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From: Lennart Nilsson <lennartn.domain.name.hidden>

Date: Thu, 6 Apr 2006 18:51:07 +0200

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.

Brent Meeker

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Received on Thu Apr 06 2006 - 12:52:22 PDT

Date: Thu, 6 Apr 2006 18:51:07 +0200

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:

parts

One

the

make

as

as

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.

which

knows

in

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.

Brent Meeker

--~--~---------~--~----~------------~-------~--~----~

You received this message because you are subscribed to the Google Groups "Everything List" group.

To post to this group, send email to everything-list.domain.name.hidden

To unsubscribe from this group, send email to everything-list-unsubscribe.domain.name.hidden

For more options, visit this group at http://groups.google.com/group/everything-list

-~----------~----~----~----~------~----~------~--~---

Received on Thu Apr 06 2006 - 12:52:22 PDT

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