On 17 Feb 2012, at 22:26, Stephen P. King wrote:
On 2/17/2012 2:24 PM, Bruno Marchal wrote:
On 17 Feb 2012, at 13:51, Stephen P. King wrote:
On 2/17/2012 4:19 AM, Bruno Marchal wrote:
On 16 Feb 2012, at 16:57, Stephen P. King wrote:
On 2/16/2012 4:49 AM, Bruno Marchal wrote:
On 15 Feb 2012, at 08:07, Stephen P. King wrote:
By the way, Darwin's theory revolves around the notion of
evolution, that "simpler objects" can evolve and change.
Numbers, by definition, cannot change and thus cannot
implement any form of change or evolution.
So you assume a primitive time?
No, there cannot be a primitive time because that would
require a primitive measure and the same reasons that we cannot
have primitive physical worlds nor primitive abstract entities
would hold. We need to discuss how measures come to occur.
First person indeterminacy. It is the classical boolean Gaussian
measure on the set of relative computations, as seen by the
machines (the "as seen" is made technically precise in AUDA).
Dear Bruno,
I had a tiny epiphany this morning as I read your remarks and
I think that it is best that I surrender to you on my complaint
that your result goes to far and is really a form of ideal monism
and turn to discussions of the ideas of measures and interactions.
My main motivation is to see how far Prof. Kitada and Pratt's
ideas are compatible with yours.
Could you elaborate a bit on Gaussian measures. They are
unfamiliar to me.
Once you accept P = 1/2 for the first person indeterminacy on a
domain with two (and only two) relative reconstitutions, you can
verify that the 2^n persons obtained after an iterated WM self-
duplication can discover that they can be partitioned by the
numbers of having gone in W (resp. M), and that those numbers are
given by the binomial coefficients. The Gaussian distribution is
obtained in the limit, by the law of big numbers. Surely you know
this.
In front of the UD, that Gaussian distribution becomes "quantum
like" due to the constraints of self-reference, and of the
appurtenance of the computational states to computations.
Intuitively we can guess that the "winning" computations will
exploit the random oracle given by the self-multiplication so that
a notion of normal histories can develop.
But comp+classical-theory of knowledge does not permit the use of
such intuition, we have to retrieve this form the self-reference
logic, so that we can distinguish the communicable and non
communicable parts. The logic of measure one have been already
retrieved, if we agree on the definition used in AUDA.
Of course we can still speculate on what such a measure can look
like.
Dear Bruno,
I will study more on the Gaussian measure (although it seems
that you are using the "Gaussian distribution idea...) no problem.
Yes. It is the gaussian distribution, with Lebegues measure in the
background, in the case of the ierated self-duplication.
What I would like to know is how we go from a very large to infinite
collection of distributive algebras to non-distributive
orthocomplete lattices, for that is what you are implying.
They are given by the logic of certain-observable, given by the
S4grz1, X1* and Z1* hypostases. (The one corresponding to the
arithmetical variants of self-reference Bp & p, Bp & Dt, Bp & Dt & p,
with p Sigma_1, and B and D like in Gödel 1931.
I can see ambiguously how this works given 1p indeterminacy, but it
would be nice to have a local approximation of this mechanism.
See the part II of sane04.
Bruno
http://iridia.ulb.ac.be/~marchal/
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