You can find some numbers here in these examples. Claude helped me to simulate two basic examples: the "Breaking Bad" story where a good chemistry teacher turns into a bad drug maker, and Jonathan Haidt's theory of moral foundations which he explains in his book "The righteous mind". The first one uses SO(3), i.e. rotations in 3 dimensions, the second one uses 6 dimensions (SO(6)). https://github.com/JochenFromm/PhilosophyBook/blob/main/Empirical%20Case%20Studies.pdf
The Python script to check the "Breaking Bad" numbers can be found here https://github.com/JochenFromm/PhilosophyBook/blob/main/breaking_bad_model_so3.py How it works is you have a "valuation" vector that represents what the agent considers as good or bad. In these toy examples we have 3 and 6 dimensions, but it works for larger dimensions too. Depending on the situations which the agent encounters the valuation vector is rotated by rotation matrices from SO(N). Rotations in SO(N) for N >= 3 are commutative only when they happen around the same axis or if they are very small. Very small or infinitesimal angles approximately commute, but larger angles do not commute. This non-commutative property (AB != BA) can be used to model the part of subjective experience that is path-dependent. It sounds paradox, but if we model cognitive processes in this abstract way, we can mathematically prove theorems about things like subjective experience and moral values which are hard to measure in real life. Jonathan Haidt has used a questionnaire to get empirical data for moral values. This is one way to get data about emotional valuations but in gene ral it is hard to get. The art is to find the right level of abstraction. Simple models are easier to understand but often describe reality poorly. If we use the "spherical cow" abstraction to model a cow as a sphere we can describe the movement precisely, but lose all properties which are characteristic for a real cow. Complex models increase the risk that the thing we want to model is true by construction. The art is to find a simple well-defined model that has complex results. As David Hilbert said "The art of doing mathematics consists in finding that special case which contains all the germs of generality". By the way the tombstone from Hilbert in Göttingen contains the words "We must know. We will know". I like this attitude of boundless curiosity. https://en.wikipedia.org/wiki/David_Hilbert -J. On 2026-10-06 16:38, glen wrote: > OK. That's somewhat helpful. But what we need are numbers, right? > > So let's go with H_k(•) being a/the primary binding point. How do we measure > it? What is it in the person's physiology that we measure? It seems like the > validation has to occur in the distance measure: > > d(x,y) = min_Q∈G max_k || H_k(y) - QH_k(x)Q^-1 || > > So we need real world bindings to those symbols. x,y ∈ people, whatever that > means. H_k is the change in the state of the person after *returning* to a > prior context. Let's just allow the state (U) to be whatever for now, glucose > levels, EEG, survey measured Virtue matrix, whatever. We simply assume it's a > high dimensional, dense space. Q is just a basis change for that space. Yeah, > therein lies the assumption that we can define such a space. But under all > the assumptions, it seems like the simplest operator. > > All those bindings seem imaginable, to me. The problem I have is the loop. To > what do we bind these "closed loops"? I don't think we can bind them to > things like loop k = 1 = {home, shower, school}, because H_1 may be 0 one day > (on "autopilot") but H_1 >> 1 on another day (you were beaten and had your > lunch money stolen). > > We might be able say k = 1 = {healthy social support group, hypercompetitive > work colleagues, casually competitive Tennis group}. These supernodes may > make sense. One person's U() may not be impacted by the higher order effects > of competition: U_0→1 = 0. Another may not need social support: U_2→0 = 0. > > But if we compare those two people H_1(x) = QH_1(y)Q^-1, where Q swaps one > node for the other. But we would hardly consider those two people to have > equivalent worldviews. Or, going back to the bullying example, if X is > bullied on Tuesday and Y is bullied on Wednesday is H_1(x) = QH_1(y)Q^-1 on > Thursday? Or maybe it takes some time? Maybe H_1(x) = QH_1(y)Q^-1 a week or > so later after the initial shock wears off? Or maybe if you shift Y's > worldview by one autopilot day, *then* it's equivalent to X's? > > I guess my point is that for us to know whether the structure of the > formalism matches, in any way at all, the structure of the system being > modeled, we need a whole "modeling relation". Encode the natural system into > the formalism. Decode the formalism into the natural system. A "data first" > approach defines the [en|de]coding, then searches for inferential structures > on either side. I'm OK with your formalism first approach as long as you > commit to the followup of searching for [en|de]codings. Don't bail halfway > through and call it "done". 