm. I thought quantum systems could be emulated by a UT.
They can. No problem, except a dramatic relative slow down. In comp
too, to emulate a piece of matter, you have to dovetail on the whole
UD* to get all decimals exact. in QM, you have to evaluate the
universal wave.
How does the no-cloning theorem apply to the emulation?
Good question. If you emulate a piece of matter with a UT you have to
emulate the many superpositions, and the observers, and the contagion
of the superposition to the observers, and you will get that the
emulated observers will realize that they cannot duplicate an
arbitrary quantum state. Indeed, they cannot be aware of the entire
quantum state they are part from. In The MWI, the non cloning is due
to the fact that quantum states contain non accessible information of
how the piece of matter behaves in "parallel realities", or branch of
the universal wave.
Likewise, with comp, the apparent "primitive matter" *is* the result
of the 1-indeterminacy relative to your actual state, and this
involves the whole UD*-infinite indeterminacy domain (like in step 7).
That's not duplicable.
Bruno
http://iridia.ulb.ac.be/~marchal/
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