4) Some of the instances of worlds indistinguishable from ours will occur
within computational devices used by sentient entities living on higher
levels, farther removed from the root of the system. Let's call them S
5) Some of the instances of worlds indistinguishable from ours will occur as
subsets of branches of mathematics per se, like fractals, without any
conscious entities producing them. Let's call them N.
6) Both N and S are infinities, and if most of the system consists of
branches which are not sentient, then N>>S.
It is not unreasonable to speculate about the logico-algebraic
structure of "automaton" universes (universes "computer"
If there is a hidden computing entity, and if this computing
entity is "universal", there is no reason to exclude the so
called (intrinsic) "calculus of propositions".
Physical properties corresponding to _experimental_ propositions
are identified - in the quantum domain - with "projection"
operators on the Hilbert space. Thus Hilbert "lattice" corresponds
to a lattice of experimental propositions. Algebraic relations and
operations between these experimental propositions are called
"calculus of propositions". Hilbert lattice and calculus of propositions
_should_ be equivalent, even in the quantum domain. (Lattice theory
is a framework for organizing structures such as experimental
or logical statements). There is no _recursive_ enumeration
of the axioms of Hilbert lattices, as far as I know.
It is not unreasonable asking something like: do we live in a
(quantum) universe created by some "universal" computation ?
Thus, to test such speculation, we must look for _phenomena_
which correspond to "automaton" calculus of propositions _not_
contained in a Hilbert lattice (or its subalgebras).
[There is some connection with Chaitin's omega
numbers? Perhaps there is not.]
These are rather technical statements, but also good hints .
I do not know if N > S, or S > N.
But, assuming that the computational "quality" of those
S-universes is lower than the computational "quality"
of those N-universes, and assuming the usual quantum
randomness, I bet (just 1 euro!) that S is not very high.
What a shame for those sentient entities, living on higher levels,
if we (human, or trashuman people) reach the perception of a
computer-generated universe !
 Karl Svozil, "Randomness & Undecidability in
Physics", World Scientific, 1993, chapters 10.2 - 10.5]
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