8^D > > > On 10/5/26 2:28 PM, Jochen Fromm wrote: >> Good question. Yes, without experimental confirmation it is just fancy >> mathematics. The model used for the proofs is an abstract model. It >> describes how mindsets/worldviews of adaptive agents diverge and converge. >> >> In a simple toy model it works like this: >> >> >> A context/nodecan be: the places the agent moves through like home, school, >> work, street. >> >> >> An edge means stepping from one context to another: home-street, home-work, >> .... >> >> >> Moving along the edges changes the internal valuation matrix of the agent. >> Every time an agent moves along an edge, their internal valuation frame gets >> rotated or updated by an edge matrix. The experience of making that specific >> transition reshapes how they evaluate things. >> >> >> If we reach the same context again we get a loop. A holonomy H measures how >> a valuation changes after a loop of contexts. It is the total, combined >> shift in the agent's worldview after completing that full loop. >> >> >> A "breaking bad" model of two agents would include two agents who start with >> slightly similar worldviews. One interacts with a group that thinks breaking >> the rules is bad, and the other joins a group that believes breaking the >> rules is necessary to survive because the world is cruel or rules have been >> imposed by bad people. >> >> >> A more complex model would be cultural dissemination. As you know Robert >> Axelrod created an agent-based model of cultural dissemination based on >> local convergence global polarization. It would be interesting to combine >> his model with the new gauge theory model. >> >> >> Other areas of experimental verification would be >> >> + Group psychology and organizational psychology (group formation and >> fragmentation, group influence in individual) >> >> + Political science (emergence of new movements, radicalization pathways, >> the threshold of schisms, etc) >> >> + Sociology (what holds societies together, and what is the role of >> socialization and institutions in maintaining social cohesion, to what >> extent is the individual shaped by society) >> >> >> -J. >> >> >> >> -------- Original message -------- >> From: glen <[email protected]> >> Date: 10/5/26 8:00 PM (GMT+01:00) >> To: [email protected] >> Subject: Re: [FRIAM] A field theory of understanding >> >> I haven't finished reading Jochen's theorems yet. But it seems obvious to me >> that he's not claiming experiences are private so much as they are unique. >> It seems more about irreversibility or unreachability than closedness. >> >> And I'm no expert on Wittgenstein, but my own perspective has been that his >> dictum was more about coherent form as opposed to ontology. I.e. if your >> language/formalism is inadequate for its target, then it's useless for >> talking about that target. It's similar to Rosen's argument that >> predicativity is inadequate for describing complex systems. Maybe some of us >> just toss up our hands and give up when our language seems inadequate. But >> others of us develop new language. And still others push the current >> language as far as it can possibly be pushed until we're convinced of its >> [in]adequacy. >> >> But back to the first theorem. This seems much closer to a theory (by which >> I mean a body of assertions falsifiable through measurement). But what still >> seems missing are the bindings. We don't need bindings for *every* symbol in >> the math. Some symbols can be internal. (What that _means_ is debatable.) >> The "numerical" sections for both give a good indication of what we have to >> bind. Theorem 1 uses {x,y,z,roll,pitch,yaw,t}. Theorem 2 doesn't seem to >> have a clear binding point. Maybe I just missed it. So we can stick to T1. >> >> I find the binding mysterious. I have no idea what the points in the space >> might be. It seems to rely on the word "concept", as in "returning to the >> same baseline situation or concept". But that seems like assuming the >> consequent to assume something like a concept, then prove something about >> independent loops returning to it. So that can't be the binding point. Maybe >> H_x is the binding point, some kind of Δconcept. That's easier to bind >> because we *can* measure the changes in the brain/CNS before an after an >> experience (e.g. showing you a picture while you're in the MRI machine). >> >> So my question is: Which of these symbols are bound to measurements we can >> (or may