Le 18-juin-05, à 20:36, Norman Samish a écrit :
> I'm no physicist, but doesn't Heisenberg's Uncertainty Principle forbid
> making exact quantum-level measurements, hence exact copies? If so,
> then
> all this talk of making exact copies is fantasy.
Many good answers has been given. And my comment will overlap some of
them.
The most physicalist one is to referindeed to Tegmark's paper where he
justifies by Everett/decoherence that the evidence is that our brain,
when seen as an information handling computing machine, acts as a
classical machine. But comp makes physicalism wrong, and Tegmark's
answer cannot be "fundamentally" genuine.
The importance of quantum decoherence in brain processes
M Tegmark 2000, quant-ph/9907009, Phys. Rev. E 61, 4194-4206
161 Why the brain is probably not a quantum computer
M Tegmark 2000, Information Sciences 128, 155-179
Then, concerning the comp 1-person indeterminacy, even if my
computational state is a quantum states, the Universal Dovetailer
Argument (UDA) is still going through. This is a consequence of the
fact that quantum computation does not violate Church's thesis. That
entails that you can simulate a quantum computer with a classical
computer. Sure, there is a relative exponential slow-down of the
computation, but this is not relevant because the universal dovetailer
is naturally slow down by its heavy dovetailing behavior, and then the
first person cannot be aware of that slow down.
And then I recall I gave an exercise: show that with comp the
no-cloning theorem can easily be justified a priori from comp. As I
said this follows easily from the Universal dovetailer Argument. The
argument shows that physical observable reality (relatively to what you
decide to measure here and now) emerges as an average on all
computations (generated by the UD) going through your actual state.
Suppose now that you decide to observe yourself with at a finer and
finer level of description. At some moment you will begin to observe
yourself at a level below you substitution level (which I recall is the
level where you survive through copy). Below that level comp predict
you will be confronted with the 1-comp indeterminacy, that is you will
"see" the many computation/histories. Now that is strictly speaking an
infinite set , and there is no reason at all, a priori, that this set
is a computational object, so there is no reason at all you could
duplicate exactly.
Here you can appreciate the difference between Schmidhuber's comp and
"my" comp. In Schmidhuber's comp the "physical" universe is a
computational object and there is no 1-indeterminacy, and non-cloning
is rather mysterious. "My" comp is the more humble bet that "I" am a
computational object. With "my" comp, I (first person) bet on the
existence of a level of substitution for some 3 description of my body
(that is a first person says "yes" to its doctor when the doctor
proposes a substitution of his body by *some* digital machine). Then,
what the UDA shows is that the universe, whatever it is, cannot be a
computational object, and no piece of "real (observable)" matter can be
cloned, a priori.
Logically, it is still logically possible that the theoretical computer
science constraints makes this reasoning invalid, but this would be a
consequence of a sort of an arithmetical conspiracy. (Given that the
logic of observable proposition *is* already proved to be highly NOT
boolean and even quantum-like, but ok here I am in the arithmetical
translation of the UDA: note that I am introducing the combinators to
just been able to interview the Lobian machine on the non-cloning
question, and also on the complete reversibility of the laws of
physics).
The easy (not quite rigorous) proof of the non-cloning theorem from
comp shows that the QM non cloning can be seen (retrospectively, sure)
as a confirmation of comp. Here is another exercise (a little bit less
easy): show that the fact we can test experimentally and share with
each other such non-cloning behavior would confirm, not only comp, but
would vindicate the differentiation between the 1-person point of view,
and the 1-person plural point of view (I just mention it in my post to
Jonathan): for a computationalist the observability of non cloning is
an evidence against solipsism! (well the observability of QM
indeterminacy also, and is perhaps more easy to use). It is also an
evidence that we share the level of substitution.
Bruno
http://iridia.ulb.ac.be/~marchal/
Received on Mon Jun 20 2005 - 10:17:36 PDT