The Basics of the iQuad Coin

The iQuad Coin is a key part of the Unified Theory of Knowledge (UTOK). On one side is the iQuad Symbol and on the other side is the UTOK Tree of Life.

The core function of the Coin in UTOK is to serve as a placeholder for the unique, particular, individual human knower as they are situated in real life. This is why the iQuad Symbol is designed the way it is. It is in the shape of an “H”, and when it is rotated 90-degrees, it becomes an “I”. In addition to saying “HI,” this also stands for the “Human Identity” function.

What does this mean? It means your “self” can be framed as a complicated network of identifications. For example, we can start with how you are identified with and self-identify by your name. We can also reflect on how you identify with your thoughts and feelings, how you direct your attention, and so on. In this way, we can say that our self is formed by the “human identity function.”

In the language of UTOK, the human identity function, as framed by the iQuad Coin, corresponds closely to the concept of the . Your psyche is your unique, subjective way of knowing about the world. As such, we can call your psyche your unique “epistemological portal” that consists of your subjective, qualitative experience of being-in-the-world. When framed this way, we can think of the iQuad Symbol being something like a mirror that symbolizes and reflects your psyche. This is why the Coin is sometimes depicted with a picture on it.

Bridging the Subjective Observer to Objective Behavior Patterns in the World

Whereas the Coin represents the point of view of a particular subject, UTOK’s Tree of Knowledge System represents the world as seen from a coherent, naturalistic, scientific perspective. That is, the ToK System depicts the unfolding patterns of behavior in nature that can be seen from the most generalizable position we have so far achieved.

This means that, as a knowledge system, science is framed by a different but complementary epistemological position to the psyche. Whereas the iQuad Coin is the unique, subjective, qualitative, first person perspective in the real world, science is the generalizable, objective, quantitative, third person behavioral perspective, grounded in scientific theories about the world. We have lacked the way to combine these epistemologies together in a coherent way, which is why UTOK is a new system for knowing about the world and our place in it.

We can practice blending the perspective of the Coin with the Tree. In UTOK, we have a saying, “Marry the Coin to the Tree in the Garden under God.”

The first part of this saying means that you work to get into “right relation” with what the case. One way to do that is to see your self as a (1) wave of energy information that is also (2) a material object in space and time that is also (3) a living organism that is also (4) a minded animal that is also a (5) self-conscious cultured person, all in a nested “ontic epistemic matrix” that can be seen from the inside-out (represented by the Coin) or outside-in (represented by the Tree of Knowledge). In doing this, you are aligning your subjective world with the world as mapped by science.

Bridging the Subject to Math and Philosophy

The iQuad Coin is not just a placeholder for the unique human subject; it is also structured to bridge the subjective world of the psyche to be more intimately connected with both mathematics and philosophy. This fact is seen in the other obvious feature of the iQuad symbol, which is the equivalency or identity between 1 and i⁴. For those who are not mathematically inclined, the i represents the imaginary number, which is the square root of negative 1. It is called an imaginary number because no real number gives a negative number when squared. Nevertheless, mathematicians have found a logical way to make sense of this.

All we need to know at this point is that, mathematically, if i is raised to the fourth power (i x i x i x i), you get 1. Thus, i⁴ = 1, and we can give it the name “iQuad”, which means that, in the language of UTOK, iQuad equals i⁴, which equals 1. If we represent this in geometry, we get the iQuad Coin equaling a complex unit circle. A complex unit circle is defined by real numbers on the x-axis and imaginary numbers on the y-axis, which also gives us the complex plane for mapping complex numbers. This set of relations is given here:

Earlier, I described the inside-out perspective of the psyche and outside-in third-person perspective as being aligned on an “ontic-epistemic matrix.” The word ontic comes from philosophy and refers to that which is real, independent of what we know about it. In contrast, the word epistemic refers to the what and how of knowing processes.

The iQuad Coin thus invites associative connections to be made between real and imaginary numbers in mathematics and the ontic and epistemic concepts in philosophy, tied together in one’s mind. One way to make this connection is to consider epistemic processes as generating “imaginal” models of the real. Knowledge about reality, then, would be conceived of as a complex set of ontic-epistemic processes.

In making these connections, we have linked the human psyche to: a) the world of natural behaviors mapped by science, b) mathematics via real and imaginary numbers and the complex unit circle and plane in geometry, and c) to philosophy through the relationship between the ontic and epistemic. The result is an interesting intersection of different kinds of knowledge systems. The relations between (a) the human psyche as the Human Identity Function, (b) natural science’s map of behaviors in the world mapped by the ToK System, (c) complex numbers in mathematics, and (d) the core concepts of philosophy make up the central ideas represented by the iQuad Coin. This diagram brings all of this together:

If you would like to learn more about the iQuad Coin and how it links up various concepts, see this blog series:

The iQuad Coin Part I

The iQuad Coin Part II (The Human Identification Matrix Lenses)

The iQuad Coin Part III (The General Identity Functions)

The iQuad Coin Part IV (The Core Subfunctions and the Equivalency Connection)

This is a depiction of the iQuad functional architecture that is laid out in those blogs:

If one is really interested in understanding the Coin, then it is recommended that they commit this architecture to memory. (Note that the last entry refers to the “formal Henriques Equivalency” does not need to be memorized, as it represents the deep architectural root of the Coin, which is spelled out in more detail here and here.).

In addition, please see this video with John Vervaeke, and these two videos with Bruce Alderman (here and here).

Going Forward with the iQuad Coin as Knowledge in Your Pocket Orienting Toward Wisdom

The next area of development for the iQuad Coin is on how one might actually use it as a talisman of transformation, to use a phrase coined by John Vervaeke. Recall the saying mentioned earlier, “Marry the Coin to the Tree in the Garden under God”? Whereas the “Marrying the Coin to the Tree” captures how to think of the knower in relationship to the known (i.e., the Coin Tree relation), UTOK is also about grounding our knowledge systems and orienting us toward wise living. This is what is meant by the second half of the sentence (“in the Garden, under God.”)

The back side of the Coin is the Tree of Life, which, as this blog explains, is the central icon of UTOK. It sits in the center of a Garden that represents wise living. And it resides “under God,” which represents one’s ultimate values or the transcendent (the UTOK icon for this is the Elephant Sun God, described here).

Ultimately, the Coin is all about getting in right relation to both what the case and what to be the case, based on one’s valued states of being. This is symbolized by the 90-degree rotation, and then flipping the Coin to the Tree of Life.

Ultimately, we can represent this with the idea that, to get in right relation with what is and what ought to be the case, we need to rotate and flip the Coin.



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Gregg Henriques

Professor Henriques is a scholar, clinician and theorist at James Madison University.