FRACTAL

Have you ever been in a fun house? If so, you probably visited the Hall of Mirrors. You enter and all around you are mirrors. You look into one mirror and see yourself, reflected endlessly at ever smaller scales. What’s happening?

The mirrors are reflecting each other’s images over and over again until the images are too small for you to see. They create the illusion of adding another dimension to space, but the images themselves never change. As they get smaller and smaller they remain identical. These images are what mathematicians call “self- similar”.

You have just experienced a fractal…from the inside!

M. C. Escher’s Print Gallery (1956) is another example. It depicts a city and in this city is an art gallery and on the wall of that gallery hangs a print and, guess what, that print is Print Gallery…a print that depicts a city that contains an art gallery with Print Gallery hanging on its wall.

Of course, we can easily see that this process must go on ad infinitum. The pattern repeats, endlessly and without variation. This too is a fractal. A fractal occurs whenever (1) the whole (Print Gallery) becomes a part of itself, Print Gallery, and (2) that part in turn becomes the whole on another scale.

Jean-Paul Sartre’s 1938 novel Nausea offers a famous literary example. It traces a young intellectual’s anguished discovery of the guiding ideas of existentialism and it concludes with the man’s decision to write a novel based on those ideas. Of course, the intellectual is Sartre and the novel is none other than Nausea itself.

A decade prior to Nausea, Andre Gide wrote The Counterfeiters – a novel about an author (Gide?) writing The Counterfeiters.

The first known example of ‘fractal literature’ is, believe it or not, Don Quixote. In volume 2, Cervantes has Quixote reacting to literary criticism of volume 1. The novel is ‘self-referential’ but not in the way that a Greek chorus might comment on the action in a drama. The written novel becomes a ‘character’ (if you will) in its own story.

When we first hear this idea, our instinctive reaction is to say, “No, that’s not possible!” A whole cannot be one of its own parts. That’s not how we’ve been trained to see the world. But it is possible…and we’ve just seen five examples.

The concept of ‘fractal’ is tied to the concept of ‘recursion’. A process is “recursive” when it applies to itself. When a process, the whole, is applied to itself, it becomes a part within that whole and that part in turn becomes the whole on another scale. We are used to 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, we may discover that most or even all processes are recursive and that other-directed processes are special cases or even abstractions from real process.

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 with such 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.

Great works of literature (e.g. Joyce) and music (e.g. Bach) display a fractal structure. 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. I will argue that according to the Christian world view, Being itself (not just the cosmos) has a fractal structure.

Let’s start with God! 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 and the Son 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 person in his own right and the Spirit is also God. So according to Christian theology, God is “self-similar” on at least three scales: Godhead (esse), Father/Son (genitere), and Spirit (procedere).

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?

  • God creates the world, both primordially (Genesis) and perpetually (John).
  • God redeems the world (I Corinthians & Revelation).
  • God is incarnate in the world in the person of Jesus Christ. So the world, which God encompasses, encompasses God. The whole is a part of itself.

So the fractal nature we identify in Trinity extends to at least one more level…the relationship of God to the World. The pattern of Creation, Redemption and Incarnation is self-similar to the pattern of Trinity.

God incarnate (Jesus Christ) is a part of a whole (the world) which in turn is entirely encompassed by an even higher order whole (God) which, of course, is also a part (Son) of that whole (world).

Does Christ (part) also function as a whole on yet another scale? If our fractal model holds, Christ (part) should be the whole on another scale and in turn a part of that whole. But is that in fact the case?

First, while God “created the heavens and the earth” (Genesis 1:1), it is through Christ (Logos) that “all things came to be..and without him nothing came to be” (John 1:3). So check: Christ the part (Logos) is Christ the whole (Logos) on another scale.

Second, while everything is ultimately subjected 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 so that God may be all in all” (I Corinthians 15:28). So check again: Christ the part (subjected to the one who subjected everything to him) is Christ the whole (everything is subjected to him) on another scale.

So at scale N, God creates and saves the world and is incarnate in that world in the person of Jesus Christ. At scale N-1, all things are made through Christ and all things are ultimately subjected to God through Christ. But does Christ (whole) become a part of that whole as well?

I think the answer is yes…through the sacraments. Christ is wholly present in every sacrament. Each sacrament in turn becomes a part of each person who receives it; but this is most evident in Eucharist. Here simple bread and wine (parts) are transubstantiated into the Body and Blood of Christ (whole). We in turn ingest that Body and Blood (whole) under the appearance of bread and wine (parts).

In each of us, Jesus’ body and blood co-mingles with our own; Christ (whole) becomes a part of each of us (whole).  In Eucharist, Christ (whole) becomes a part of each of us and so we in turn each become the Body of Christ (whole). Furthermore, according to the theology of the Eucharist, when we (whole) ingest Jesus’ Body and Blood (part), we (part) simultaneously become part of 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 (whole) becomes part of each of us and we in turn become parts of Christ who has become part of us. This is a very special example of a fractal because it is not concerned with space (mirrors) but with time. The Eucharist is a process in which Christ becomes part of us who become part of Christ who becomes part of us ad infinitum. Linear time is suspended and replaced with circular time. Eucharist is an indivisible quantum of time; it is a process which, fractal-like, repeats endlessly. Yet it is a single event; time does not ‘flow’. It stops!

According to our consciousness, Eucharist took place between the hours of a:b and a:c. We have ‘moved on’; but the Eucharist itself has not. It will not, it cannot; it is an eternal process. As such, it is an important paradigm of process liberated from the crushing constraints of sequential time.

So through the sacraments, Jesus becomes part of the whole on the N-1 scale. So check again. Christ, God incarnate in the world that God makes and saves, is Logos through whom all things were made (Nicene Creed), Redeemer through whom all things are subjected to God (1 Corinthians) and High Priest (Hebrews) whose body and blood are ingested by individual men and women throughout the world. He is part on one scale, whole on another scale and then part of that whole. So check, check and check!

what about N-2? Now the Church takes over. Through the Sacraments of Baptism, Confirmation, Penance, Marriage, Holy Orders, and even Extreme Unction, the Church ensures that that there is an endless supply of new Christians from which come new priests from which come new bishops, bishops who will continue the sacraments, and therefore the fractal pattern, indefinitely.

So the fractal pattern described by Christian theology begins with Godhead, extends to the Trinity and then to the person of the Holy Spirit in the Trinity. It further extends to the creation and redemption of the world and to the Incarnation, then to the special role of God incarnate (Jesus Christ) in the creation and redemption of that world, then to the institution of the sacraments and ultimately to the founding of the Church whose processes ensure that the fractal pattern will extend indefinitely.

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