We exist in an infinite number of simulations. Any arbitrary number of simulations  less than infinity would require a reason. We are led to this conclusion by assuming a TOE which by definition has no a-priori reason. (This is the philosophical rationale for postulating the plenitude)

Discreteness may be important in our world for the development of consciousness, but it is certainly not necessary across worlds. I believe therefore that the differences between the simulations is infinitesimal - not discrete - and therefore that the number of simulations is infinite like the continuum.

Not only is the number of simulations infinite but the number of levels in simulation may also be infinite. The levels are discrete - I cannot imagine how they could be otherwise.

Given the above, let's consider one particular conscious being. His awareness of his own states is likely to be uncertain. Another way of saying this is that several states transitions could generate the same consciousness stream. Modeling the state transitions as an algorithm, for example, there may be multiple algorithmic paths that could generate the same output.

Hence his consciousness will have "thickness across the multi-worlds," overlapping a set of  multi-worlds each slightly differing from the others. How many multi-worlds will it overlap? An infinite number since they differ as in a continuum. 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. Each individual simulation implementation becomes infinitesimal and unimportant in comparison with the the whole infinite set of implementations that the consciousness covers. A particular simulation that stops operating (for example because the plug is pulled) will hardly affect or be missed by the consciousness as a whole. In fact I rather think of the "simulations" as static states in the plenitude, and consciousness as a locus in the plenitude linking these states in a causally and logically significant manner. We live in the plenitude, not in any  particular simulation. Each point in the conscious locus perceives the world that gives it meaning.


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