“… God Said”: Toward a Quantum Theology of Creation

2.1.1 Defined

The first noteworthy background discipline is category theory, which is the branch of mathematics concerned with maximizing abstraction by seeking unifying formal structures so that findings apply to the broadest possible range of disciplines and problems. Category theory is key because it provides a foundational mathematical and abstract unity between physics and grammar. This is achieved by creating a definition of a category and then applying different rules and stipulations to the said category until it adequately represents observable phenomena or correctly describes the behavior of a system. Due to their flexibility, there are a wide variety of categories.^[10] Only the most basic type must be considered here.

All categories are constructed of objects and morphisms.^[11] Objects look like dots or circles and are the nouns of a category. They can be thought of the things inside the category. Morphisms, on the other hand, look like arrows and are the verbs – the transformations an object can undergo to, for example, change it into a different object – within the category. Mathematically speaking, morphisms have a domain and a co-domain, which are objects within the category. Simply put, the domain is the input – like a vertex in a graph – into a morphism, and the co-domain is the corresponding output – another vertex.^[12] Aside from objects and morphisms, it is crucial that categories allow composition, meaning that morphisms within a category can be nested.^[13] This nesting of morphisms is roughly equivalent to function composition in algebra in that the nested function is calculated first with its output being provided as the input into the next function – i.e., f ( g ( x ) ) . In category theory notation, the most basic composition equivalent to the prior example is typically represented as f ∘ g – read as “f after g.”^[14] This composition is required to be associative – the order of computation is irrelevant – and there must be an identity morphism that maps an object onto itself – a vertex with an arrow circling back on itself.^[15] Formally, associativity is defined by the following equation: ( f ∘ g ) ∘ h = f ∘ ( g ∘ h ) , and identity is defined as f = f ∘ I w = I x ∘ f . Figure 2 provides a visual aid with a graph and labels to aid understanding. While it is possible to add additional rules and restrictions – more structure – to categories, only objects, morphisms, and compositionality with associativity and identity are required; therefore, those elements are the basic definition of a category.

Figure 2

Example category theory graph and compositional equations.

The core of Figure 2 is the graph with its four vertices – objects – and seven edges – morphisms. The edges are more correctly described as three directed edges, which are morphisms between objects, and four loops that represent the identity morphisms. The object W is the starting point of the graph’s flow. The morphisms f, g, and h move one along the graph toward its terminal point – object Z. The identity morphisms are, again, represented by loops, which circle back onto the vertices from which they originate. This means the origin vertex and terminus vertex are the same for each identity morphism. Thus, the identity morphisms are labeled with an I that has a unique subscript to specify the object to which it is the identity. For example, I _w is the identity morphism that originates from and terminates on object W. The rest of the image is layered and uses brackets to illustrate the symbolic mathematical expressions’ referents. For example, the associativity equation – the topmost equation – states that the path from W to Z is the same path regardless of whether f ∘ g or g ∘ f is calculated first.

2.1.2 Category of Creation

The highly abstract nature of category theory allows it to represent many different things, including the theistic universe. The theistic universe is based on ancient cosmology and contains two types of substances: heaven-stuff and earth-stuff.^[16] The heaven-stuff makes up the spiritual aspect of life, such as souls, wisdom, the breath of life, consciousness, angels, demons, and so forth. Heaven-stuff provides meaning, hierarchical causality, and life among other things. On the other hand, earth-stuff provides the material aspects of life, like flesh, metals, dirt, water, fire, and air. Any categorical representation of the theistic universe must have objects that represent these two distinct kinds. Beyond these two objects, a wider diversity of possible representations begins to emerge depending on one’s particular theological preferences. In particular, the theistic universe has a third object to describe where heaven-stuff and earth-stuff meet: symbol.^[17] Symbols, then, are the third kind that holds the intersection of heaven-stuff and earth-stuff. In Christian theology, this would include human beings themselves as they are made from earth-stuff and filled with the breath of God.^[18] In sacramental theologies that recognize transubstantiation, this would also include, among other things, the Eucharistic Host. Figure 3 shows a pictorial depiction of the theistic universe that will serve as the starting point for building a notional categorical representation.

