On 03 Jul 2014, at 06:51, Richard Ruquist wrote:
Quantum measure is the result of solving Schrodinger's Eq.
yielding a different probability for each quantum state
and a different measure for each different scenario
unlike the invariant measure of the reals.
Do you disagree?
Richard
The quantum measure is a measure on solutions of an equation, like
square normed functions or operators in a linear (Hilbert) space (like
in both QM and functional analysis). The measure on the reals is a
measure on real numbers. With comp, the measure is on the relative
states. It is really a measure on the transition <a I b>. In quantum
mechanics it is given by [<a I b>]^2, but with comp this must be
explained by a measure on all the computations going from a mind state
corresponding to observing 'a to a mind state of observing 'b, taking
into account the fact that an infinity of universal numbers justifies
those transitions (= makes them belonging to a computation).
The protocol of the iterated WM-duplication is a very particular case.
The first person histories with computable sequence like "WWWWWW...",
or "WMWMWMWMWM... ", becomes the white rabbits event, and the norm is
high incompressibility (a very strong form of randomness).
The ultimate protocol is the "logical" structure of the sigma_1
arithmetic. By the dovetailing on the reals, it mixes a random oracle
with the halting oracle so that we can expect a "non-machine" for the
first person truth. But it is already a non machine, from the machine
view, by simple incompleteness.
The interview of the löbian machine does not provide the measure
calculus (Plato-Plotinus 'bastard' calculus with the Plotinus
lexicon), but it provides the logic of the measure one, from which the
measure calculus + the arithmetical constraints) should be derivable
(and the measure one admits a quantization confirming things go well
there).
Bruno
On Thu, Jul 3, 2014 at 12:44 AM, Russell Standish <[email protected]
> wrote:
On Thu, Jul 03, 2014 at 12:23:35AM -0400, Richard Ruquist wrote:
> On Wed, Jul 2, 2014 at 10:34 PM, Russell Standish <[email protected]
>
> wrote:
>
> > On Tue, Jul 01, 2014 at 04:30:52PM -0400, Stephen Paul King wrote:
> > > Hi Russell,
> > >
> > > Ah! I don't quite grok it completely, but thank you for this
example. We
> > > had to assume an already existing measure on the Reals. Where
does that
> > > come from?
> > >
> >
> > The standard measure on the reals is based on the observation
that we
> > expect the set of real numbers starting with 0.110... to have
the same
> > measure as those starting with 0.111... That would be a reasonable
> > default assumption for most purposes.
>
>
> The measure obtained by compression of the reals in binary form is
close to
> the quantum mechanic measure, but not exact.
> In fact, the quantum measure varies with the scenario, whereas the
measure
> of the reals is invariant.
> Richard
>
What do you mean? What is this "quantum measure"?
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