John Collins wrote:
   
George Levy wrote:
>Everytime a "measurement" is made, the set of worlds spanned >by this consciousness is defined more narrowly, but the >number in the set remains infinite.  In addition, each >simulation in the set need not belong to the same "level."
>We're faced with the strange possibility that the >consciousness spans an infinite number of simulations >distributed over widely different levels.
I agree that we are simultaneously in many simulations, and I would agree that there are uncountably many possible 'histories' or situations consistent with our consiousness and known history. But I think only a countable number
Why countable? What is the actual count? Can you even give an approximate answer? In fact I could ask "why infinitely countable (aleph nul)?"

of the 'classical universes' (and certainly only a small fraction) we might be in are simulations. If we look at the 'total knowledge' of any living being, including the things not consciously known but constrained to be decided by the classical history they evolved from (so, for instance, 'what killed the dinosaurs' is probably a question with a definite answer, for us, but the trajectory of a certain electron is not; the former would form part of my 'total knowledge' because if I worked out the answer by looking at enough historical evidence, I would get the same answer each time), it is always finite.
    As you suggest, any arrangement of matter consistent with this 'total knowledge' is a possibility for the universe we will find ourselves in on making further measurements, and if we live forever, and keep making new measurements, then there will be a countable number of possible universes we will encounter. But at any finite time, we will only know a finite amount, and therefore only impose a finite number of constraints on the possible universe
precisely, this is why our perception is fuzzy, because it corresponds to many universes.

we will find ourselves in (see my note below on living forever versus having lived forever for more on this). the relevance of this to the current issue is that the super-beings who would emulate us obey the same rules: The 'whole world' of any living being at any given time in their history, being determined only by their thoughts, and the classical histories likely to give rise to those thoughts, can be described by a finite amount of information. Therefore the total number of situations in which a conscious being is simulating our universe is countable. 
Not really, because you could still have an infinite number of identical copies. So the types may be countable but the instances.are uncountably infinite.

George

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