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The "4 directions" are on the flat plane, whereas seeing the 4 as simultaneous faces-directions of the tetrahedron () gives a space-filling (rather than plane-covering) sense of 4-ness.I am within that tetrahedra (the story-theater or game-space), then can cross a boundary to step outside (, canal jumping). That moves me from a first-hand experience of internal/intrinsic coherence (the wholeness of the tet), into a coherent/perspectival 4+? scenario (the ?'s existence empirically validated by that which views/models the tet), which is to say another always already level of (meta-)awareness. That is the , the space and referent of . The saddle point between Euclidean (planar) and Non-Euclidian (generalized) (meta-)awareness is the grounded belief that in the limit of large spheres, the planar framework can be adaptive heuristic (e.g. NEWS maps are flat even though Earth is spherical, compasses can be useful locally)). If you zoom into a curve it will appear to flatten, if you zoom out it will tend to appear spherical. That is the multiscale nesting-balance-crossover-relevance meta-cognitive moment symbolized by the circumpunct. Both and hold some of this planar-spatial (3D-4D ) “perspective swapping as unity and at minimum two” (Rimbaud’s “I is another”). They are pointing in their different ways (Fuller from the -Analytical view, Blake from the mytho-poetic).
The reason I share and expand on it in Connections with AK “”. I am also seeking to understand deeply as a person and thinker (as a sensemaker how he figured things out, as a trimtab/actor how he acted [and the unity of sensemaking and action in ]). In making those maps of how different people (whether famous or unknown), or domains, or even figure things out — AK enacts investigation (the dance), practices (making of the ‘”ways of figuring things out” diagrams), contributes to open source, and refines/develops a format that is also a nexus to topics like , ). In the use of this “private language (some aspects of which I also externally communicate):
Personally this material is “my private sky”. Personally and publicly, this is my culture!
With some of my works — I am describing something like some of the products, as well as “dance moves”, and exercises of this culture (like [maybe AK has some exercise like “pullups for the 3 Minds”, maybe that is doing review of ]). There is a “view from the outside” or propositional aspects to this culture (e.g. you can learn and other topics without needing to know ‘s or about or anyone else’s specifically). And also I can share my first-hand experience.First-hand experience and development of practices (and language of inquiry, like ) is the first-hand experience of culture itself. A shared culture, like the shared culture of investigation, , etc. at At M4W I am leading the group (). Other people are independent investigators in different projects/areas. They externalize and welcome participation in their projects — giving direct apprentice and peer learning affordances, advancing the topic of investigation (e.g. actually advancing action research/work), and also through juxtaposition/pollination, upskilling us all as investigators (like an academic community with career stages from undergraduate, through postdoc and PI).
Allow
Geometry
,
I just wrote this now, with some tetrahedral thoughts as well as
@Andrius Kulikauskas
connections (DAF 11-20-2025). 
Context: Some colleagues were discussing using the NEWS directions (North, East, West, South) as a sort of cognitive navigational compass, or embodied mnemonic. That usage/discussed invoked some of the core aspects and memes of my phenomenology and . Here are some thought (only partially in structured order 🤣).
Connections with
here, is because the topics and 100% manually written thoughts are possibly like a “private language”, along the lines of what is for AK, and possibly like that which everyone (all minds have ?) implicitly-enactingly (firstly) or explicitly-propositionally (secondly) — and possibly even thirdly (intelligent modulation of 1st and 2nd mind), has. 
— curates, scaffolds, cultivates the possibility for multiple investigators to convene and discuss at the levels within and above their domain-specific inquiry. The investigator’s primary domains (e.g. for JH, Ecology/Art for JN) are like their firstness (areas where they know things [these people learn and know a lot within domain because they are lead by their curiosity/secondness]), their areas where they have Experience. Thus then when it comes to shared culture of 
we connect on what we don’t know, lest it be a textbook cross-disciplinary sharing. In sharing our and what we don’t know, we actually share what we know within our own domain (e.g. what I am curious about with 
), and thus can have camaraderie, empirical comparison, practice, and formal development of investigation itself. 
