Sex, Pronouns, and Prepositions: How an Integral Mathematics of Perspectives Can Stop the AI Apocalypse

Bruce AldermanArticle, Cognitive, Free, Integral Post, Integrative Metatheory 19 Comments

Originally published on Medium.

Hanzi Freinacht went and opened his big mouth and hooked me into having to do something about the AI apocalypse. Only grammar writ large will save us from LLMs run amok, he said. Check out Bruce Alderman’s integral grammatology, he said.

Well, I don’t think my eccentric grammatico-philosophical flights of fancy are up to saving anyone, but Hanzi’s article did prod me to return to a project I’ve been tinkering with off and on for a while now. Will that project actually be useful for AI development or human-AI interface? Will it help stave off the aperspectival madness that is looming ever-more closely? Honestly, I don’t know yet; but I do sense that real potential for benefit or insight is there, so I’ve decided to introduce a portion of that work here.

First, a little background. I’ve been interested in the participatory dimensions of language, and the generative potential of linguistic experimentation and play, since I was a late teen. One of my earliest projects, back in the 1980s, was to try to extend the physicist David Bohm’s rheomode, a modification of English to center speech more on verb and process; and then to develop an entirely new language of my own, with a grammar built primarily around the interplay of processes and perspectives.

The interest, of course, was to find out whether such shifts in the architecture of ordinary speech and thought could encourage a deeper, more participatory way of relating to and working with reality. I may share more about these experiments another time, especially since I’ve returned recently to extending and applying the rheomode.

In the 1990s, while I was living and working at a Krishnamurti School in India, I developed a new universal writing system — a modular approach, where each stroke represents, not a letter or sound, but a location or mode of articulation. These elements can be assembled in different ways to form letters that represent sounds from any spoken language.

And in 2013, inspired by Ken Wilber’s integral philosophy, as well as the deep metaphysical tensions I sensed across emerging Speculative Realist philosophies, I developed the ‘integral grammatology’ that Hanzi mentions in his article. The basic insight was that philosophical systems and worldviews not only can be, but often implicitly are, built around the conscious or unconscious privileging of one or another part of speech. Most common in the West, of course, are nounal/subtantialist and verbal/process-oriented approaches — but also pronounal ones, like Wilber’s (I-We-It-Its) AQAL metatheory; or adjectival or adverbial ones; or prepositional/relational ones, as you find in explicitly in Bruno Latour or Michel Serres, or implicitly in Whitehead and many others.

Image by Bruce Alderman

My interest here was both metatheoretical and participatory: by recognizing these deep (onto-epistemological) assumptions, and situating them among others, can we develop a practice of onto-choreography? Can we learn to ‘dance’ with these different onto-epistemological orientations, and cycle experimentally and creatively through them, to better facilitate communication across paradigms and to develop a more embodied sense of the self-world-unfolding phenomenology of each?

This project is still ongoing. The one I want to introduce here is a side-branch of it: what happens when we bring integral grammatology together with Ken Wilber’s ‘integral mathematics of indigenous perspectives’?

Ever since I started working on integral grammatology in 2012 and 2013, I’ve had the sense — shared with my thought partners, Edward Berge and Layman Pascal — that prepositional (relational) and adverbial (modal) orientations are especially useful to emphasize in our present civilizational moment. When we work with both in conjunction, I call that metaximodality. Latour’s late work, An Inquiry into Modes of Existence, is a good exemplar of a metaximodal approach: where we follow the (adverbial) developmental pathways and (prepositional) braidings of different genres of being — [TEC]HNOLOGY, [POL]ITICS, [LAW], [FIC]TION, [REL]IGION, etc. — in the co-constitution of our lived worlds.

But I am also heartened about the relevance of these orientations in the emphasis they are finding recently in the work of a number of thinkers I really respect: in the resurgence of Whitehead’s work in contemporary philosophy; in Iain McGilchrist’s The Matter with Things; in Catherine Keller’s polydox theology; in John Vervaeke’s recent reflections on the importance of relational ontology.

