The iQuad Coin (Part IV):
The Four Core Subfunctions of the Coin
This is the fourth in a blog series devoted to delineating the conceptual architecture of the iQuad Coin. Part I clarified the two primary referents in the iQuad Symbol, which are the complex unit circle and the Human Identity Function. Part II deepened the central meaning of the Human Identity Function by aligning with the Human Identification Matrix, and used the metaphor of iQuad glasses to see the world via four lenses, two of which aligned with the subjective interior (i.e., Self and Pure Awareness) and two of which aligned with the objective exterior (i.e., Reality and Science). Part III delineated the four General Identity Functions, which work to extend one’s identity in the world and also connect it to UTOK’s worldview. This blog finishes the summary of what the iQuad Coin symbolizes by explaining its Four Core Subfunctions, which are: 1) the Quantity-Quality (Q2) Relation; 2) the Conscious Field Function; 3) the Quadrant-Quadratic Formulation (Q4); and 4) the Formal Equivalency Identity. This concludes the iQuad Symbol architecture, and sets up the bridge to the what is the ultimate “root” of the Coin, which will be the topic of the next blog.
The Unified Theory Of Knowledge (UTOK) is a new synthetic philosophy that is structured to afford us a framework that resolves the Enlightenment Gap and clarifies the proper relations between matter and mind and science and social knowledge. As this blog notes, UTOK’s core architecture can be framed by the Tree, the Garden and the Coin. Specifically, the Tree of Knowledge System functions to provide a new map of Big History and gives a coherent naturalistic ontology that can solve the problem of psychology and thus set the stage for a unified approach to psychotherapy. The UTOK Garden can be understood as offering a scientific humanistic theory of knowledge that is oriented toward the collective cultural cultivation of wisdom. And, finally, the iQuad Coin functions to frame the specific, unique, idiographic human knower in relation to what is and, relative to the values of the Garden, what ought to be. As such, the UTOK functions to weave together science, wisdom, and the subject into a coherent system of understanding. This makes it well-suited to be part of an emergent metamodern sensibility that is organized around a coherent, integrated pluralism. (For more on this concept, see this recent dialogos with Jordan Hall).
Although originally minted back in April of 2018 for the first Theory Of Knowledge Conference, the many meanings of the iQuad Coin have not been previously spelled out in detail. The purpose of this blog series is to fill this void. At is core, the iQuad Coin works to bridge, make adjacent, or “conceptually entangle” two domains of human inquiry: 1) the unique particular subjective phenomenological experience of being in the world; and 2) the world of mathematics, especially as it is framed by the relationship between real, imaginary, and complex number plane. This linkage was outlined in Part I. Parts II and III extended the way the Coin frames and situates the specific human knower, both in terms of the four lenses of the Human Identification Matrix and via the four General Identity functions. This blog completes the core architecture of the iQuad symbol by explaining its four Core Subfunctions. [For those who are interested in a “guided tour” of these core subfunctions, please see this Special “iQuad Edition” of UTOKing with Gregg, where I give the philosopher and integral theorist Bruce Alderman an overview of them.]
The Quantity-Quality (or Q2) Subfunction
To truly grok UTOK, it is crucial to understand that the system uses the iQuad Coin and the Tree of Knowledge System to frame two different epistemological positions. Specifically, the Coin frames the position of an idiographic, subjective, and qualitative knower, and the ToK System frames the position of the generalizable, objective, and quantitative scientific knower. This linkage is referred to as the Quantity-Quality, or Q2, subfunction, and can be depicted as follows:
Modern empirical natural science arguably represents the most significant achievement in human knowledge to date. To understand it, it is crucial to realize that it was a different kind justification system that consisted of shifts in both epistemology and ontology. The ontological shift was the philosophically grounded argument and methodological assumption that there was a single, “closed” natural world and that changes in the world occur as a function of discoverable lawful regularities, coupled with historical contingencies. Natural science also made the assumption that nature is stratified, and it can be understood by exploring the most basic constituents that are operating in the world. That is, we can understand rocks and planets by understanding them as groups of molecules which are groups of atoms which are groups of participles, all of which are operating based on core generative causal forces, such as gravity. This can be thought of as the ontology of physicalism and reductionism. (Note, as this blog makes clear, there are many possible variations of this ontology; the UTOK embraces a particular form that can be framed as an emergent and extended naturalistic worldview that embraces the concept of God as a “divine imaginal” construct).
The epistemological shift natural science made was to ground our understanding of the world in what can be called a “third person” or “exterior” or “scientific” empiricism. Scientific empiricism refers to the process of engaging in the systematic observation and quantification of entities and change via measurement, such that the data and results of experimentation can be intersubjectively verified by trained observers and also subject to the rigors of mathematical logic.