Discussion
Andrius: Daniel, I think of you often. I am glad to hear from you. I would like to talk and reconnect, perhaps after Thanksgiving.
@Daniel Ari Friedman
I respect you as a thinker, creative, multitalented, engaging, understanding, knowledgeable in many fields. Most relevant for me, though, is to know your personal view on life, your private language for that, and so I was very interested to read your paper “On Cognitive Art & Science”. I would love to engage you, cross-examine you, understand you and your phenomenology and private language. I’m also interested in your new Push and Pull conceptions.
I am also glad to know that you think of connections with Wondrous Wisdom and Math 4 Wisdom. You have perspectives of both an insider and an outsider, or as I would say, “stepped in” and “stepped out”, or perhaps inside and outside of the cultural tetrahedron. These last few years I keep learning more explicitly what seems important to the investigatory culture. With regard to your thoughts, for me, for genuine dialogue and understanding...
It’s important to distinguish the views we are truly, authentically, personally identifying with as opposed to just playing around with
it’s important to distinguish our testimony of what we personally, recurrently experience inside of us from any formalism we might choose to express that
it’s important to seek a universal structural language that would honor and make sense of our private languages and meaningfully communicate them rather than assume that we can’t and won’t understand each other fundamentally
Daniel, from your writing above I feel that you appreciate these distinctions I make, you are understanding and supportive. With that in mind, I am very interested, as ever, to consider how you and I and perhaps others could try to work together as investigators.
Certainly, we could collect the ways that Buckminster Fuller figured thing out. We could try to systematize them, perhaps in more than one way. I expect that the 24-fold pattern could arise and then that would help to communicate the building blocks of Wondrous Wisdom.
We could likewise attempt that for ant colonies. I think we could start by considering broadly their potential overall as exhibited by the richness of behavior of the many species, just to make it easy for us.
I am very interested to design an AI capability to generate such systematizations (or “cheat-sheets” as Kirby calls them) for any discipline or personality. I have called them “houses of knowledge” but they could also be called “knowledge palaces”. We can think of them as memory palaces whose structure directly corresponds to the relationships amongst what we are trying to remember.
In every case, the 24-fold pattern is a summary of the building blocks of Wondrous Wisdom. This includes the 4+6 structure of a system, having 4 levels and 6 pairs of levels. Formally, this can be visualized with a tetrahedron or a NEWS compass but the formal structures typically add features that may be irrelevant and confusing, for example, the notion of distance or periodicity, etc.
So personally I stay away from the formalism. But rather, with Math 4 Wisdom, I try to show how the underlying thinking can be observed in advanced mathematics.
Another topic that I am working to present is an alternative interpretation of the math of Active Inference and the Free Energy Principle. You saw my presentation and today I had another realization. The “knowledge lens” (the weights that yield the expected value) is holistic, whereas the “knowledge gained” is disparate, specific to one item. This suggest that the knowledge lens should be the answering mind, whereas the knowledge gained should be the questioning mind. Currently, the way the math is written, it is the other way around. But from my point of view, for a dialogue between P(x,y) and Q(x), why can’t the knowledge lens be P(x,y) and the knowledge gained be log 1/(Q(x)/P(x,y) or log 1/Q(x) or log 1/P(x,y)? This would mean that the sensory mind P(x,y) is used to break up the disequiilbrium with the conceptual mind Q(x) into two pieces, one of which sees Q(x) in terms of P(x,y) and gives the useful energy, and the other which sees the useless energy inherent in P(x,y) as entropy. That would work for me. It would clash with the current math of Active Inference. Anyways, I will overview Karl Friston’s keynote address and redo his math to my liking and present that to Peter Thestrup Waade. I would be very glad to talk with you about it. My thought is to make a Math 4 Wisdom video. And then Luca Possati is interested to coauthor an academic paper where he would figure out how to present this to an academic audience that would care. So this is what is on my mind.
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