On 9/7/2012 3:14 AM, Bruno Marchal wrote:
On 07 Sep 2012, at 04:20, Stephen P. King wrote:
On 9/6/2012 1:44 PM, Bruno Marchal wrote:
On 05 Sep 2012, at 08:38, Stephen P. King wrote:
On 9/5/2012 2:03 AM, meekerdb wrote:
On 9/4/2012 10:07 PM, Stephen P. King wrote:
On 9/5/2012 12:38 AM, meekerdb wrote:
On 9/4/2012 8:59 PM, Stephen P. King wrote:
What is most interesting is that the QC can run an arbitrary
number of classical computations, all at the same time. The CC
can only barely compute the emulation of a single QC.
You are talking about QC and CC as though they were material
computers with finite resources. Once you've assumed material
resources you've lost any non-circular possibility of explaining them.
No, I am pointing out that real computations require real
resources. Only when we ignore this fact we can get away with
floating castles in midair.
Brent just point out that arithmetic contains infinite resource.
What do you mean by "real computations"? Do you mean "physical
computations"? Why would they lack resources?
I am talking about physical systems that have the capacity of
carrying out in their dynamics the functions that implement the
abstract computations that you are considering. The very thing that
you claim is unnecessary.
But you claim that too, as matter is not primitive. or you lost me again.
I need matter to communicate with you, but that matter is explained in
comp as a a persistent relational entity, so I don't see the problem.
It is necessary in the sense that it is implied by the comp
hypothesis, even constructively (making comp testable). It is even
more stable and "solid" than anything we might extrapolate from
observation, as we might be dreaming. Indeed it comes from the
atemporal ultra-stable relations between numbers, that you recently
mention as not created by man (I am very glad :).
Matter is not primitive as it is not irreducible. My claim is that
matter is, explained very crudely, patterns of invariances for some
collection of inter-communicating observers (where an observer can be
merely a photon detector that records its states). This is not
contradictory to your explanation of it as "persistent relational
entity", but my definition is very explicit about the requirements that
give rise to the "persistent relations". I believe that these might be
second order relations between computational streams. and can be defined
in terms of bisimulation relations between streams.
I question the very idea of "atemporal ultra-stable relations
between numbers" since numbers cannot be considered consistently as just
entities that correspond to 0, 1, 2, 3, ... We have to consider all
possible denotations of the signified. See
http://www.aber.ac.uk/media/Documents/S4B/sem02.html#signified for an
explanation. Additionally, there are not just a single type of number as
there is a dependence on the model of arithmetic that one is using. For
example Robinson Arithmetic and Peano Arithmetic do not define the same
So we have multiple signified and multiple signifiers and cannot
assume a single mapping scheme between them. I suppose that a canonical
map exists in terms of the Tennebaum theorem, but I need to discuss this
more with you to resolve my understanding of this question.
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