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.
Bruno
http://iridia.ulb.ac.be/~marchal/
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