Figure 3

Recursive structure of the theistic universe.

Figure 3 comes from Pageau’s 2018 work.^[19] The left-hand side of the image shows the meeting of heaven-stuff and earth-stuff in Adam, which is elaborated below. The heaven-stuff and earth-stuff are depicted in semicircles that, when combined, form a whole circle that represents all of creation. Intuitively, heaven would be the upper portion of the circle, and earth would be the lower portion. Next, inward-facing directed edges are used throughout Pageau’s work to graphically depict the formation of symbols – the items depicted in the center – out of their heavenly and earthly elements. A second important observation is shown on the right-hand side. The theistic universe is multi-tiered and recursively depicts the same cosmic structure at different levels of granularity, which are called macrocosms and microcosms. This is represented in the figure by zooming into the center of the macrocosm circle to see the microcosm as if looking through a microscope. The current level of granularity being discussed can be discerned by the topmost directed edge. On the left, the granularity is that of the divine. On the right, it is that of humanity.

Figure 4 takes the next step, providing a simple abstraction of the theistic universe as a proto-category – a nascent, potential category lacking full definition – with three objects and morphisms between them. Before viewing the figure, the morphisms require definition. There are four in total: I, R, E, and S. Borrowing from computer science, each of these morphisms has been assigned a meaningful name with the single character designations functioning as helpful shorthand. I stands for “informs;” R for “returns;” E for “embodies;” and finally, S stands for “supports.” The rationale behind the names is simple enough to ascertain. Beginning from the lower right-hand portion of the image and proceeding counterclockwise, the earth supports the symbol. It provides the material element that gives the symbol form, supporting the meaning in a weighty, tangible vessel. The symbol, then embodies the ideal – the wisdom, the breath – of heaven. This also implies, third, that heaven is informing the symbol with a higher principle or meaning; otherwise, the symbol would have nothing to embody. Lastly, now on the bottom-left, the symbol can return to the earth. This would signify the departure of heaven – the desacralization or desecration – from the symbol, rendering the symbol nothing more than an empty vessel – an object devoid of heaven-stuff.

Figure 4

Proto-category for the theistic universe.

Figure 4 is nothing more than the conceptual starting point for the formation of a category proper, hence the use of the term proto-category. It is worth noting that the four morphisms break down into two sets and that identity morphisms are not yet considered here. There are only those morphisms that pair heaven with the symbol and those that pair earth with the symbol. These two sets can be envisioned as two circular cycles: heaven-symbol and earth-symbol. Envisioning these groups this way can be helpful when considering mathematical representations of these abstract concepts. For example, it is possible to represent each cycle with an isomorphic invertible function so that the heaven-symbol and earth-symbol sets use the same function. Implementation details like this are simply notional as fully defining the optimal categorical representation of the theistic universe is beyond the scope of this introduction to the concept; however, it is important to recognize that this sort of representation can be formalized mathematically.

Notice that the word “humanity” is also included in the symbol object’s circle. This is not an accident. It is the prototypical example! Human beings, as represented by Adam in Figure 2, are the primordial^[20] blend of heaven-stuff – breath of life – and earth-stuff – dust – because humans are a unity of body and soul.^[21] Adam is formed out of the dust of the earth and the breath of God from heaven enters Adam’s nostrils. He is, therefore and clearly, a symbol – the combination of heaven and earth – in the category of the theistic universe. Humanity, then, through Adam is the symbol of the unity of heaven with earth more broadly. So, when living righteously, the human being is properly functioning in the theistic universe as the embodiment of heaven on earth. When living wickedly, the human being fails to properly instantiate heaven as a symbol and, therefore, sins. It follows then that the very structure of the theistic universe defines sin as the botched embodiment of heaven on the earth.

The human being’s physical and spiritual lifecycle illumines how the morphisms move the human between the objects in the category. At the moment of death, the breath leaves the body and returns to heaven. The breath, then, no longer informs the meaning of the body. This is the great tragedy of death. The soul of the loved one is now gone back to its Maker, and the bereaved have nothing left to do but await their own turns to join their loved one’s soul in heaven as well.^[22] Meanwhile, the soulless body slowly turns back to dust, returning to the earth, after burial.^[23] Each of these categorical changes can be mapped as a morphism from the domain of symbol to the co-domain of earth or heaven, respectively. Figure 5 provides a notional, graphical example of such a mapping from a sacramental theology’s perspective.

