This "density - idea is the first one that brings me a
bit "less far" from the big (infinite?) number idea.
It is still not reaching to the problem, how number
qualia can turn into other meaning qualia - without
outside (other) input.
Thanks Lennart
John M
--- Lennart Nilsson <lennartn.domain.name.hidden> wrote:
>
> Nick Boström have been trying to calculate the
> probability that
> we live in a computer simulation. His answer to how
> you go about
> this (below) if we live in an infinite universe with
> infinite simulations
> seems to fit how one could do probabilities in a
> multiverse with an
> infinite number of universes as well.
>
> Lennart Nilsson
>
>
> "To deal with these infinite cases, we need to do
> something like thinking in
> terms of densities rather than total populations. A
> suitable density-measure
> can be finite even if the total population is
> infinite. It is important to
> note that we to use some kind of density-measure of
> observation types quite
> independently of the simulation argument. In a “Big
> World” cosmology, all
> possible human observations are in fact made by
> somebody somewhere. (Our
> world is may well be a big world, so this is not a
> farfetched possibility.).
> To be able to derive any observational consequences
> from our scientific
> theories in a Big World, we need to be able to say
> that certain types of
> observations are more typical than others. (See my
> paper “Self-Locating
> Belief in Big Worlds” for more details on this.)
>
> The most straightforward way of making this notion
> precise in an infinite
> universe is via the idea of limit density. Start by
> picking an arbitrary
> spacetime point. Then consider a hypersphere
> centered on that point with
> radius R. Let f(A) be the fraction of all
> observations that are of kind A
> that takes place within this hypersphere. Then
> expand the sphere. Let the
> typicality of type-A observations be the limit of
> f(A) as R--->infinity."
>
>
>
> -----Ursprungligt meddelande-----
> Från: everything-list.domain.name.hidden
> [mailto:everything-list.domain.name.hidden] För Brent
> Meeker
> Skickat: den 6 april 2006 18:21
> Till: everything-list.domain.name.hidden
> Ämne: Re: Do prime numbers have free will?
>
>
> Stathis Papaioannou wrote:
> > Tom Caylor writes:
> >
> >
> >>1) The reductionist definition that something is
> determined by the
> >>sum of atomic parts and rules.
> >
> >
> > So how about this: EITHER something is determined
> by the sum of atomic
> parts
> > and rules OR it is truly random.
> >
> > There are two mechanisms which make events seem
> random in ordinary life.
> One
> > is the difficulty of actually making the required
> measurements, finding
> the
> > appropriate rules and then doing the calculations.
> Classical chaos may
> make
> > this practically impossible, but we still
> understand that the event (such
> as
> > a coin toss) is fundamentally deterministic, and
> the randomness is only
> > apparent.
> >
> > The other mechanism is quantum randomness, for
> example in the case of
> > radioctive decay. In a single world interpretation
> of QM this is, as far
> as
> > I am aware, true randomness.
>
> Unfortunately there is no way to distinguish "true
> randomness" from just
> "unpredictable" randomness. So there are theories
> of QM in which the
> randomness
> is just unpredictable, like Bohm's - and here's a
> recent paper on that theme
> you
> may find interesting:
>
> quant-ph/0604008
>
> From: Gerard Hooft 't [view email]
> Date: Mon, 3 Apr 2006 18:17:08 GMT (23kb)
>
> The mathematical basis for deterministic quantum
> mechanics
> Authors: Gerard 't Hooft
> Comments: 15 pages, 3 figures
> Report-no: ITP-UU-06/14, SPIN-06/12
>
> If there exists a classical, i.e. deterministic
> theory underlying
> quantum
> mechanics, an explanation must be found of the fact
> that the Hamiltonian,
> which
> is defined to be the operator that generates
> evolution in time, is bounded
> from
> below. The mechanism that can produce exactly such a
> constraint is
> identified in
> this paper. It is the fact that not all classical
> data are registered in the
>
> quantum description. Large sets of values of these
> data are assumed to be
> indistinguishable, forming equivalence classes. It
> is argued that this
> should be
> attributed to information loss, such as what one
> might suspect to happen
> during
> the formation and annihilation of virtual black
> holes.
> The nature of the equivalence classes is
> further elucidated, as it
> follows
> from the positivity of the Hamiltonian. Our world is
> assumed to consist of a
>
> very large number of subsystems that may be regarded
> as approximately
> independent, or weakly interacting with one another.
> As long as two (or
> more)
> sectors of our world are treated as being
> independent, they all must be
> demanded
> to be restricted to positive energy states only.
> What follows from these
> considerations is a unique definition of energy in
> the quantum system in
> terms
> of the periodicity of the limit cycles of the
> deterministic model.
>
>
> >In a no-collapse/ many worlds interpretation
> > there is no true randomness because all outcomes
> occur deterministically
> > according to the SWE. However, there is apparent
> randomness due to what
> > Bruno calls the first person indeterminacy: the
> observer does not know
> which
> > world he will end up in from a first person
> viewpoint, even though he
> knows
> > that from a third person viewpoint he will end up
> in all of them.
> >
> > I find the randomness resulting from first person
> indeterminacy in the MWI
>
> > difficult to get my mind around. In the case of
> the chaotic coin toss one
> > can imagine God being able to do the calculations
> and predict the outcome,
>
> > but even God would not be able to tell me which
> world I will find myself
> in
> > when a quantum event induces splitting. And yet, I
> am stuck thinking of
> > quantum events in the MWI as fundamentally
> non-random.
>
> It's also unclear as to what "probability" means in
> the MWI. Omnes' points
> out
> that "probability" means some things happen and some
> don't.
>
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Received on Thu Apr 06 2006 - 18:37:08 PDT