Dear Stephen,
On 31 Dec 2013, at 20:19, Stephen Paul King wrote:
I really do appreciate the details!
On Tue, Dec 31, 2013 at 5:04 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 30 Dec 2013, at 19:33, meekerdb wrote:
On 12/30/2013 1:41 AM, Bruno Marchal wrote:
On 30 Dec 2013, at 02:59, meekerdb wrote:
On 12/29/2013 4:41 PM, LizR wrote:
On 30 December 2013 09:35, Edgar L. Owen <edgaro...@att.net>
wrote:
Liz,
Good questions. The computations take place in P-time which is
the universal processor cycle in which they execute. The results
of the computations compute dimensional space and CLOCK time.
So an external time dimension is required.
So imagine a universe with a time dimension and some space-less
computations...I'll try.
This shouldn't be any harder than imagining Bruno's Turing
machine computing everything...including space and time.
Space, time and physical things are not computed. They emerge in
the view of "self-aware" Löbian machine, which exist in arithmetic.
But not all of arithmetic is computed by the UD,
OK. The UD, seen as a prover, proves only the "ExP(x)" truth, but of
course it obeys itself to the whole of arithmetic, for example, it
will never emulate a correct machine proving a false pi_1 statements
(AxP(x)).
The notion of self-obedience, is that a form of self-reference?
Define 'self-obedience'.
so how can you be sure that this Lobian machine emerges?
Because the existence of some Löbian machine is a sigma_1 (even
sigma_0) sentence, as his the existence of their finite piece of
computational histories.
OK. Does this follow from Lowenheim-Skolem?
?
It follows from the sigma_1 completeness of RA. (p -> Bp, for p
sigma_1, is true for RA. It is not provable as RA is not Löbian).
(Lowenheim-Skolem is invoked to explain why arithmetic from inside can
seem infinitely bigger than from outside, but this is not used here).
How does it emerge?
The UD, alias RA, emulates all machines.
I see this as true, but in the sense of a static representational
model. There is no "action" involved!
Then RA would only describe the computations, not emulate them. But it
does. "Action" is recognized by the machine inside. Actions and
changes are defined and measure internally by machines *relatively* to
universal numbers. Here comp generalized Special relativity, somehow.
There is no absolute time, except, if we want see it in that way, in
the 0, 1, 2, 3, .... number sequence.
And if there is one, aren't there indefinitely many emerging?
Yes, there are infinitely many emerging, and that is why there is a
global relative 1-indeterminacy on the whole UD*, or RA emulation.
Are you saying that the FPI obtains from the infinite number of
"emergings"?
There are two notions of "emergence" used here. The emergence by the
"theoremhood", like when saying that once God created the natural
numbers and said "add & multiply", you can define the prime numbers
and they emerge from all arithmetical relations definable in
arithmetic. Then there is the FPI emergence, which is made of all
finite union of the finite piece of the UD work. You can say that the
FPI bears on all what emerge in the first sense, yes.
Does it have to be "global"?
Yes. like in step 7, we are confronted to the whole of UD* (or to the
whole of the Sigma_1 truth).
I worry about this because it seems to assume a privileged observer
that has the ability to simultaneously perceive all of the emergings.
He perceives only one "outcome" (like in the WM-duplication), selected
among the infinities of possible computations emulated in RA.
I reject that "God's eye view".
The outer 3p God's view is given, in comp, by the arithmetical truth.
It is a little and simple God, like in Plotinus. It is far simpler
than the Noùs or than the Universal Soul.
Bruno
http://iridia.ulb.ac.be/~marchal/
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