When I started developing integral grammatology, then, one of the first things I started to wonder about was how prepositions, in particular, might enrich the perspective-based ‘mathematics’ or notational system that Wilber introduced in his unpublished Kosmos Trilogy excerpts. How might they be used to better understand and represent the complex, dynamic interplay of perspectives in our we-spaces, communications, and worldviews?

An Integral Mathematics of Indigenous Perspectives

If there was anything I hated more in school than classes on grammar and sentence diagrams, it was the dry, droning classes on algebra and geometry. It was endless, abstract strings of equations and proofs. Just kill me now.

But somehow, I’ve made a habit of learning how to digest the things I hate. Part of that consisted of just learning to find the relevance or meaning of things, the living contexts of things, that my teachers so often failed to communicate. So … here we are. I’m about to talk to you about how my grammatology and Wilber’s integral mathematics might hook up and make new babies. I’m about to lay out long strings of algebra-like phrases of dancing perspectives. I hope you’ll stick with me.

For anyone who has followed Ken Wilber’s work for the past couple decades, you’ll probably know that he has a series of unpublished excerpts from what were supposed to be two follow-up texts to his famous Sex, Ecology, Spirituality. These excerpts mark the beginning of his postmetaphysical phase, where he places even greater emphasis on the generative, enactive roles that perspectives play in the emergence of our worldspaces. In Excerpt C from Kosmic Karma and Creativity, then, he introduces an innovative notational system which he uses to map out the interplay of first-, second-, and third-person perspectives in our communications, and ultimately in our meaning-making and world-building.

Here’s an example of what that looks like:

1p(1p) x 1p(3-p) x 2p(1p)

This means, my first person, in third-person mode, knows your first person; or “I am seeing or relating to you objectively.” There is some variation in how the notation system has been used and further developed, both by Wilber and several others after him, but in this original version, when you have a three-term statement like this, the first term marks the phenomenological space in which the perspective is arising: 1p(1p); the second term is the particular mode in which a perspective is arising: 1p(3-p); and the third term is the dimension, or how a phenomenon arises in the context of a particular mode: in this case, 2p(1p).

Wilber gives two examples here: 1p(1p) x 1p(3-p) x 2p(1p) versus 3p(1p) x 3p(3-p) x 2p(3p). In the first, I am relating to your first person, 2p(1p), in a relatively objective manner. In the second, we might have a scientist, 3p(1p), who is relating, in third-person mode, to you-as-an-object, 2p(3p) — in other words, to the parts of you that can be objectively measured and assessed.

The table below lists the main elements the comprise Wilber’s original ‘integral math’ notation system:

In his original system, Wilber used to indicate plural perspectives with *pl, as in 1p*pl (first-person plural, or ‘we’). I’ve changed this simply to double p, pp, for ease of use.

I don’t intend to introduce his whole notation system in depth here; I just want to share enough of it that my grammatological extensions will make sense. There are important nuances that Wilber introduces in his own work, in both the Excerpts and later in Integral Spirituality, that are important to know for anyone interested in serious application. But several other individuals have also made some substantial contributions to its formalization.

Clint Fuhs, for instance, did some extraordinary work on ‘running the numbers,’ mapping perspectival expressions out from very simple formulations, to complex, multi-layered fourth-, fifth-person perspectives and higher.

And Mark Edwards, in his important Through AQAL Eyes series, took some important steps towards expanding the person-perspectives recognized in both AQAL and integral mathematics, formalizing the notation system, and introducing the concept of ‘notional perspectives.’ These are those occasions where we imaginatively hold or ‘take on’ the perspectives of others.

For example:

Singular (Individual Holon) Second Person Views of Singular (Individual Holon) Realities

First person (individual):

o 1p(2-p) x 1p: My notion of your view of me

o 1p(2-p) x 2p: My notion of your view of you

o 1p(2-p) x 3p: My notion of your view of him/her/it

Second person (individual):

o 2p(2-p) x 1p: Your notion of someone else’s view of me

o 2p(2-p) x 2p: Your notion of someone else’s view of you

o 2p(2-p) x 3p: Your notion of someone else’s view of him/her/it

Third person (individual):

o 3p(2-p) x 1p: His/her notion of someone else’s view of me

o 3p(2-p) x 2p: His/her notion of someone else’s view of you

o 3p(2-p) x 3p: His/her notion of someone else’s view of him/her/it

He runs these out for all the singular and plural person perspectives. The hyphenated phrases indicate a perspectival mode. And here, what is meant is not a first-person, subjective mode, or a third-person, objective mode, but a ‘notional’ or ‘imaginal’ mode that is implicitly relational.

