How Geometry Shows that Existence is Relational

There is a secular tendency to view belief in God as a kind of personal expression or an aspect of our psychology that may or may not bring health benefits. For someone who genuinely believes that God is the starting point for understanding everything, it’s difficult to express how backwards the secular God-as-commodity approach really is. Getting to the root of the misunderstanding requires reframing the entire world as fundamentally relational. Here’s what I mean:

If you remember the first days of your high school geometry class, as I’m sure you do, you’ll recall that a line is what connects two points (try to keep up). Now, while there are an infinite number of points along that line, the line is not composed of points. You can’t build a line by stacking up a whole bunch of points, because a point is dimensionless – it has no length. Adding points together to try to create a line is like adding 0+0+0+0… on into infinity, and you won’t actually get anywhere. You can’t cross the infinite expanse that way. So a line is not an aggregate of bits, it is a relationship between points.

This is another example of something trite that ripples into the profound. It is relationship that makes dimesionality possible. Relationship creates a broader, more expansive kind of existence. And because our world is stretched across an expanse, it is best understood in terms of relationship and not in terms of the aggregation of bits. Without relationship, each point, each center, each self, would collapse into an infinitely small existence that ultimately winks into nothingness. But with relationship, that otherwise unknowable point is able to manifest, to be known, to come into being.

The point at the center of a circle is infinitely small, dimensionless, and so has a different sort of existence from the extension around it. As the wheel turns, the center remains motionless. The space around that center is properly ordered to the extent that it is properly oriented to that center. This image can help us grasp the relationship between the eternal and the temporal.

You can imagine the dimensionless center alternatively, not as something infinitely small, but as something infinitely high. The center is where you find Jacob’s ladder, the portal to heaven – again, a different sort of existence. And because the ladder is infinitely high, it can’t actually be ascended in flesh-and-blood terms. That center is knowable only in terms of relationship. Just as relationships in our own lives take on a character or spirit of their own, so the ladder that Jacob sees in Genesis is traversed only by angels, spiritual beings.

As in geometry, here again we see that only relationship can traverse what would otherwise be an infinite expanse. It is a connection between two points, two selves.

We can also think of the self as a kind of infinite center-point, whose temporal manifestation centers around something eternal. This is the traditional Christian understanding that underlies the supreme value we place on human life. It is expressed throughout history, from David saying that God has put eternity in our hearts to C.S. Lewis saying that nobody has ever met a mere mortal. Understood as points, humans are either infinitely small and meaningless within themselves, or eternal center-points that embody meaning when brought into relationship with other points, and ultimate meaning when rightly aligned with God as highest Center-point.

For example, I do not know my wife by means of comprehensively mapping out her personhood. Because there is something infinite about her, I cannot possibly do that. In a sense I can see her personhood always pouring forth into embodiment, into her words, her actions, her clothes, her unconscious gestures and expressions. But these embodiments are not her, they are only the circle around the center. If I ever believed to fully understand her, she would no doubt break that mold within the hour. That is the joy of loving a person. You are always approaching that infinite center without ever fully grasping it.

The macro-version of this pattern is how we relate to God. The fact that we cannot comprehend or understand God is beside the point. I can’t “comprehend” my own wife. But that does not preclude the possibility of a relationship with God. Relationship can pierce that infinite expanse. It gives us a direct line to the center, like Jacob’s ladder. That is the nature of all relationships.

The relationship between eternal selves gives rise to extension, dimensionality, a broader kind of world – our cosmos. And its existence is relational all the way down to the eternal loving unity within the Trinity at its center. In the end, the only way to exist is to be tied into that network of Being, grafted into the Tree of Life.

In the same way, without relationality, in the end there is only nothingness. That is the danger of being unable to sacrifice or submit yourself to another. Viewing the self as something which must be satisfied rather than sacrificed, a vessel to be filled rather than emptied, ironically leads to a diminishing existence. If we follow the demonic logic of Screwtape, that to exist means to bring desires into oneself, we are fated to imprisonment in our own solipsistic ego. In Lewis’ The Great Divorce, Hell is envisioned both as a limitless expanse of relationless individuals and, paradoxically, as something infinitely small, squeezed into a crack in the dirt on the outskirts of Heaven.

Unfortunately this is exactly the path urged upon us, both by a technologized culture of instant gratification and a philosophical undercurrent that elevates preference-satisfaction and self-fulfillment as guiding moral ideals. The result of our consumer-based ethic is predictable: unparallelled material wealth and debilitating psychological dysfunction. To exist requires relationship, and relationship requires sacrifice, giving up the things we have a right to. Selfhood by way of satisfaction can only end in diminishment, becoming a point infinitely small, disappearing into a crack in the dirt on the outskirts of Heaven.

So when we speak of a relationship with God, this religiosity is not a mere belief subsumed into our personality like some kind of psychological accoutrement. The infinity and eternality of God make subsumption impossible. But that’s equally true of an infant and his mother. The infant does not “believe” in his mother, does not understand the fullness of her being, cannot empathize with the depth of her love, joy, or grief. But to deny that he has relationship with her is absurd. And it is that relationship that brings endless joy to mother and son alike, and sustains Life itself.