Kingreaper comments on Consciousness of simulations & uploads: a reductio - Less Wrong
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The simulation is "all the information you contain (and then possibly some more)" running through an algorithm at least as complex as your own.
The shadow is "a very very small subset of the information about you, none of which is even particularly relevant to consciousness", and isn't being run at all.
So, I would disagree fundamentally with your claim that they are in any way similar.
This may be a point of divergence. You're thinking of the brain as active, and the Graphite-Paper-Person simulator as passive.
If you talk about "patterns of energy flow in the brain" the analogous statement for the GPP is "patterns of marking creation/destruction on the paper"
If you talk about "patterns of graphite on paper" the analogous statement for brains is "patterns of electrochemical potential in cells"