Until we recognize the role of perception in terms like 'identical'
and 'equal', we cannot make sensible predictions about duplication or
emulation. Because we have, through science, encountered truths which
contradict our naive realism, we have assumed now that those truths
are final, and that viewing our native perception through this
reflection produces a new class of unquestioned assumptions about the
limits of our own perception.
We assume that since two rooms in different parts of the world appear
'identical' to us visually, that there is no way for someone who wakes
up in one room to know that they are not in the other. My position is
that vision is only one channel of sense that we can be conscious of.
We already know that we experience a synergistic effect from our
multiple sense organs and sense channels (the visual quality of depth
would not likely be anticipated from the fact of our stereo eyes -
just as we might assume that insects with compound eyes experience
multiple images rather than a single wholistic image with multiplicity
of fixed options for intentional focus).
There may be many sense channels which are subconscious to most of us
most of the time, but impact our consciousness nonetheless.
I would guess that a person who had no reason to believe that they had
been knocked unconscious or moved to a different room could not be
sure that they were moved, but I think that a thorough physiological
exam there is very likely to be a difference in how some parts of the
brain behave. A twin in Moscow and a twin in Honolulu may very well be
able to track their own position on Earth. Even something like
elevation would make an obvious difference, even in a windowless,
humidity controlled room.
Ideas of 'identical' are, I think pretty obviously, a function of our
own perceptual limitation. Nothing can be truly identical because all
events occur in a unique spacetime context relative to the rest of the
universe. An event can only be 'duplicated' or 'repeated' to the
extent that our memory and pattern recognition are satisfied that we
can't tell the difference right away. Perceptual equivalence, however,
is not existential equivalence, and in the most all-encompassing
terms, equivalence itself can only be a pattern which is recognized
from a particular perspective and scale, and set of detection-
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