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).
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
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.
I will study more on the Gaussian measure (although it seems that
you are using the "Gaussian distribution idea...) no problem. 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. I can see ambiguously how this works
given 1p indeterminacy, but it would be nice to have a local
approximation of this mechanism.
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