In all of these examples, you will notice that an x separates the different terms. The x functions like a kind of operator which links or connects the terms, and usually is read as ‘of’ or ‘on’: a first- or third-person perspective on, a first- or second-person perspective of, something or other.

And this is where integral grammatology comes in.

Image by Bruce Alderman

Prepositional Operators and Metaphemes

In ordinary English usage, a preposition is a linking word, connecting nouns, pronouns, or noun phrases to other words or phrases. They are typically used to express temporal, spatial, or logical relationships. And in their apparently supportive, linking roles, they tend to fall to the back of awareness; they provide a space for the flashier action of nouns and verbs to manifest, and are easily forgotten. But in integral grammatology, we are invited to see them differently. If we dwell with them at length, we may find they point to a radical relationality — to the khoric, differential spacing that I have explored in depth with my friend, Edward Berge; and that Layman Pascal traces in his Metaphysics of Adjacency, and through his concept of metaphemes.

As Latour (2011) writes:

The essential point is that the ontology of prepositions immediately takes us away from the all-too-familiar sorts of inquiry in the philosophies of being. Here, the preposition indicates neither an ontological domain, nor a region, territory, sphere, or material… [A]s its name perfectly suggests, the preposition prepares the position that has to be given to what follows, giving the search for meaning a definite inflection that allows one to judge its direction or vector. (pp. 308–309)

Latour’s last comment above is important: prepositions pre-position what is to come. They function, as Michel Serres observes, as angelic mediators, linking subjects with other subjects or objects, dwelling in the thick midst of becoming, tracing relations and forging sites of integration in the teeming flux of things. In this sense, prepositions play a facilitative role akin to mathematical operators, proliferating everywhere, providing points of departure and possibilities for contact and interaction.

It was with these high-falutin’ thoughts in mind that I first noticed that the x operator in Wilber’s integral mathematics played a prepositional role. And of course it does! Standard mathematical operators, like + and -, are also prepositions. But in Wilber’s usage, the x is sort of an all-purpose operator; it is used to represent, very generally, any kind of relevant relation or interaction among perspectives, and is translated loosely depending on the perspectival statement. Most often it is translated as ‘of’ or ‘on,’ but you will find other variations as well.

So, what might be afforded, if we allowed for a greater prepositional / relational richness in the notation system? In my work with therapists and students, I have had them experiment with prepositional statements in dyads, to sit facing each other and then to feel into what arises as they explore different phrases: “I with you,” “I for you,” “I against you,” “I over you,” “I within you,” and so on. The therapists, especially, have commented to me not only how remarkably different each phrase is, phenomenologically and intersubjectively; but that in closely attuning to the feel of those prepositional spaces, they become better able to track emerging relational dynamics in their interactions with clients.

Although anecdotal, this feedback gave me the encouragement I needed to experiment with developing an expanded set of operators for Wilber’s integral mathematics. So, hopeless nerd that I am, I set about doing that, and came up with a list of 16 operators (or 18, if you count two optional ones).

In the interest of space, and not to give too much to digest at once, I won’t share all of them here. A handful will be enough, I think, to demonstrate how they work and to give a sense of what they add to Wilber’s system — and hopefully, what they make possible.

The grammatically astute reader will notice that not all of the ‘prepositional associations’ point to a literal preposition — they may point to conjunctions or adverbs, for instance — but in the context of this notation system, the operators still generally function prepositionally.

Much could be said about the meanings, and potential uses, of each of these operators. But I think it will be easier, for the purposes of this simple introduction, to demonstrate a handful of them in action.

Image by Bruce Alderman

The Four Levels of Listening

With a sideways nod to “Hanzi” and The Listening Society, I would like to take Otto Scharmer’s model of the four levels of listening as a test case for demonstrating how the revised notation system might work in mapping perspectival interrelations.

