On 20 Jan 2013, at 23:57, Russell Standish wrote:
On Sun, Jan 20, 2013 at 01:53:49PM +0100, Bruno Marchal wrote:
On 19 Jan 2013, at 00:15, Stephen P. King wrote:
You seem to not understand a simple idea that is axiomatic for
me. I am trying to understand why this is. Do you understand the
thesis of Russell Standish's book and the concept of "Nothing" he
describes?
Sure no problem. It is not always enough clearcut, as Russell did
acknowledge, as to see if it is coherent with comp and its reversal,
but that can evolve.
In some sense, my work is not ontology, as I do not ask the question
"what is fundamental" like you two are doing. Indeed, I believe the
question to be largely meaningless (I had a long debate with Colin
Hales on this topic).
My point is that IF we are machine, then physics is 100% retrievable
by the math of the comp first person indeterminacy, making comp
testable (and partially tested).
More on this later today, if I get time. I had some thoughts during
the night crystallising my understanding of the UDA.
I do acknowledge Bruno's point that set theory is already too
rich. Yet none of my work is based on controversial aspects of set
theory, such as the axiom of choice, so I don't see a big problem
here.
No problem there, except that your assumption are not entirely clear,
but I have no doubt they can be made clearer. In part you build on an
intuition which I show to be necessary once we assume comp, so indeed
there is no problem.
To really compare you would need to formalised, but this would be a
long work in logic.
As for compatibility with COMP, UD* is already the Nothing I refer
to.
This is not alway clear. Of course UD*, or the equivalent sigma_1
truth (the tiny part of elementary arithmetic) is a nothing in the
sense of "no physical reality", but this is not nothingness with
respect to the mathematical assumption. I insist on this for Stephen.
Assuming UD* is equivalent with assuming elementary arithmetic, or the
axioms:
x + 0 = x
x + s(y) = s(x + y)
x *0 = 0
x*s(y) = x*y + x
I do use the uniform measure over the reals
What is the *uniform* measure on the reals? I am not sure this makes
sense.
as a means for motivating
the use of Solomonoff-Levin's universal prior measure, and Bruno has
criticised this, however the S-L measure over the semantic space is
rather insensitive to the assumed measure over the underlying
syntactic
space.
What do you mean by "semantic space". The book did not help me too
much on this.
The physics is very sensitive to the measure of the comp histories in
the UD*, but only thanks to its super-redundancy. Indeed: physics *is*
the measure.
Solomonof approach (certainly good for doing inductive inference, and
he does not pretend to do anything else) is of no use to extract
physics, as his measure compress the redundancy into the non-computable.
Chaitin's number can be seen as the compression (the suppression of
all redundancy) of Post number (where the ith digit tells if the ith
machine stops or not).
It is, of course, an open problem whether the measure induced
by the universal dovetailer over UD* makes any difference, as that
measure has not been calculated.
We don't need to calculate it to understand that such a measure is
equivalent with the physical laws. Comp makes physics a measure
theory, and this is arguably the case for quantum mechanics. That is
not an open problem.
I am not sure we talk about the same measure. I show that physics is
equal to the computationalist first person indeterminacy measure on
UD*. different measure will give different physics, that is different
probabilities for the result of the experiments we can do.
Solomonof approach can make sense for the study of biological
evolution, as it is non computable, but still limit computable. the
first person indeterminacy is a priori much less computable (not even
limit-computable), but it is the one we are living, and the overall
logic bearing on the indeterminacy domain can be found without any
algorithm to compute it; and it has been found: it is the Z1* and X1*
logic, probably S4Grz1, which all gives an arithmetical quantization.
It is just an open problem if this gives rise to quantum computation
in our most probable neighborhoods.
Bruno
My gut feeling is that it wouldn't
make any difference, however.
--
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Prof Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics hpco...@hpcoders.com.au
University of New South Wales http://www.hpcoders.com.au
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