An evil surgeon has performed a dreadful experiment.  The subject,
whom we'll call "Holo", has had his entire nervous system transected
right down the middle.  Through advances in accelerated cloning, the
surgeon has prepared two biological bodies, each genetially identical
to Holo's original body.  Into one body he transplants the left half
of Holo's nervous system, and into the other goes the right half.
Though evil, the surgeon is extremely skilled, and both halves of the
nervous system survive and are active.
<P>
To talk about the case after the surgery, we'll use "Holo-Left" to
refer to the left half of the nervous system, and "Holo-Right" to
refer to the right half, each in separate bodies.  Note that Holo-Left
is paralyzed on the left half of his body, and similarly for
Holo-Right.  Both are capable of speaking, however, and except for
their paralysis, and blindness in half the visual field, they do not
report any serious apparent changes.  That is, both Holo-Left and
Holo-Right can reflect on their condition, before and after the
experiment, with a clear memory, and report feeling as if they are the
same person.  But are they really?  What has happened here?

[This case assumes some pretty unlikely science, but for the sake of
philosophical progress, we'll take it as given.]