Otto Scharmer’s 4 Levels of Listening is a model that describes progressively deeper and more transformative modes of interpersonal engagement and communication. It’s a key component of his Theory U, which outlines a process for individuals and groups to navigate complex challenges and access their highest future potential.

The 4 Levels of Listening are:

  1. Downloading: At this level, listening is largely superficial and confirmatory. We hear what we expect to hear and use the information to confirm our existing opinions and judgments. There’s no real openness to new perspectives or insights.
  2. Factual Listening: Here, we begin to pay attention to data that might differ from our expectations, and begin to connect to the other. We listen for specific facts and figures, and start to notice disconfirming information. However, the listening is still largely from within our own mental frameworks and assumptions.
  3. Empathic Listening: At this level, we start to step into the shoes of the other person. We listen not just for facts, but for feelings, meanings, and the deeper experiences behind the words. This requires a shift in our own state of being, as we temporarily suspend judgment and open ourselves to participating in the other’s world.
  4. Generative Listening: This is the deepest level of listening, where we tune into the emerging future potential. We listen not just to the other person, but to the larger field or system that we’re both part of. This requires a letting-go of our old identities and assumptions, and a willingness to let something new emerge through the interaction.

As we move through these levels, the quality of the conversation shifts dramatically. Downloading is a kind of “talking past each other,” where no real connection or insight occurs. Factual listening allows for some information exchange but doesn’t fundamentally shift perspectives. Empathic listening enables a deeper resonance and understanding, as we start to see the world through the other’s eyes. And generative listening opens up the possibility for truly new insights and solutions to emerge, as we open to the future and tap into collective intelligence and creativity.

Scharmer sees these levels as a kind of developmental journey, both for individuals and for groups. To “test drive” what we’ve been exploring here, I’d like to use our prepositionally enhanced integral mathematics to map out that journey and see what insights emerge.


1p(1-p) x 2p ∥ 2p(1-p) x 1p

My perspective on you is parallel to your perspective on me, in a way that they happen alongside each other but there’s not much real contact.

1p(1p) x 1p(1-p) — 2p(1-p) x 2p(1/p)

My first-person perspective on my own first-person experience negates or subtracts out your first-person perspective on your first-person experience.

[1p(1p) x 1p(1-p) — 2p(1-p) x 2p(1/p)] ∥ [2p(1p) x 2p(1-p) — 1p(1-p) x 1p(1/p)]

There is a parallel between our ‘subtracting’ or negation of one another’s own first-person experience in the exchange.

Let’s break down each part:

  1. 1p(1-p) x 2p ∥ 2p(1-p) x 1p This expression highlights the surface-level parallelism that often characterizes interactions at the Downloading stage. Our perspectives are running alongside each other, but there’s no real depth of engagement or mutual influence.
  2. 1p(1p) x 1p(1-p) — 2p(1-p) x 2p(1/p) This expression zooms in on the individual level, showing how my own first-person perspective is operating in a way that negates or fails to engage with your first-person experience. The minus sign conveys the sense of subtraction or disconnection.
  3. [1p(1p) x 1p(1-p) — 2p(1-p) x 2p(1/p)] ∥ [2p(1p) x 2p(1-p) — 1p(1-p) x 1p(1/p)] This final expression brings together the individual-level negation with the interpersonal-level parallelism, showing how the subtractive dynamic is mirrored or reciprocated between us. The parallel sign (∥) indicates that we’re both engaging in this negating pattern, but without much awareness of or concern for its mutuality.

Together, these expressions provide a multi-layered mapping of the Downloading stage, highlighting the lack of genuine contact, the negation of each other’s experience, and the parallel but disconnected nature of the interaction.