As scientific empiricism emerged, it became necessary to separate it from first person or subjective empiricism. Early Enlightenment philosophers like John Locke introduced the distinction between what are called primary and secondary qualities. Primary qualities were defined as aspects of reality that could be assessed via third person empiricism because they could be quantified and demonstrated to interact with the material world. Thus, the mass of an object was a primary quality that could be quantified and then turned into the data that could then be mathematically analyzed. Secondary qualities, such as the subjective experience of a rock as looking brown or feeling cold, were not directly accessible nor quantifiable. These “qualia” were then bracketed off from the enterprise of modern empirical natural science. Although this distinction would come under criticism as overly simplistic, it nonetheless is crucial to understanding it as part of the epistemological revolution that modern empirical science engendered.
This bracketing off of secondary qualities — properly understood as a particular individual’s idiographic subjective conscious experience of being in the world at that moment — was both very helpful and deeply problematic. It was helpful in that scientists were able to create a powerful way to understand the world as patterns of behavior across the levels and dimensions of existence that could be observed, quantified, and analyzed. However, it led to many philosophical problems regarding how we understand subjective qualia and their relationship to the so called “objective” reality. (For more on this from a panpsychic perspective, see Philip Goff’s Galileo's Error: Foundations for a New Theory of Consciousness).
UTOK directly addresses the metaphysics associated with behavioral quantities analyzed by natural science and the consciously experienced qualities (i.e., qualia) felt by particular subjects. This should not be a surprise, as UTOK is fundamentally structured to address both the science of psychology and the practice of psychotherapy. As such, its core is framed to deal the many layered complexities that arise between the language of natural science and the phenomenologically grounded lived reality of a specific human being in the world. More specifically, UTOK gives the Tree of Knowledge System as providing a map of scientific knowledge from a “pan-behavioral” perspective, starting with the Energy-Information Singularity at the beginning of our observable universe into Matter, Life, Mind and Culture. And, as we have discussed throughout this series, UTOK gives the iQuad Coin as a complement to this frame. The Coin is explicitly designed as a placeholder for the specific subjective conscious human knower and all the qualities she experiences via her particular epistemological portal. Working together, the Tree and Coin allow us to place primary, third-person empirical behavioral quantities and secondary first person subjective empirical qualities in proper metaphysical relation, such that they can be seen as, well, two sides of an interior-exterior coin.
This complementarity between the Tree and the Coin is the called the Quantity-Quality or “Q2” core subfunction. You can think of it as follows: The primary behavioral qualities that are readily accessible by the epistemology of natural science are mapped by the ToK, and further organized by the Periodic Table of Behavior. In contrast, the idiographic qualitative experiences you have from “behind your eyes” is framed by the iQuad Coin and its Human Identity Function. This graphic depicts the perspectival relationship. The Coin represents each of our unique perspectival epistemological portals to the world. The Tree gives the updated map of Big History from a natural science vantage point.
The Conscious Field Subfunction
The next subfunction allows us to use the UTOK as a lens that can provide a more fine-grained structure to your subjective conscious field. We can start this process first by applying the Map of Mind1,2,3 to identify different domains of mental processes. In the language of UTOK, the inner subjective field of conscious experience is called “Mind2.” Mind2 emerges out of Mind1, which refers to the non-to-subconscious neurocognitive processes. Mind1 can be effectively divided into neurocognitive processes that take place within the nervous system, (Mind1a) and overt animal actions that are mediated by the muscular-skeletal system and can be seen by others (Mind1b). Here is the Map of Mind diagram:
To see the distinction between Mind2, Mind1a, and Mind1b, let’s consider, as an example, rolling over in your sleep. When you are in a deep, dreamless sleep, your Mind2 is offline. However, your Mind1 is still operating. Consider how, via nonconscious processing (the domain of Mind1a), it detects when your body needs to shift and then you roll over (the overt activity being the domain of Mind1b).
The relationship between Mind1 and Mind2 is, of course, complicated. Indeed, the ontological emergence of subjective experience from Mind1 is the “hard problem” of consciousness. Here we will simply state that the essential relationship is regulated by what might be called a “conscious attentional filter.” This is because Mind2 is organized by a focal attentional system that brings the conscious field together to orient on relevant aspects of an object or event. Here is not the place to get into the weeds defending this argument. See here for a whole educational video series on how to understand conscious experience via focal recursive relevance realization.