one day) be able to make? Without that binding, all this math is >> merely decorative, great for hypnotizing your math-envious friends but >> useless for science. >> >> On 10/4/26 7:40 AM, Eric Charles wrote: >> > As some of you know, I recently finished a draft of The Book (the one I >> have been writing for around 15 years now, with a foundation in Nick's >> writing, but extended beyond that). I have circulated drafts to some >> readers... so if any of you are interested.... >> > >> > This appears in the epilogue and speaks directly to the question here: >> > >> > Wittgenstein laid down a gauntlet to 21^st century philosophers, “Wovon >> man nicht sprechen kann, darüber muss man schweigen,” which is often >> translated to, “About what one can not speak, one must remain silent.” This >> has been broadly taken to indicate that we should shut the heck up about a >> wide range of topics regarding the mind, under the assumption that /all/ >> such talk is a prime example of that-about-which-we-cannot-speak. /If/ >> mind-body dualism is true, either in its classical form or its modern neural >> form, then your “feeling of anger” or “experience of blue” is something that >> exists only in your mental space, that only you could access, and my >> “feeling of anger” or “experience of blue” is something that exists only in >> my mental space, that only I could access. And /if/ that is how minds work, >> then we can try to talk about such things all we want, but ultimately it is >> /impossible/ for us to talk about them sensibly. Wittgenstein’s various >> though t experiments >> > demonstrated this repeatedly. Understood in this fashion — understood in >> combination with a /separate/ commitment to dualism — many people have >> understood Wittgenstein to be one more philosopher offering proof that a >> science of psychology is impossible. >> > >> > However, given [William] James’s influence on Wittgenstein, we do not see >> his dictum as pointing to a fatal flaw. Instead, we understand his dictum as >> pointing out a dilemma faced by the field of psychology: Those interested in >> psychology must /decide/ whether the phenomena they are discussing are, >> inherently, an example of that-of-which-we-/cannot/-speak, or if the >> phenomena they are discussing might very well be the types of thing we /can/ >> speak about sensibly. >> > >> > We assume, if you got this far, that you are the type of person deeply >> interested in psychological happenings. If, after all the scrutinizing you >> can muster, you believe you are interested in something that cannot be >> talked about sensibly, then you should find a way to deal with the >> inevitable sadness and disappointment of that situation, and then you should >> try to find other things to be interested in. We, however, prefer the other >> option. We believe psychological phenomena are the types of things that >> /can/ be talked about sensibly, and we have endeavored to show that such a >> position can work, in practice. We believe there is nothing within our >> attempt to understand psychological terms that is fundamentally different >> than Lavoisier’s attempt to understand the elements. Like Lavoisier, we may >> be right or wrong about particular details, but only in the types of ways >> that can be readily corrected over time… because the things we are talking >> about can be investigated readily, >> > with no magic or vital essence, or other mystical factors having been >> included. >> > >> > We believe that psychological phenomena are the types of things that >> /can/evolve, that /can/develop, and that /can/be studied. They are aspects >> of behavioral design. And that design deserves to be recognized and >> accounted for, to be both described accurately and explained well. >> > >> > >> > >> > Best, >> > Eric >> > >> > >> > <mailto:[email protected]> >> > >> > >> > On Sun, Oct 4, 2026 at 4:40 AM <[email protected] >> <mailto:[email protected]>> wrote: >> > >> > If this is a polite way to say shut up then please ignore the rest. >> What Wittgenstein wants to say by "whereof one cannot speak, thereof one >> must remain silent" is apparently that things like anxiety, pain, >> nothingness, religion, the meaning of life, subjective experience or >> feelings lie outside the logical world and cannot be meaningfully described >> in words. That is one way to see it. I see it differently. The problem is if >> we remain silent we will never understand it. I prefer Karl Popper's >> optimistic view to the depressive pessimism of Wittgenstein. Popper argued >> that substantial, real-world problems exist in philosophy, not just >> linguistic puzzles as Wittgenstein claims. >> > >> > For me the things we cannot describe meaningful (yet) are the >> interesting ones. We