Figure 5

Prototype morphism mapping for a sacramental theology.

A full exploration of domains and codomains must be left to a future work. There are certainly multiple ways to implement this mapping, so this is only a notional example to aid comprehension. The arrows are precisely those morphisms that are indicated in Figure 4. Additionally, BBSD is an abbreviation meaning “Body, Blood, Soul, and Divinity,” which is the view of transubstantiation regarding the Eucharist. There are other theological positions, but the underlying framework represented here still functions regardless of theological preference. Sacramental theologies tend to have more symbols to consider.

With the logical considerations for how the theistic universe is constructed now prototyped, it is time to formalize those considerations into a category proper. The first step to doing this is to convert the logical proto-category of Figure 4 into a process theoretic representation. Such a representation automatically provides a formalized mathematical structure that lends itself to implementation on a quantum computer.^[24] This includes composition structured with associativity and identity. Figure 6 shows the necessary conversion.

Figure 6

Converting proto-category into process theoretic representation.

Figure 4 here is split into two sections representing cycles of heaven-stuff to symbol – top – and earth-stuff to symbol – bottom. These sections are then juxtaposed with the equivalent process diagram. This is done to illustrate the conversion to process theory in steps. The two processes will be composed again in Figure 7.

Figure 7

Composition of the theistic universe as a process diagram.

The convention employed here is for the processes to be read from top to bottom; therefore, time is labeled with an arrow pointing downward to remove any ambiguity as to the direction of the flow. In that same spirit, the top conversion will be considered first. The abstract morphisms I and E have been collapsed into a single process – a proper morphism – called sacralize. The inputs into this process are the proper objects H – heaven-stuff – and E – earth-stuff. Here, notice that the structure, both physical and logical, of heaven-stuff and earth-stuff is preserved. Heaven-stuff is above the earth. However, it is crucial to realize that connectivity is the key to interpreting these diagrams. Even though E is written in the place of earth-stuff, it connects to the process box on the top, meaning it is an input and not an output. Therefore, attention must be paid to the wires and their connection points rather than the relative positions of the labels. The inputs into – the domain of – the sacralize morphism, then, are the objects H and E. The output – the codomain – is S, meaning a symbol. The same logic is used to create the diagram for the desecrate process, which collapses the notions of the S and R proto-morphisms into a proper morphism. In this case, the symbol S is the domain, and the codomain is H and E. Again, the logical location of H’s label is preserved in this image, but that is not necessary.

Next, the composition is demonstrated in Figure 7. Associativity is included in the composition without needing any diagrammatic amendments or annotations. This is because the top portion of the diagram or the bottom portion of the diagram is calculated first. As long as both portions are composed and calculated, the result is the same and the image will look the same. Therefore, the composition is associative in process diagrams representative of category theory by default. Identity is shown for objects in the same manner as time. For an object, it is simply an arrow that does not go through a process. The identity morphism is different. It is not depicted here because it is simply an empty diagram. A process that makes no change to objects has no need to be represented. Therefore, the composition here perfectly meets the definition of a category.

For ease of understanding the objects, morphisms, domains, and codomains are labeled in this figure. Domain and codomain are from the perspective of time in this example. So, the inputs are always entering the top of the process box, and outputs are always flowing out of the bottom. Objects are always represented by wires, and morphisms are always represented by boxes and are synonymous with processes.

In Figure 7, the labels for objects are no longer bound by the logical structure of Figure 4. That structure can be simplified because the bends in the wire can be straightened out. Again, so long as the connection point is preserved, only connectivity matters. The image here is now a formalized graph of a category-theoretic process and inherits all the structure and benefits implied.

