It is not just decorative math. Decorative math would be an equation or a theorem without substance to make the text look better or smarter. Here it is the opposite. The theorem is the core. We can consider it as the real reason behind the explanatory gap of the hard problem which Joeseph Levine has observed.
It is similar to the "Hard Problem of Algebra" in mathematics. As you know mathematicians struggled for centuries with the "Hard Problem of Algebra" — trying to find a general formula using radicals to solve 5th-degree polynomial equations. Quadratic, cubic, and quartic equations could be solved, but no one could find a general formula for fifth-degree (quintic) or higher equations. Until Galois figured out the exact algebraic conditions required for any polynomial equation to be solvable by radical, and Abel and Ruffini proved the Abel–Ruffini Theorem which showed that a general algebraic solution for 5th-degree polynomial equations is mathematically impossible due to the symmetry group structures of polynomials. After Galois created the Galois theory and Abel and Ruffine found the Abel–Ruffini Theorem the "Hard Problem of Algebra" disappeared. The "Hard Problem of Algebra" was the shadow cast by the Abel–Ruffini Theorem, the result of a group-theoretic impossibility. In the same way "the hard problem of consciousness" will disappear if we have found the impossibility theorem behind it. What the proposed LNC (Levine-Nagel-Chalmers) impossibility theorem states is that exact subjective equivalence between two conscious agents is impossible, because each of them has a unique emotional valuation matrix which is the foundation of their subjective experience. By emotional valuation matrix I mean the system of value calculation in the ventromedial prefrontal cortex (vmPFC) that Emily Falk describes in her book "What we value". It is modeled here as a path-dependent graph or matrix (every graph can be described by an adjacency matrix). Just like two persons never have the same fingerprints, because their unique patterns are shaped by a combination of genetic instructions and random environmental factors, no two persons have exactly the same "emotional valuation matrix". It is a similar combination of random fluctuations and growth which creates a unique non-ergodic path-dependent structure. Although exact subjective equivalence is not possible, we can narrow the gap between the subjective experiences of two conscious adaptive agents if they share the same path. The longer the path is shared, the more the gap is closed, the more the agents share the same impression and emotional valuations, as-if it one agent would perceive the world like the other agent. This is what the second "Asymptotic Qualia Theorem" says. Why is the second theorem useful? It is the reason why we have cinemas and movie theaters, and why they look the way they do. They are what-it-is-like-to-be machines that show us what is like to be someone else. Plus it helps to understand the limits. The theorem mentions an epsilon_0 > 0 which is the irreducible limit we can reach. This epsilon_0 values is lowest for two humans (human - human), higher for two mammals (human - bat or human - whale) and even higher for a mammal and a reptile (human - chameleon) or mammal and insect (human - butterfly). While it is relatively easy for us to imagine what it is like to be another human, it is much more difficult what it is like to be a sperm whale in the eternal darkness of the deep sea hunting for squids, or what it is like to be a chameleon in Madagascar that changes its color and eats insects. -J. On 2026-09-26 02:42, glen wrote: > What work are these formalizations doing for the program? I mean, it seems > like it would be pretty easy to doubt the fidelity of the formalism to the > real system (e.g. discrete time, synchronous updating, lack of equivalence > classes or neutral networks, etc.). That's OK as long as you have a > relatively complete virtual world (e.g. not only are G,E,W synchronously > chunked but the entire universe is cellular automata like). So in *that* type > of universe, the theorem would show something about that portion of the > universe. But it doesn't seem like you're doing that. > > The worry I have can be described as "decorative math". (To be clear, I'm as > guilty of it as anyone ... but I'm not writing a book. 8^D) If there's not a > clear purpose to the formalization, I'd resist including it. If you really > feel it's doing some rhetorical work, then I'd recommend softening the main > text from: > > "We can in fact create a mathematical proof that solving the hard problem is > not possible completely. We could call it it the “LNC Impossibility Theorem” > (see Appendix D), named after Joseph Levine, Thomas Nagel, David Chalmers who > first formulated the hard problem. The LNC Impossibility Theorem states that > exact subjective equivalence between two conscious agents is impossible. The > hard problem is a shadow of this theorem." > > to something like: > > "There may be many ways the Hard Problem might be formalized. We provide one > such formalization in the LNC Impossibility Theorem (see Appendix D) ..." > > Softening the language may allow curmudgeon readers to look past their > persnickety nits and ride along with you. > > > On 9/25/26 1:37 PM, Jochen Fromm wrote: >> The post from Dan Piponi inspired me to invent two new theorems. Google's >> Gemini helped a bit to formulate them. You can find them in the appendix D >> and E of my new book. >> https://jochenfromm.github.io/PhilosophyBook/ >> <https://jochenfromm.github.io/PhilosophyBook/> >> >> The "LNC Impossibility Theorem" states that exact subjective equivalence >> between two conscious agents is impossible. I have named it after Joseph >> Levine, Thomas Nagel, and David Chalmers who first formulated the hard >> problem. >> >> I guess for mathematicians too sloppy and for philosophers too formal, but I >> am convinced a true solution looks like this. Maybe not exactly but similar. >> >> -J. .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. 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/