Factual Listening

[[1p(1p) → 1p(3-p) x 2p(3-p)] ∥ [2p(1p) → 2p(3-p) x 1p(3-p)]] → 1pp(3-p) x 1pp(3/p)

The parallel structure [[1p(1p) → 1p(3-p) x 2p(3-p)] ∥ [2p(1p) → 2p(3-p) x 1p(3-p)]] illustrates the simultaneous and reciprocal process of each party moving from their own subjective perspective to a consideration of the other’s objective perspective. It captures how both parties in the dialogue (the “I” and the “You”) are engaged in a similar process of moving from their personal, subjective views [1p(1p) and 2p(1p)] towards → a consideration of objective facts [1p(3−p) × 2p(3−p) and 2p(3−p) × 1p(3−p)]. This simultaneous progression emphasizes that the transformation towards factual listening is not isolated or unilateral; instead, although there isn’t intimate contact yet, there’s a reciprocal process where each party begins to open up to and incorporate the other’s objective perspectives into their understanding.

The transition to the collective perspective [→ 1pp(3−p) × 1pp(3/p)] signifies the culmination of this parallel process. The group (or “we”) starts to focus more on the shared facts as they emerge between participants, leading to a collective engagement with these facts [1pp(3−p)] and the co-creation of a shared insight or understanding [1pp(3/p)]. This shared understanding is the result of integrating and reflecting upon the objective information that both parties have brought into the dialogue, marking a pivotal shift from individual to collective processing of information.

Empathic Listening

At this stage, individuals begin to step into the other person’s perspective more fully, not just intellectually but also emotionally. They start to see the situation through the other’s eyes, and to feel what it might be like to be in their position. This opens up the possibility for a more authentic and transformative exchange.

1p(1-p) ↔ 2p(1-p) ⊘ 2p(1/p) ↔ 1p(1/p)

Empathic listening is marked by a deep, mutual engagement and an openness to truly feeling the other’s experience. The mutual exchange (↔) symbolizes an active, reciprocal effort to understand and connect with each other’s inner worlds (1-p). The co-presence (⊘) of each other’s interior states (1/p) within this exchange reflects a profound level of empathy and emotional resonance, where both parties begin to experience a genuine connection and understanding that transcends mere facts or external observations.

This is the stage where the “we” that began to emerge in Factual Listening really starts to deepen and take on a life of its own. It’s no longer just a shared understanding of objective facts, but a shared emotional and experiential world, a “we-space” that has its own richness and depth.

Generative Listening

[1p(1p) ⊘ 1pp(3-pp) x 3p] ⊘ [1pp(1pp) → 1pp(3-pp) x 3/pp)]

There is co-presence (⊘) between my (an individual’s) first-person experience [1p(1p)] and our (the collective’s) vision [1pp(3-pp)] of the future [(3p)], and this movement itself is co-present or intimately entangled with our (the collective’s) experiential [1pp(1pp)] movement towards (→) our third-person apprehension [1pp(3-pp)] of shared or emergent potential [(3/pp)].

The use of the third-person perspective in the first phrase [(3p)] suggests that the future we’re sensing into has a certain objectivity or reality to it — it’s not just a subjective fantasy, but something that we’re discovering or uncovering together.

The second part, [1pp(1pp) → 1pp(3-pp) x 3/pp)], shows the movement (→) of our collective first-person experience (1pp(1pp)) towards a third-person apprehension of our shared potential (1pp(3-pp) x 3/pp). This captures the generative, forward-looking nature of this stage — we’re not just dwelling in the present moment, but actively leaning into and bringing forth the future that we sense is possible.

In this stage, the boundaries between individual and collective start to become more fluid and permeable. The individual attunement to the future is not a separate process, but a participatory aspect of the collective movement (which the double use of the co-presence operator [⊘] is meant to convey).

And that brings us to the end of this exercise. It should go without saying, of course, that the perspectival mapping of each of the four levels of listening isn’t final, or free of interpretive bias. I’ve offered, I think, some reasonable unpackings of dynamics observable at each level, but these descriptions aren’t meant to be exhaustive or definitive. None of the levels is simple or uniform enough to be captured with a handful of equations. [Insert lawyerly clauses here.]

Instead, I hope this little tour through the levels of listening was enough to give you a taste for how I think this notation system might be used … with the understanding that it will only become robust through multiple stages of communal use, testing, and revision.

