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[Rafal]

<snip>

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.

<snip>

___________

It is not unreasonable to speculate about the logico-algebraic

structure of "automaton" universes (universes "computer"

generated).

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 [1].

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 !

Regards,

-s.

[1] Karl Svozil, "Randomness & Undecidability in

Physics", World Scientific, 1993, chapters 10.2 - 10.5]

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