Lastly, it remains to consider which underlying implementation could be used to concretize this category. There is not one simple answer as more than one category is a candidate. The optimal match or best candidate is an area for further research as that is beyond the scope of this contribution, which aims only to invite further research into the intersection of category theory and theology. Therefore, a simple implementation is offered here. Namely, the category of relations known as Rel, which is defined rigorously in Coecke and Paquette and used often to model conceptual spaces among other things.^[25] Using Rel, the objects in Figure 7 become mathematical sets. The morphisms become mathematical relations, which map sets onto sets. The composition is defined by two relations that relate three sets preserving the same structure found in Figure 2. Formally, if there is a relation R 1 : X → Y and a second relation R 2 : Y → Z , then the composition R 2 ∘ R 1 ⊆ X × Z ≔ { ( x , z ) | there exists a y ∈ Y such that x R 1 y and y R 2 z } holds.^[26] Effectively, this is saying that when two relations are composed using the Cartesian product – represented by the multiplication sign – the left-hand side of the relation is populated by an element of the leftmost set, and the right-hand side of the relation is populated by an element of the rightmost set. Again, this structure is exactly that found in the composition defined in Figure 2. Since these properties all hold, then Rel provides a feasible implementation of the theistic universe where the category of earth-stuff is defined as E ≔ { ( e , 0 ) | e ∈ E } ; heaven-stuff is defined as H ≔ { ( 0 , h ) | h ∈ H } ; symbol is defined as S ≔ { ( e , h ) | e ∈ E , h ∈ H } . Symbol, then, is the Cartesian product of earth-stuff and heaven-stuff, which takes e from earth-stuff and the h from heaven stuff and creates a tuple from them. This structure is a good starting point since it mandates that symbols be constituted by both heaven-stuff and earth-stuff, which fits the abstract proto-categorical model of Figure 4. Further, the use of integers Z for values allows for a gradation of sacredness – positive values – and profanity – negative values. 0, obviously, would reflect neutrality, which would at the very least be useful as an initial value. Such a gradation makes sense as it could model differences in sanctity between marks on the soul – baptism, ordination, consecration, priests, bishops, and the like – and the relative sacredness of religious objects – bibles, crosses, holy water, rosaries, prayer ropes, and so on. Rel, then, seems like a good starting point for the implementation of the theistic universe as conceived here and in Pageau’s work.^[27]

Now, it may seem like this discussion is a rabbit hole, but it is certainly not. The categorical understanding of the theistic universe postulated here is the spiritual twin of the physical world, and necessarily follows from the main argument of this article as it is a requirement of QNLP that such a unifying, abstract, and mathematical structure exists. Therefore, this portion points toward and lays the foundation for the category theoretical understanding of spiritual realities and, by extension, abstract objects – the first contribution of this work. It is already documented that category theory can be used for philosophical considerations.^[28] It is time to apply it theologically, develop it, and put it to the test.

2.4.1 Theology

Within the realm of theology, it is crucial to consider the epistemic priority of Christ, natural theology, and scholastic realism. It is, furthermore, helpful to consider the parallels between quantum philosophy and the mystic tradition. All these parts, perhaps seemingly disjointed to some, all play a role in observing the spoken cosmos in a quantum circuit. When taken together, they are the first ingredients to a quantum theistic interpretive framework. The investigation begins with an abbreviated journey to scholastic realism. Epistemology and natural theology will emerge on the way.

2.4.1.1 The Augustinian Argument

Saint Augustine, and those in his thought tradition, have argued for the existence of God on the grounds that abstract objects, also known as eternal truths, exist in the mind of a divine intellect – a notion commonly known as scholastic realism.^[43] While the present work does not aim to provide an argument for the existence of God, the Augustinian proof presupposes much of the metaphysical background needed to buttress this work’s primary contribution. In fact, the extension of this theological proof is the spine of this work. An abbreviated gloss of the argument, a distillation of Feser’s much more complete formulation, is as follows:^[44]

1. Abstract objects like propositions, universal truths, mathematical numbers and concepts, and possible worlds all exist. Figure 10 provides one such example.

2. Realism, nominalism, and conceptualism are the three possible explanations for the existence of abstract objects. Realism holds that abstract objects have a real existence and are not reducible to anything material. Nominalism denies that abstract objects are real instead asserting that they are phantasms of language. Lastly, conceptualism asserts that abstract objects are real but are nothing more than constructs of the human mind. Of these three explanations, there are strong arguments in favor of realism. Additionally, there are insurmountable arguments against nominalism and conceptualism. Therefore, realism must be true.