The last domain of human mental processes is framed by Mind3. This refers to self-conscious justification. We can think of this as your ego, and consists of the part of you that interacts on the Culture-Person plane of existence as mapped on the ToK System. The private self-talk is the domain of Mind3a, whereas what you verbally and publicly share with others is Mind3b. Here is a graph that links the observational domain of Mind2, with the interactions with the exterior behaving world, and corresponded with the Mind and Culture planes.
With this vocabulary of mental processes in hand, we can proceed to deepen our understanding of the major domains of Mind2. Take a moment and reflect on the kinds of subjective inner experiences you typically have. According to Russell T. Hurlburt, who has done good empirical research on what he calls “pristine inner experiences,” your mind’s eye should be able to quickly categorize four different kinds of inner experiences, which he calls: 1) Sensory awareness; 2) Bodily feelings; 3) Perceptual images; and 4) Inner speech. I briefly describe each below, and then allude to the fifth category he identified.
Sensory awareness refers to the basic Mind2 experiences we have of the exterior world. If you grab your car door handle and experience it as cold or bite into a strawberry and experience it as sweet, these are sensory awareness experiences. Linking this to the Q2 core subfunction, these are often considered the fundamental elements of qualia. The second class of conscious experiences Hurlburt’s research identified was bodily feelings. These refer to the motives and drives in the body, as well as things like bodily position. So, in this category, we would include things like hunger, pain, anger, sexual arousal, and the like.
The third class refers to perceptual images that serve as organized and extended representations of the world. For example, when you think of your house, you “see” all the things that your house affords you and identify all the components by their functions and interrelations. This category also includes mental manipulation and perceptual rotations, as well as reflecting on past episodes in one’s mind’s eye. We can think of this perceptual map of the landscape as relating closely to your Human Identification Matrix, which we discussed in Part II.
The fourth category is inner speech. Framed as Mind3a because it is mediated by propositional thought and can be shared with others, this is what the UTOK identifies as the narrating ego, which is engaged in private question-answer justification dialogues and reason giving for understanding what is and why.
[We should note that Hurlburt identified a fifth category of inner experience, which he called “unsymbolized thought.” He acknowledged this was controversial but made the case that if you vaguely wondered above what the fifth category was by did not reflect on it or imagine it, the absence of it that you were considering would be an example of unsymbolized thought. Although this category is more controversial in terms of exactly how to frame it, for now we can just consider the basic domains of the conscious field to be the four readily identifiable fields and then consider that there may well be other categories to consider, such as wondering about absence or perhaps intuition. We also would need to consider the relationship to the dynamic subconscious.]
Another angle we can take on the human conscious field is to frame it “vertically.” As described in this blog, in UTOK, the vertical frame of the conscious field starts with bodily feelings. However, it divides them into two layers of: (a) the animal body; and (b) the primate heart. The “animal body” layer consists of basic sensory-motivational and emotional feeling states that can be aligned with the core of our animal-mental nature, and includes experiences such as pleasure and pain, energy and arousal level, drives for sex, defense, territory, temperature regulation, food, and water. The “primate heart” corresponds to the “human relationship system,” and it consists of how one feels in and experiences the relational world. This includes socio-emotional domains mapped by the Influence Matrix, such as attachment security, felt sense of relational value, threats of rejection and abandonment, and related feelings like shame, pride, love, and contempt. Hulbert’s sensory awareness would also be included in these domains.
The next level is the domain of the “thinking mind.” This can also be usefully framed as the “head.” It includes both the narrating portion of the ego and how it works with the more abstract perceptual reasoning to consciously deliberate about the world and what should be. Finally, there is the layer of “above” one’s egoic place in the world, which can be framed as the spiritual dimension of conscious experience. The diagram below shows some parallels between these vertical layers of the human conscious field and the core energy centers found in chakra traditions.
The point of the Conscious Field core subfunction is to deepen one’s map of the domains of inner experience, both horizontally and vertically. You can think of your inner world as a cathedral and the Conscious Field function is about exploring that inner world. As such, it aligns strongly with movements like yogic science, phenomenology, humanistic and psychodynamic perspectives.
The Quadrant-Quadratic (or Q4) Subfunction
The next Human Identity core subfunction is structured to deepen our epistemological and ontological grounding. The Quadrant-Quadratic or Q4 subfunction does this by explicitly linking the iQuad Coin to Ken Wilber’s Integral Theory, specifically his four quadrants. The quadrants are central to Integral Theory, and they are formed by a two-by-two matrix, framed by interior versus exterior epistemological positions and individual versus communal levels of analysis, as shown here:
The Upper Left quadrant is the interior individual quadrant, and, as such, it directly aligns with the initial starting point of the iQuad Coin. It should be noted that we can differentiate the particular experience of the specific individual in the moment from the analysis of human consciousness in general. Indeed, in its abstract description, the conscious field subfunction can be framed as a more general analysis of human conscious. For a more detailed analysis of the structures of human consciousness from a UTOK perspective, see this blog.
