Dear Alastair:
I will read your paper, but it seems to me that the no information
approach to formulating an Everything precludes selection. Selection
assigns a property to a subset of the ensemble that the other members do
not share. This destroys the ensemble.
Prevalence being a property I would conclude from this that no allowed type
of universe can be more prevalent than any other allowed type.
Speculation:
Is it possible to use this approach to exclude certain types of universes?
First distinguish two types of evolving universes [universes that change
state]:
1) Those that have rules of state succession that forbid a source of
external information [true noise]
2) Those that have rules of state succession that allow a source of true
noise [external information] to some degree [from zero true noise to
nothing but true noise].
This distinction is already a selection so one or the other type must be
absent from an informationless Everything.
I think the first step to resolution is to notice that type #2 could
include type #1 as an extreme lower limit case, but type #1 can not include
type #2 at all.
However, is the extreme lower limit case for #2 allowed to be zero true noise?
Perhaps to resolve this ask whether either of these types is a larger
set. Since type #2 is a continuum is also type #1?
If an infinite rule set and/or data string is equivalent to number #2 then
universes in #1 must have finite rule sets and finite data strings
[finitely describable]. The number of such universes would be merely
countable. At any non zero degree of true noise - say 2% or 20% etc. there
would be an infinite number of ways to allow that percentage. The
conclusion would be that universes with zero true noise would be extremely
rare relative to any of those with a non zero degree of true noise and so
such an information generating lower limit is excluded. The extreme lower
limit for true noise in #2 must be greater than zero.
However, this itself seems like a breach of the no information approach.
This could be fixed if type #1 were reclassified as non evolving universes
and a door is opened between the two types. A type #2 universe with the
right dose of true noise can surely convert to a type #1. This would
balance the quantity issue. Can type #1 universes become type #2
universes. They must be able to or again there would be a selection.
It seems this is just a way of saying that universes do not have fixed
rules of state succession.
Hal
At 2/17/02, you wrote:
Thanks for your comments - the 'difficulty' that you refer to is none other
than the White Rabbit problem, on which there has been much discussion in
this forum. My own approach addresses the problem from the standpoint of all
logical possibilities (rather than any particular model or set of rules),
which can make the problem non-trivial to solve.
Alastair