3. There are, however, multiple flavors of realism from which to choose such as Platonic realism, Aristotelian realism, and scholastic realism. Platonic realism is the belief that abstract objects exist in a third world – neither the world of the intellect nor the material world. This third world would be that of ideal forms. Aristotelian realism states that abstract objects exist both outside the mind in the essence of material objects as well as inside the mind performing abstract thought, making the existence of abstract object contingent on the existence of the material world and human minds. Scholastic realism holds that abstract objects exist inside the eternal, divine intellect. Of these three options, Scholastic realism has strong arguments in its favor. There are insurmountable arguments against Platonic realism and Aristotelian realism. Therefore, Scholastic realism is true.

4. There are strong arguments that the necessarily existing intellect in which abstract objects themselves exist is God’s own intellect. Therefore, God exists.

Figure 10

The principle of abstraction or the hierarchy of eternal truths.

The notion of two-ness, duality, or the pair has many different physical representations. All of which are accidental. The substance of two has no physical form itself, but it is still very real from the perspective of scholastic realism as it exists inside the mind of God – it is not contingent on the existence of human minds to any degree. It is, therefore, an abstract object.

Rather than delve into the intricacies of the Augustinian argument, it suffices to state that the proof is relevant here insofar as it asserts and supports the real existence of abstract objects, and that these abstract objects are physically instantiated into the material world from the divine intellect – the Logos and the basis of being itself. In other words, scholastic realism is a prerequisite for seeing the created world in quantum circuits. Now, there are two points to clarify here. First, grammar is an abstract object because grammar is mathematical. Second and therefore, the eeriness of mathematics – the interplay of abstract objects, to model, represent, and describe the workings of the material world to such a degree that they must be conceived of as real – also applies to grammar. This is significant because it allows one to swap the word “grammar” for the word “math” in all theological arguments from mathematics without compromising said arguments. Grammar and mathematics are equally abstract, equally eerie, and equally real. Therefore, the grand insight of the Augustinian argument that abstraction tends heavenward and that abstract objects are real firmly undergirds this work’s primary contribution.

2.4.2 Philosophy

Apart from quantum theology, there also exists a branch of quantum philosophy, which seeks to reinvigorate classical philosophy given the discoveries of quantum mechanics. Quantum philosophical thought, as with its theological counterpart, also begins with “togetherness,” another word synonymous with participation, as Coecke aptly observes.^[56] Branching out from the root of togetherness, Omnès seeks to harmonize quantum mechanics with the philosophical discipline to inspire further inquiry into the nature of reality and its interplay with the Logos.^[57] Even from an atheistic worldview, there is still a metaphysical urge to reevaluate the way humanity has come to understand philosophy, religion, and the scientific disciplines in light of quantum mechanics. This urge often manifests itself in a search for what is universal, be it in grammar, a theory of everything, or the unifying structures of category theory.^[58] It is also noteworthy that even in secular quantum philosophy, “realism is unassailable.”^[59] Abstract objects must exist in some real way because, even in the shadow of quantum mechanics, the observations, conclusions, and abstractions of common-sense perception will continue to hold true. It is these observations that constitute reality. Yet there is a wider and deeper reality available to the contemporary thinker who deigns to dive into the subatomic precisely because there is more to observe than meets the naked eye. There are still more abstractions to discover precisely because when there is more to see, there is more to infer and learn.

Indeed, observation is the lynchpin of science, and science is, therefore, the discipline that studies reality. The Logos is defined distinctly from reality in that it is the underlying rational principle through which all things operate; further, it is the epistemic reality through which all things ought to be interpreted. It is itself, seemingly, abstract, and unobservable. It must, therefore, be within the realm of mathematics and logic. In quantum philosophy, the Logos exists in the abstract and permeates, or impregnates, reality. It is, thus, observable only insofar as its principles are embodied by a scientific object which is subject to some scientific discipline and study. Figure 11 provides a graphical depiction of this relationship.

Figure 11

Reality and logos. Image is reconstructed based on Omnès, Quantum Philosophy, 268.