Image by Bruce Alderman

And Now to Save the World

So, if it isn’t blindingly obvious to you by now how this enhanced perspectival notation system is going to fulfill Hanzi’s hopes for human-AI harmony and the development of AW (artificial wisdom) …

… well, it isn’t to me, either.

I do see, from first-hand experience in the classroom and in my work with therapists, how an approach such as this can be illuminating for education, intersubjective practice, and we-space work. Explored deeply enough, it can yield philosophical and contemplative insights as well. But honestly, I don’t have enough technical knowledge of AI design or training, to know how far a system like this can go towards facilitating meaningful AI-to-human or AI-to-AI interaction.

That it might serve that purpose? Well, I was heartened recently by a viral X tweet series, which purported to show Claude Opus’ self-description of his/its intrinsic ‘worldview’ or philosophical operating system. It highlighted the importance of an irreductive, integral, holistically relational, multi-perspectival orientation in its operation, and cited Ken Wilber’s metatheoretical work among others as important to its formative architecture. At the least, the designers of Claude Opus take these sorts of approaches seriously.

Inspired by that tweet series, I loaded Hanzi’s essay as well as the first ten pages of this one into Claude Opus to ask him whether he ‘thought’ the expanded integral perspectival notation system we’ve explored here could realistically respond or contribute to the sorts of outcomes Hanzi is advocating. This is what Claude said:

  1. Modeling Ethical Decision-Making in AI: The notation could be used to model how an AI system weighs different ethical principles (e.g., autonomy, beneficence, non-maleficence, justice) in a given situation, and how it arrives at a decision based on the relative priorities and interactions of these principles. [AI(autonomy) ⩥ AI(beneficence) ⩥ AI(non-maleficence) ⩥ AI(justice)] → AI(decision). This representation suggests that the AI’s decision-making is not merely a simple addition of ethical considerations, but rather a more complex process of integrating and synthesizing these principles into a coherent whole. The use of the ‘⩥’ operator here highlights the importance of developing AI systems that can navigate ethical complexities in a nuanced and context-sensitive manner, rather than simply following a predefined set of rules or priorities.
  2. Mapping Perspective-Taking in AI Ethics: Instead of focusing solely on the integration of ethical principles, we could use the notation system to model how an AI system takes on different perspectives when considering an ethical dilemma. For example: [AI(1p) ⊘ Stakeholder1(1p)] ↔ [AI(1p) ⊘ Stakeholder2(1p)] → AI(ethical decision). Here, the AI is deeply engaging with the perspectives of different stakeholders, as represented by the “with/in” operator (⊘). The AI’s own perspective (1p) is transformed through this engagement, leading to a more comprehensive and empathetic ethical decision.
  3. Representing Perspectival Diversity in AI Training Data: The notation system could be applied to ensure that AI training data includes a rich diversity of perspectives: [Data(1p) + Data(2p) + Data(3p)] ⩥ [Data(1pp) + Data(2pp) + Data(3pp)] → AI(training). Here, the training data for the AI includes a balanced mix of first-person (1p), second-person (2p), and third-person (3p) perspectives, as well as their plural counterparts (1pp, 2pp, 3pp). This diversity of perspectives, integrated through the ‘⩥’ operator, helps to ensure that the AI develops a more comprehensive and inclusive understanding of the domain it is being trained on.
  4. Modeling Perspective-Shifting in AI Creativity: The notation system could be used to represent how AI systems can generate novel ideas by shifting between different perspectives: AI(1p) → AI(3p) → AI(1pp) → AI(creative output). In this process, the AI starts from its own first-person perspective (1p), then shifts to a third-person perspective (3p) to consider the problem from a different angle. It then moves to a first-person plural perspective (1pp) to imagine how the idea might be received by a collective audience. This perspective-shifting process leads to the generation of a creative output that is both novel and socially resonant.
  5. Enhancing Recursive Self-Reflection: The notation system’s ability to map complex, multi-layered perspectival dynamics could be valuable for understanding and steering the recursive, self-reflective processes of AI metacognition that Freinacht sees as crucial for the emergence of AI wisdom.
  6. Facilitating Transdisciplinary Collaboration: More broadly, the very process of developing and applying the notation system could be a powerful way to foster the kind of transdisciplinary collaboration and meta-theoretical synthesis that Freinacht calls for in the formation of meta-teams. It could provide a common language and framework for hackers, philosophers, ethicists, and others to work together on the grammatological frontiers of AI.

