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. > > .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / > > ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. > > FRIAM Applied Complexity Group listserv > > Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom > > https://bit.ly/virtualfriam > > to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > > FRIAM-COMIC http://friam-comic.blogspot.com/ > > archives: 5/2017 thru present > > https://redfish.com/pipermail/friam_redfish.com/ > > 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ > > .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... > --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. > FRIAM Applied Complexity Group listserv > Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom > https://bit.ly/virtualfriam > to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: 5/2017 thru present > https://redfish.com/pipermail/friam_redfish.com/ > 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders [email protected] http://www.hpcoders.com.au ---------------------------------------------------------------------------- .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. 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