Christ and the Cosmic Fractal

1600 words, 8 minute read.

Have you ever been to a Carnival? Did you visit the Hall of Mirrors? You enter and all around you are, well you guessed it, mirrors. You shut the door behind you…and yikes, it’s another mirror! You are struck inside a polyhedron, the inside faces of which are all mirrors. Look into one mirror, any mirror, and you see yourself reflected endlessly but at ever smaller scale. 

The mirrors are reflecting each other’s images over and over again until the images are too faint for you to see…but know that they continue infinitely, albeit imperceptibly. They create the ‘illusion’ of adding another dimension to space. The mirrors have height, width, and thickness just as you’d expect; but now they also appear to have a 4^th dimension…depth. 

Adding this 4^th dimension does not increase the overall information content of the complex. The mirror images simply repeat, over and over again, what already is. They add nothing new. In the same way that all the information related to a Black Hole resides on its surface, so all the information related to a Hall of Mirrors resides in just 3 dimensions. The images are self-similar (congruent if you’re currently sitting in a high school geometry class); only the scale changes!

If you’re not too hung over after spending Saturday night at the Carnival, I’ll pick you up Sunday morning on my way to Mass (Roman Catholic Liturgy). I know you’re not into religion, but I think you’ll find this interesting. Christians believe that God (Father) made ‘the heavens and the earth’ but they also believe that God (Son) was ‘born of the Virgin Mary’ 2025 years ago. 

Ridiculous, you say! Who could believe that? How soon you have forgotten last night’s trip to the Carnival! (Suggestion: Drink less next year!) May I remind you? Last night your image was incarnate in endless reflections of your reflection. (Note: a reflection of reflection is recursive.)

But you don’t need to wait for the carnival to come to town next year to be reminded. Fractals are all around us and they are a frequent subject of artists working in various media. For example, Escher’s Print Gallery (1956) depicts a city and in this city is an art gallery and on the wall of that gallery hangs a painting and, guess what, that painting is Print Gallery…a painting that depicts a city with an art gallery that has Print Gallery hanging on one of its walls.

Jean-Paul Sartre’s 1938 novel Nausea offers a literary example of this relationship. It chronicles a young intellectual’s anguished discovery of the principles of Existentialism, and it concludes with him deciding to write a novel based on those ideas. Of course, the intellectual is Sartre and the novel is none other than Nausea itself.

Sartre’s novel is itself recursive. As such it joins a rich literary tradition stretching from Don Quixote to Neverending Story. In Volume Two of Don Quixote, our hero learns that he is the subject of an eponymous novel and he takes time to respond to critics’ comments on Volume One. The novel has become a ‘character’ in its own story. That’s recursion!

When we first hear this idea, our instinctive reaction is to say, “No, that’s not possible! The whole cannot be one of its own parts. It’s illogical.” And yet, through carnivals, liturgies, paintings, and novels, we clearly see that it is not only possible but actual, perhaps even necessary…Bertrand Russell notwithstanding.

We are used to vectored processes that impact things outside themselves but there is no good reason why a process shouldn’t act on itself as well, why it should not be recursive. In fact, most process is recursive. Processes directed exclusively at another, if they exist at all, are special cases of, or abstractions from, process generally.

Sidebar: Does every process apply to itself? Is that the meaning of Karma? It’s certainly the message of Judeo-Christianity’s Great Commandment: “…love your neighbor as yourself.” And of Newton: Every action entails an equal and opposite reaction. Every subject has itself for an object. 

There is ever increasing evidence that the cosmos itself is fractal in nature. The distribution of galactic groups in space is self-similar to the distribution of galaxies within those groups; that distribution in turn is self-similar to the distribution of stars within individual galaxies…which is self-similar to the distribution of quarks in an atomic nucleus.

Many great works of literature (e.g. Joyce) and music (e.g. Bach) are structured as fractals. Fractals also have applications in math, logic, and computer science. But here we are exclusively concerned with metaphysical applications, applications in ontology, cosmology, and theology. The Christian world view suggests that Being itself has a fractal structure.