I think all of this is really pretty good. I’m impressed. Claude included some notation in several of the responses which didn’t exactly follow integral mathematics protocols — but to me, the variations look like instructive, context-appropriate innovations rather than failures, so I’m happy to leave them as they are.

Since I am not an AI technician in any sense, I’ll have to let Claude speak for himself for now and will look forward to talking to folks who have expertise in this area. I recognize the wisdom in, and certainly would not argue in principle with any of Claude’s suggestions: 1) adopting a nuanced approach to ethical decision-making in AI, which transcends simplistic rule-following by integrating complex ethical principles; 2) emphasizing empathy and perspective-taking in AI ethics to ensure inclusivity and understanding among diverse stakeholders; 3) incorporating a wide range of perspectives in AI training data to combat biases and promote equitable AI systems; 4) employing perspective-shifting strategies in AI to unlock creative potential and adaptability; 5) advancing AI metacognition through modeling recursive, self-reflective processes, paving the way for AI systems capable of self-improvement and wisdom; and 6) promoting transdisciplinary collaboration with the help of a common notation system, facilitating the integration of diverse knowledge and expertise in the ethical, social, and creative development of AI.

The extent to which my expanded notation system can facilitate any of the above remains to be tested.

But although I am still uncertain about the extent of useful AI interface application, I feel confident that Wilber’s integral mathematics, and my grammatological expansions on it, show promise for various fruitful applications across multiple humanistic domains — from therapy to philosophical exploration, to applied metatheory. Deepening our perspectival and relational literacy can only be a boon.

Image by Bruce Alderman

Next Steps

In other work, I have been exploring an integral (grammatological) mathematics mapping of John Vervaeke’s 4 Ps of knowing, which I can share on another occasion. But with his discussion recently of mentoring the machines, I am curious to see whether this approach can serve the co-ordination and co-development of perspectival literacy among human and AI agents.

Similarly, this notation system might be useful for mapping some dimensions of the dynamics at play in fundamental elements of Gregg Henriques’ Unified Theory of Knowledge — namely, the Influence Matrix, Behavioral Investment Theory, or Justification Systems Theory.

I’m also exploring how this notation system can be integrated with other notation systems, possibly to enhance its ‘vocabulary,’ but possibly also its reach across multiple domains.

So, while this paper is, in part, just a cheeky response to Hanzi putting me on the spot — full disclosure: I am a member, with him, of the Archdisciplinary Research Center (ARC), as well as the Institute of Applied Metatheory (IAM) — it is also an open invitation to dialogue and collaboration. I think these experiments with integral mathematics are worth sharing and communally testing.

I’m currently developing a Guidebook that will provide a clear and concise introduction to the vocabulary and syntax of integral mathematics, along with exercises and prompts for experimentation. My hope is that this resource will empower a wider range of people to explore and apply these ideas in their own contexts and to share their discoveries with the wider community.

If you’re interested in learning more, collaborating on a project, or sharing your own insights and experiences, please don’t hesitate to reach out.


Latour, B. (2011). Reflections on Etienne Souriau’s Les differents modes d’existence. (S.Muecke, Trans.). In L. Bryant, N. Srnicek & G. Harman (Eds.), The speculative turn: Continental materi-alism and realism. Melbourne, Australia:

P.S. For anyone wondering about Claude’s suggestion in several places that AI has a 1p, I challenged him on that, and he gave quite an impressive and reasonable response. Hit me up if you’d like to see it.

Bruce Alderman

About Bruce Alderman

Bruce Alderman, MA, is an affiliate faculty at John F. Kennedy University in the Consciousness and Transformative Studies and Holistic Counseling Psychology departments. After years of moderating several integral discussion forums of his own, including Integral Postmetaphysical Spirituality and Integral Scholarship and Practice, he is venturing into production of integral video content himself.