On 28 Sep 2014, at 01:39, Russell Standish wrote:
On Sat, Sep 27, 2014 at 03:43:56PM +0200, Platonist Guitar Cowboy
wrote:
On Sat, Sep 27, 2014 at 8:29 AM, Russell Standish <li...@hpcoders.com.au
>
wrote:
On Sat, Sep 27, 2014 at 05:33:00AM +0200, Platonist Guitar Cowboy
wrote:
On Sat, Sep 27, 2014 at 3:39 AM, Russell Standish <li...@hpcoders.com.au
wrote:
So I don't see: robust universe => all integers exist
Nor do I. But then that is the exact inverse of what I stated: the
arithmetic reality assumption in COMP entails a robust reality
(one in
which the UD runs to completion).
If I remember the thesis correctly, than robust is a placeholder
for some
grandmother notion of physical reality, with enough consistency in
historical/spatial/causal relations to allow the UD to run. Once
reversal
step is reached, the notion is dropped and isn't further needed.
I think you're thinking of the term "concrete", which was somehow
synonymous with "primitive physical".
This term was always problematic, as neither "concrete", "primitive"
nor "physical" were ever defined. I could not understand why the
integers, which were supposed to exist, could not satisfy "primitive
physicality".
The physical is defined by the observable, measurable by engineers,
etc. By the global FPI, like in step 7, the physical is the FPI
calculus (and by Solovay we get the quanta and the qualia, with the
usual definition). It is a modality, a point of view.
The number are primitive, because I defined "primitive" by what we
need to assume and can't reduce to anything simpler. Primitive
materialist, or physicalist, assumes that we have to assume some
particle, or some quantum vacuum, that is some physical objects.
What is true, however, is that if the universe is robust, then the
reversal holds - whatever it is that is primitive, the only property
that is relevant to phenomenal physics is Turing completeness.
OK.
This seques into the ontological problem that Jean de la Haye brings
up - and so does David Deutsch in his own way. If the primitive
universe were something like the Hilbert hotel, then we would expect
that the sorts of computations available in our empirical reality to
include hypercomputations - computations that go beyond the ability of
Turing machines. It is a fact that these hypercomputations are
conspicuously absent, so that raises the obvious question: why is the
primitive ontology restricted to just Turing complete systems?
That is almost equivalent as asking why comp would be true. Also, it
is not so easy to prove that there are no Hilbert hotel below our
substitution level, and QC get close, but there are none there.
Indeed the main mystery, the measure problem, is to explain why things
seem so much computable. Why the computations, which are of measure
zero in the set of all functions seems to win. The answer are in the
self-reference and in the exploitation of the random oracle, probably.
The self-reference structure shapes the available logic of physics,
but does not yet explain why the physical is locally computable or
continuous, or linear. "physically" I think the unitary transformation
wins because they randomize the lengthy computational path, and
destroyed them by the destructive interference. U = e^iH. For this to
work, we need a semantic of comp quantum logic in term of basis,
projector, ... then on the sigma_1 truth the graded quantum logic
seems to have a Temperley-Lieb structure, knots and space might be on
the horizon, but the math are not easy.
Bruno
Therefore I can't see bi-conditional implication or material
implication
either way between the extravagant "for all practical purposes robust
assumption" and properties of arithmetic in terms of ultrafinite,
infinities etc. PGC
When you say "for all practical purposes robust assumption" is
extravagant, are you arguing for ultrafinitism? This seems to
contradict your name. If you are truly Platonist, your reality is
robust. The weaker "for all practical purposes robust" shouldn't be a
problem for you.
The point of the FAPPRA is that it also includes finite, but large
multiverses, like the 10^500 string landscape.
Cheers
--
----------------------------------------------------------------------------
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
Latest project: The Amoeba's Secret
(http://www.hpcoders.com.au/AmoebasSecret.html)
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