Let’s start with God! Why not? The Christian idea of God is Trinitarian. God is three persons (Father, Son and Spirit). But these ‘persons’ are not ‘parts’ of God; they are God, individually and collectively. The Father is God, the Son is God, the Spirit is God. 

According to the Nicene Creed, the Son is “begotten not made, God from God, light from light, true God from true God.” The Spirit “proceeds from the Father and the Son”, i.e. is the relationship between the Father and the Son. 

But the Spirit is also a ‘divine person’; the Spirit is also God. So according to Christian theology, God is ‘triple-self-similar’: Father (est), Son (incarnatus est), and Spirit (procedit). If we map Christian cosmology onto English syntax, God is the subject, the object, and the verb.

What about the ‘world’ and God’s relationship to that world? Does the fractal structure of Trinity extend to the physical world? What are the fundamental things we can say about God’s relationship to the world?

1. God creates the world, primordially (Genesis) and perpetually (John).

2. God redeems the world (I Corinthians), immediately and eschatologically.

3. God is incarnate in the world in the person of Jesus Christ. 

So the world, which God encompasses, encompasses God. The whole is part of itself. (Colossians). The fractal pattern we identify with Trinity extends at least one level beyond…to the relationship of God with the World. 

The pattern of Creation, Incarnation and Redemption is self-similar to the structure of Trinity. God incarnate (Jesus Christ) is one element of a whole (world) which in turn is encompassed by a higher order whole (God) which, of course, is also a part (Son) of the whole (world).

While God “created the heavens and the earth” (Genesis 1:1), it is through Christ (Logos) that “all things came to be…and without whom nothing came to be” (John 1:3). Christ the part (logos) on one scale is Christ the whole (Logos) on another. God and Creation are self-similar (not identical or equivalent); it is by the power of the Holy Spirit (God) that we are the image and likeness of God.

While everything is ultimately subject to God, it is subjected to God through Christ. “When everything is subjected to him (Son), then the Son will be subjected to the one who subjected everything to him (Father) so that God may be all in all” (I Corinthians 15:28). Christ, an element on one scale, is Christ the whole on another: “Christ is all in all.” (Col. 3: 11)

So at scale N, God creates and saves the world and is incarnate in that world in the person of Jesus. At scale N-1, all things are made through Christ and ultimately subjected to God through Christ. Christ (the whole) becomes Christ (the part) first through Incarnation and then through each of the Sacraments (especially Eucharist), i.e. reiterations of Incarnation. 

Christ is wholly present in every sacrament. In Eucharist, however, bread and wine (parts) are transubstantiated into the Body and Blood of Christ (whole). We (wholes) in turn ingest that Body and Blood (whole) under the appearance of bread and wine (parts).

In each of us, Jesus’ body and blood comingles with our own; Christ (whole) becomes a part of each of us so that we in turn each become the Body of Christ (whole). A part (Christ) of a part (us) is also a whole of which we are each a part. According to the theology of the Eucharist, when we (whole) ingest Jesus’ Body and Blood (part), we (part) are simultaneously uploaded into Christ’s Body (whole). St. Paul summed it up beautifully: “Now you are Christ’s body and individually parts of it.” (I Cor. 12: 27)

In Eucharist, Christ becomes part of us who become part of Christ who becomes part of us ad infinitum. Reminiscent of our Hall of Mirrors, wouldn’t you say?

Eucharist is a special example of a fractal because it is not concerned with space (mirrors) but with time. It is a Time Crystal. Linear time is suspended and replaced by perpetual loops. Therefore, Eucharist is an indivisible quantum of time; as such, it is the eternal now. Eucharist is a process which, fractal-like, repeats the Incarnation perpetually. 

So does Being itself have a fractal structure according to Christian theology? Q.E.D.

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The Heavenly and Earthly Trinities by Bartolomé Esteban Murillo (c. 1675–82) juxtaposes the Holy Family (Mary, the Christ Child, and Joseph) with the divine Trinity (God the Father, the Son, and the Holy Spirit as a dove) to visually express Christ’s dual nature as both human and divine.