The Lower Left quadrant frames the interior collective beliefs, and it corresponds to one’s connection to Culture as large-scale systems of justification. For example, if an individual is, say, a Democrat and a Christian, then they would both identify with these groups and see the world through this belief-value network. In anthropology, the view from inside a cultural belief-value system is called the “emic” perspective.
The Upper Right quadrant is the behavioral perspective at the individual object level. As such, this involves identifying a specific entity and tracking its behavioral patterns from an exterior or objective perspective. In UTOK, this point of view can be framed as seeing the world via the lens of the Periodic Table of Behavior. The Lower Right quadrant is the systems point of view. That is, it is an exterior holistic view that starts with the context and the interplay and relations between domains then moves “down” into subsystems or individuals. These systems can be physical systems, like the solar system, or biological systems like an ecology, or social systems such as a nation. In anthropology, the view of a social system from the outside is called the “etic” perspective. Thus, a social scientist might study how the group of Christian Democrats responded to Trump’s Presidency.
The diagram below gives the correspondence between Wilber’s quadrants and the primary frameworks the UTOK has developed to see the world through them (i.e., the iQuad Coin and the unified approach to human consciousness for the UL; Justification Systems Theory and the UTOK Garden for the LL; the Periodic Table of Behavior for the UR; and the ToK System for the LR).
From UTOK’s vantage point, Integral Theory affords a brilliant heuristic for human epistemology. However, it is less strong when it comes to ontology. UTOK is agnostic about the ultimate ground of being, and, consistent with modern science, adopts a naturalistic ontology that starts with an “Energy-Information Singularity,” out of which the four different dimensions of complexification or planes of existence emerged. These dimensions (i.e., Matter, Life, Mind, and Culture) then afford us a “quadratic” to understand our selves as human persons operating across the different energy-information planes.
The easiest is the Culture-Person plane of existence. So, you are reading this blog and thinking about it. That is the Culture-Person plane, which is mediated by linguistic justification. Then you are imaging things, having feelings and experiences, and moving around. This is the animal mental plane. It consists of both Mind1 and Mind2 processes (i.e., nonconscious, subconscious, and subjective conscious experiences and overt mental behavioral patterns). We can then drop down a dimension and note that you are a living organism. Your cells, organ systems, and physiology are all exchanging energy-information and managing your biological complexity. Finally, you are a physical object, with characteristics like mass, temperature, and a position in space and time. From the UTOK naturalistic perspective, death can be framed as the breakdown or “popping of the complexity bubbles” that are operating at the Life, Mind, and Culture planes of existence.
In sum, the Quadrant-Quadratic core subfunction represents the combination of Integral’s “quadrant epistemology,” with UTOK’s “quadratic ontology” (i.e., Matter, Life, Mind, and Culture). As such, the Q4 subfunction works to deepen our onto-epistemological frame.
As suggested by this diagram, if we go back to the four iQuad lenses of the Human Identification Matrix, we can align the two subjective and two objective sets of lenses with the Q4 core subfunction. Specifically, we can introspect and see our UL self and awareness, and then position ourselves into specific systems and contexts of justification (LL). Then, we can look out at the world and see reality as it appears to us or as it might appear to others or as it might appear via the lens of science. We can think about that across different scales, parts, wholes, or systems, which corresponds to moving up into UR or down in LR. And we can move between these lenses with an ontology that frames frequencies of energy-information patterns across the four planes of existence. Moreover, in a broader sense, the Q4 function affords a useful way to bridge between UTOK and Integral Theory.
The Formal-Equivalency Identity Subfunction
My hope is that this tour of what the iQuad Coin represents has afforded some clarity in how to the UTOK structures the world from the vantage point of a specific human knower. In addition, I hope it also has opened up the possibility that there are useful parallels to be made between the relations between the real, imaginal, and complex in both the Human Identity Function and the complex unit circle. The final core subfunction potentially moves this set of relations from an interesting alignment to something that is profound.
Indeed, as the above diagram suggest, the final subfunction brings us full circle. The Formal-Equivalency subfunction links the Human Identity Function and the complex unit circle with two addition concepts. One idea it connects with is the Euler Identity/Euler Formula. The other key concept is called the “Henriques Equivalency.” What these concepts do is return to the original project of aligning the Human Identity Function and the complex unit circle, and tying them together with greater specificity. In fact, it is the relationship between the Euler Identity/Formula and the Henriques Equivalency that is the fundamental root of the iQuad Coin. That is, I constructed the iQuad Coin as a function of my journey in connecting the Equivalency to the Euler Identity.
