The Trinity and Multidimensional Mathematics

Not long ago I had a discussion with someone about the Trinity. He explained that he couldn’t accept it because no one had explained the Trinity to him in a manner that made sense. Now it is never a good reason to reject something simply because we don’t understand it. In this way we might end up rejecting a great many things that are true on account of our dullness. However, this man’s objection points to one of the Trinity’s greatest difficulties, its explanation.

The problem is really unavoidable. If a supreme, all-powerful God exists, his mode of being will be on a level far beyond our own. Whenever we talk about God we must, in a sense, bring him down to our level. We can only describe him in terms of human language, no matter how inadequate human language is at times. Most often this doesn’t cause any noticeable difficulty. We call God good even if, on reflection, we would be forced to admit that our idea of goodness is only a vague shadow of the Good. Are humans even capable of imagining perfect goodness, completely untainted by evil? The problem is more obvious when we describe God as fully merciful and fully just; two attributes which appear to conflict. Theologians throughout the ages have done excellent work in pointing to the Cross of Christ as the means by which God reconciles the two. A whole other set of problems arise when we attempt to describe God’s Triunity.

The Trinity exposes the distance between our mode of existence and God’s. There is nothing inherently impossible with three co-equal persons existing simultaneous in one being when the life of that being is of a higher order than our own. We, however, have nothing like it in the physical world. Any attempt to express a reality greater than our own in human terms is like being asked to capture the vibrant colors of a sunset with nothing more than a No. 2 pencil and a single sheet of paper. We immediately cry that our instruments are insufficient.

An example of a similar difficulty is found in the task of describing four dimensional objects. Take a tesseract for example. Besides the name for a comic-book stone, it is a four dimensional figure that is related to a cube in the same way that a cube is related to a square. Squares are two-dimensional objects. When extended into another dimension they become cubes. Tesseracts are cubes extended into another dimension. Thus a square is made of four lines, a cube of six squares, and a tesseract of eight cubes. Mathematicians attempting to make models of tesseract must always come up short of the real thing.

Here is one model of a tesseract. It is in some ways hampered by being a two-dimensional image of a three-dimensional model of a four-dimensional object. The edges of a real tesseract would be of equal length as would all angles. The eight cubes which make up a tesseract are of equal size, not stretched or shrunk as here.

Theologians attempting to describe the Trinity face the same difficulty as a mathematician attempting to model a tesseract. Human reason cannot give an accurate description of the Trinity without paradox. However, it is a reasonable difficulty. Reason can point to where reason no longer works. Of course this does not prove that the Trinity or a tesseract exist. Rather reason shows that if some condition existed (a supreme God/a fourth-dimension) then such things (the Trinity/a tesseract) could reasonably exist.



  1. Aaron · October 5, 2015

    Nor is it ever a good idea to believe something simply because we don’t understand it. In this way we we might end up accepting a great many things that are untrue on account of our own dullness. Acceptance and compromise can cause much trouble. But, then again some things are extremely difficult to comprehend (eg. the Trinity/tesseract). That would leave us in a place of poor understanding and standing between black and white sides. I suppose that’s where faith arises?

    • Caleb · October 11, 2015

      Academics are really good at using overly complex and incomprehensible language. Whether they do this intentionally or not, the effect is that some things can sound credible which in plain language would clearly be nonsense. For that and other reasons you are right. We shouldn’t believe in something simply because we can’t understand it. “Simply” is the key word. When choosing to believe or not to believe, we need to draw on all our resources.

      I think faith arises in every area of knowing. Faith is trust in something or someone. 1+1=2 takes almost zero faith because it is self evident. Friendships, on the other hand, involve a lot of trust in someone. It is trust based on lived experience with a person and knowledge of him or her. You have good reasons to trust them, even if they can’t be simplified into formal logic. A lot of life and knowing depends on this kind of trust/faith. I tried to explore this in another post. Belief in the Trinity does take faith, but that doesn’t exclude reasons or “proofs” anymore than trust in a friend excludes reasons. It is not a matter of certainty vs. uncertainty, but whether you have enough cause to trust and to what degree.

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