Interesting idea. Parfit's "Combined Spectrum" thought experiment is from his
1984 book "Reasons and Persons". I have not heard of him before.I we apply this
to the hard problem then we come to the conclusion that qualia sameness is a
matter of degree and experiences become functionally and phenomenology "close
enough" long before they hit 100% physical alignment. -J.
-------- Original message --------From: Russell Standish
<[email protected]> Date: 10/1/26 12:27 PM (GMT+01:00) To: The Friday
Morning Applied Complexity Coffee Group <[email protected]> Subject: Re:
[FRIAM] LNC Impossibility Theorem Actually, this conversation sparked a recall
on my objection toParfit's Napoleon thought experiment. Parfit supposed that
one couldfind a continuous path between the subject's brain and Napoleon's
byreplacing one neuron after another. My counter was that I couldn't seehow any
such path could exist - in a scenario similar to thepercolation threshold of
random graphs, eventually the probability ofreaching an unconsious state
becomes one once sufficient neurons havebeen replaced.Not exactly formulated to
a rigorous extent, but that was the gist ofit anyway.On Sat, Sep 26, 2026 at
09:50:11PM +0200, [email protected] wrote:> Yes, good point. You are right,
the proof is not completely waterproof yet. It is based on the assumption that
each of us is wired in a unique way. > > Just as no two fermions can occupy the
exact same quantum state or location (the Pauli exclusion principle), no two
persons can be in the same location or follow the exact same path in their
lives. The "slice of the world" we experience (how Nick used to call it) is
different for each of us. Because we are adaptive and learn from experience,
the unique paths we take and slices we experience lead to different, unique
results. But you are right, even if two path-dependent processes are unlikely
to generate the same graph, it is not the same as proving they cannot.> > I
have asked Gemini, and it says the proof can be made more waterproof by arguing
the fact that no two persons can be in the same location at the same time is
enough to guarantee unique subjective experience. It argues as long as you have
two separate people in two separate places, the two first-person views can
never become identical. To be 100% identical, every single detail of the inner
experiences must match — including where you feel you are in space. Your mind
knows where you are: a part of your subjective experience is the feeling: "I am
standing over here. The other person knows where it is: a part of its
subjective experience includes the feeling: "I am standing over here." The
Contradiction: because the two are standing in different spots, the inner
experiences must be slightly different. The only way two minds could ever be
100% identical is if they were standing in the exact same space at the exact
same time — which means they wouldn't be two different people anymore.> They
would be the exact same physical person.> > Gemini mentioned two other ways to
make it waterproof, but I liked this one most. These AI models are becoming
better in programming, coding and now even in mathematics than we are. It is a
little bit frightening.> > -J.> > On 2026-09-26 19:20, Jon Zingale wrote:> >
While I can appreciate the sentiment regarding Abel and Galois, the> >
impossibility of solving the general quintic by radicals has a> > strikingly
different form. Its Galois group is not solvable, giving a> > precise
obstruction to a solution by radicals. In your case, it seems> > less like an
impossibility that two graphs could be the same and more> > like a claim that
they are unlikely to be the same. Perhaps two> > path-dependent processes are
unlikely to generate the same graph, but> > that is not the same as proving
they cannot.> > > > My own tendency is to think that a graph generated by
material> > processes over a finite life may have only finitely many> >
distinguishable configurations. That leaves open the possibility of> >
collisions. The birthday problem or hash collisions seem like closer> >
analogies to me.> > > > There also seems to be more work to do in showing why
*consciousness*> > (whatever is meant by the word) should be modeled by an
adjacency> > graph, and why a theorem about such graphs would resolve the hard>
> problem.> > .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. ---
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Russell Standish Phone 0425 253119 (mobile)Principal, High
Performance Coders [email protected]
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