just need to find the right languages, theories, >> perspectives or metaphors. One useful metaphor for pain is as you said "an >> emergency organization of behavior in which the agent deploys physical and >> social defenses of various sorts". If we describe pain as a mechanism to >> protect a person it is personal by definition. And yet we all can understand >> what it is like to feel pain in general. If we watch the movie "Marley & Me" >> for instance we can understand what it is like to lose a loved dog because >> most of us have experienced such a loss of a cat or dog or hamster or horse >> ourselves ( by the way we have a new horse now named Mack which looks like >> this https://www.youtube.com/shorts/VDyNyTsMccg >> <https://www.youtube.com/shorts/VDyNyTsMccg> ). >> > >> > This is in my opinion the solution to the hard problem: the film >> maker turns a 1st-person view in a 3rd-person view, the cinema conveys the >> 3rd-person view to the persons in the audience, and they are able to >> understand roughly what-it-is-like-to-be the lead actor because they see and >> hear what it goes through and they know what it feels like to experience >> pain, loss, and suffering. According to Wittgenstein cinemas should not be >> allowed to exist ("one must remain silent"). But people like them because >> they want to know what-it-is-like-to-be someone else. Cinemas help to solve >> the hard problem. >> > >> > -J. >> > >> > On 2026-10-04 03:35, Nicholas Thompson wrote: >> > > You can say that. But you end by reasserting the privacy of pain. >> And >> > > … >> > > >> > > Wovon man nicht sprechen kann, darüber muss man schweigen >> > > >> > > You just cannot have it both ways. >> > > >> > > N >> > > >> > > Sent from my Dumb Phone >> > > >> > > On Oct 3, 2026, at 2:26 PM, [email protected] >> <mailto:[email protected]> wrote: >> > > >> > > Claude was not happy about the theorem proofs that Gemini created. >> > > And Jon also mentioned that they are not waterproof. So I asked >> Claude >> > > and Gemini if they could write a new proof. They could. I asked >> them >> > > if we could use gauge theory to explain subjective experience - >> gauge >> > > invariance to describe objectivity, and symmetry breaking for >> > > subjectivity. Both Claude and Gemini said yes, and Claude was able >> to >> > > formulate a proof that both could agree on (combining two AIs which >> > > have different personalities often gives better results than just >> > > using one). Gemini is curious and creative, Claude is accurate and >> > > precise. The result was a proof for a theorem of a new "field >> theory >> > > of understanding". I understand only half of the mathematics, but >> the >> > > physicist who use gauge theory for quantum field theories also >> > > understand only half of it. >> > > >> > > I have uploaded the new proofs here. The theorems are named the >> same, >> > > only the proofs are different. If they are more convincing than the >> > > old ones, then the idea is to replace the proofs in the appendix >> with >> > > this version. In my opinion the solution to the hard problem looks >> > > similar to this - in combination with the other things written in >> the >> > > rest of the book. >> > > https://jochenfromm.github.io/PhilosophyBook/QualiaTheorems.pdf >> <https://jochenfromm.github.io/PhilosophyBook/QualiaTheorems.pdf> >> > > >> > > Paradoxically the qualia part that is most mysterious for some >> > > researchers is not a problem for others at all. Nick for example >> wrote >> > > he does not believe in qualia and sees emotions as regulations. In >> a >> > > post he argued "To me, pain is an emergency organization of my >> > > behavior in which I deploy physical and social defenses of various >> > > sorts.... To me, the question, “What is it like to be X?”, has >> > > been fully answered when you have said where X-like people can be >> > > found and what they will be doing there... for me, feeling is a >> kind >> > > of doing, an exploring of the world". I would agree to most of it >> but >> > > for me what an animal is doing alone gives us only a hint what it >> > > feels. If a horse for example is injured and feels pain, it does >> not >> > > scream or cry, and you see no tears. Only if you know the animal >> well >> > > you realize that the behavior is slightly different, for example by >> > > the things it is not doing. I am certain animals feel pain just as >> > > intense as we do, but it is hard to recognize from th >> > > eir behavior alone. If it would be better visible, would we still >> eat >> > > pigs and cows in large amounts (this reminds me of "Why We Love >> Dogs, >> > > Eat Pigs, and Wear Cows" from Melanie Joy)? >> > > >> > > -J. >> > >
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