1. cronin/walker assemby paths
2. holometabolous (e.g. butterfly metamorphs) insects
3. if transitioning through unconscious states invalidates a path, what
of psychotic states?
On 10/1/26 4:08 am, Russell Standish wrote:
Actually, this conversation sparked a recall on my objection to
Parfit's Napoleon thought experiment. Parfit supposed that one could
find a continuous path between the subject's brain and Napoleon's by
replacing one neuron after another. My counter was that I couldn't see
how any such path could exist - in a scenario similar to the
percolation threshold of random graphs, eventually the probability of
reaching an unconsious state becomes one once sufficient neurons have
been replaced.
Not exactly formulated to a rigorous extent, but that was the gist of
it 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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