We can start with the Euler Identity. As this video notes, we can be certain that the Euler Identity is important because it has been referenced in the Simpsons at least three separate times. It is one of the most famous equations in all of mathematics. It is given as the following:
It combines five of the most important concepts in classical mathematics together (e, π, i, 1, and 0) into one elegant equation. Researchers have found that it is consistently rated to be the most beautiful of all mathematical formulas. Here is a description about what makes this such an important Identity:
The number 1, that most concrete of numbers, is the beginning of counting, the basis of all commerce, engineering, science, and music. As 1 is to counting, pi is to geometry, the measure of that most perfectly symmetrical of shapes, the circle — though like an eager young debutante, pi has a habit of showing up in the most unexpected of places. As for e, to lift her veil you need to plunge into the depths of calculus — humankind’s most successful attempt to grapple with the infinite. And i, that most mysterious square root of -1, surely nothing in mathematics could seem further removed from the familiar world around us.
Four different numbers, with different origins, built on very different mental conceptions, invented to address very different issues. And yet all come together in one glorious, intricate equation, each playing with perfect pitch to blend and bind together to form a single whole that is far greater than any of the parts. A perfect mathematical composition.
For more evidence of its import, here is a map of mathematics, and, as circled in white, you can see that on this map, the Euler Identity sits near the center:
If you do not have a background in mathematics, you will likely be scratching your head as to what this is all about. Trust me, I do not speak advanced math, and I can empathize. Do not despair. I can assure you that you do not need a deep knowledge of mathematics to follow the linkages I am going to make in the final section of this essay. Folks who do have a background in math and complex numbers will know that there is a deep connection with the complex unit circle and Euler’s Identity/Formula. This blog explains in some depth exactly why and so does this video at about the 20 minute mark, but for our purposes we can just look at this diagram.
It shows the intimate relationship between the complex unit circle and the Euler Identity, which is captured on the left hand side with the box. And, interestingly, in the box on the right, we see the basic iQuad equivalency.
What does this have to do with the iQuad Coin? The answer is found in what is the root of the iQuad Coin, which is an idea I call the “Henriques Equivalency”. I stumbled on the Henriques Equivalency way back in 2001. The next blog tackles the Equivalency and how it relates to all of this. For now, we can simply drop the Coin and the “shape of the equivalency” on the Euler/Complex Unit Circle grid to show the relation that we will be unpacking going forward.
Conclusion: Toward an iQuad Aspect Monism
One of the great struggles of the Enlightenment is to place, in proper relation, the objective behavioral patterns revealed by science with the subjective experience of being. As this recent podcast by Sean Carroll and Anil Seth clearly demonstrates, we remain deeply confused about how we might obtain a proper metaphysics for this relationship. As this blog series has demonstrated, the UTOK gives two fundamental epistemological frameworks, one for natural science and one for subjective personal experience of being in the world, and then places them in proper relation.
The resulting metaphysical-ontological-epistemological frame that emerges can perhaps be considered an iQuad Aspect Monism. This is a play off of dual aspect or double aspect monism, which argues that the physical and mental are two sides of the same coin. The UTOK frames this slightly differently. Instead, it identifies different frames of reference that aspectualize different features of the ontic reality. In particular, it suggests, at the very least, an objective natural scientific behavioral frame, and a subjective personal experiential lens, which are placed in relation by the Tree and Coin. In addition, we would need to add an intersubjective, socially constructionist lens of cultural systems of justification, as well as a transjective, participatory complex dynamic frame. Indeed, as this blog series suggests, we can then extend and adjust our epistemological lens via an almost infinite number of ways. And, at the same time, it also is the case that there is one world. Thus, we arrive at kind of iQuad Aspect Monism, such that we have the real ontic world, the many varied perspectives of unique specific knowers, and the generalizable, objective onto-epistemological frame given by natural science, at least as framed by UTOK. Here is a depiction that captures this framing:
The next blog in this series shifts the focus to the root of the Coin, which is the Henriques Equivalency. Initially formulated in 2001, three years later I encountered the Euler Identity/Formula and found that there was a deep connection between the two. Indeed, as folks who know the UTOK Garden well know, I formalized the relationship between the two ideas in what is called “the Radical Mathematical Humanistic Equation” and placed it on the Seed in the UTOK Garden, as shown here:
The RMH Equation is the true root of the Coin, and so, next we turn to the Equivalency and begin to tie together these core threads. The result might just be a fundamentally new way to coherently frame matter and mind, subjectively, naturalistically, and mathematically.
