Wednesday, December 14, 2011

Trinitarianism and three-dimensional solids

The last few days we have been discussing Jesus Incarnate—specifically, the hypostasis (fully God, fully man) part of His character, and how this helps define what Christians are, and what we believe. This line of discussion often leads to a bigger mystery of our faith, one that is a stumbling block for many believers and non-believers: how can God be a Trinity? How can He be three-in-one? All too often for such a fundamental tenant of our faith, this is a poorly answered question—because it is poorly understood.

Some use an analogy, like saying that the Trinity is a like a candle flame, which is both a burning wick and light and heat all at once. But this is a poor analogy, at least to the scientist—for the wick, the light, and the heat are all fundamentally separate things (a physical object, a portion of the electromagnetic spectrum, and excitement of air molecules, respectively). What we need is a better way of understanding and illustrating the Trinity. And I think I have an analogy which will hold a bit more water and help you understand.

Picture a cylinder—a three-dimensional solid made of acircle extruded up to a given height.

A cylinder has three basic geometric features: two circles (the base and top), and the side is (in a flat pattern) a rectangle which has been curved around to meet itself. These are three faces of the same solid. So you see, the cylinder has three surfaces, which we call its faces—the rectangular side, the circular base, and the circular top. The key point is—these are faces, not components. If, for example, I slide a washer on a bolt and attach a nut, the three items are separate components—they retain their individual identity; the assembly can be removed and separated into its three smaller parts.

But a geometric figure like a cylinder cannot.

Let us further imagine that our solid cylinder shown above is made of metal, and say the height is 10cm tall. Got that picture in your head? Now, let’s try to cut it to separate the circle on the base.

It can’t be done. If you cut the cylinder 0.1 cm from the base, you do not get a circle—you get two new solids: a 0.1 cm-tall cylinder, and a 9.9 cm tall cylinder. No matter how finely you cut it, you can never separate the circle at the bottom from the rest of the cylinder. Likewise,try cutting off the rectangle. Can’t be done. If you slice the entire cylinder right up the long axis, you end up with two semi-cylinders. If you slice 1mm deep all the way up and “peel” off a layer of the face, you still leave behind a cylinder, and the thing you peeled off is not a rectangle, but a rectangular block.

Do you see the fundamental difference between an assembly (like our nut-bolt-washer example) and a solid object? A solid object has different faces, with different attributes, but it is irreducible—it cannot be made into those individual components by any method. Separating the circle from the cylinder is logically and mathematically impossible; likewise it is impossible to have a cylinder which does not have two circular faces—to do so would not be a cylinder at all.

In the same way, God is a Trinity—Father, Son, and Spirit. One essence (hypostatic), but with differing faces which comprise it. You cannot separate Jesus from His Godhood, any more than you can take the circle base out of the rectangle; and you cannot have the Christian God without those three faces, any more than you can have a cylinder without a rectangular face for its side.

Unlike the analogy with the flame, whose sub-components are distinct physical phenomena, a solid cylinder’s very definition requires the two circles and a rectangle, and thus it cannot be subdivided without destroying the essence of what it is.

You cannot have a cylindrical solid with just one circle (it becomes a hollow, non-solid at that point); likewise, you cannot have the Christian God with just God the Father.

You cannot slice a cylindrical solid into two separate circles and a separate rectangle; likewise, you cannot separate the Godhood from the Father, or the Son, or the Spirit.

It is the three faces together which logically make the object a cylindrical solid; it is the three persons of the Godhood together which logically make it God. Subdivision is impossible, for they are of the same essence or substance—just as a metallic solid cylinder can never be anything else without destroying its very nature.

The Cylinder Incarnate
Okay, now is where it gets more fun. What does it mean that God became incarnate in the man of Jesus? It means that one face of Jesus was known. As Josh pointed out in our post a few days ago, one question that some have is—if Jesus was God, why did He (while a man) have to learn things, have to ask questions, be limited by space-time, etc.?

One way to picture that is to use our cylinder analogy again.

Let us say that there is a race of two dimensional creatures called Flatlanders (to borrow from one of my favorite math books), living on a piece of paper in front of you. This race is comprised of Triangles and Circles and Squares and the like—but of course no solids, because they live only on a flat piece of paper. Now imagine that we place our cylinder (we will call him Mr. Cylinder) on top of the paper, so that it touches their world. What would they experience?

Well of course, the beings on Flatland have no concept of a third dimension called “height.” They cannot picture a cylinder, nor can it be described to them. Think about it—how would you define height to a two dimensional creature? “It’s kind of like "north” and “south”, but in another direction that, um, you can’t see…”. You’d sound like a crazy person.

No, they would only be able to see one ‘face’ of Mr. Cylinder—the face that was directly touching their world. What they would clearly see before them was a Circle-man, just like them—the other dimensions and faces of the cylinder would remain impossible to comprehend.

So, they see this Circle-man, who calls himself a Cylinder (a meaningless term to them). He lives among them for a while. Now, our cylinder of course still has access to the third dimension, right? After all, most of Mr. Cylinder is still in the third dimension, as it sits on top of the paper! He did not cease being a cylinder just because the Flatlanders could only perceive of one aspect of him.

However, Mr. Cylinder is limited somewhat, isn’t he? Not only can he not describe the third dimension, but what happens if he tries to move around in it? Well, if he moves “down” into the paper, but remains touching the paper, he will still just look like a Circle-man; they will see no change or evidence of his miraculous nature. But if he moves up off of the paper…then what will they see? Only him disappear! He will vanish. Then if he touches down on another part of the paper later, what will they think happened? That he teleported, I suppose…or died and was resurrected.

You see, if Mr. Cylinder is to interact with the two dimensional creatures of Flatland, he is restricted by their restrictions, even while maintaining his nature as a cylindrical solid.

In the same way, when Jesus became man, a face of God was literally among us. That is why, as Jesus says, when you looked upon Him you literally saw the Father (just as our Circle might say, “If you look at me you are literally seeing Mr. Cylinder”).

But just as the part of our cylinder touching their world is “bound”, as it is, to their form—unable to use the third dimension, but forced to move along the two-dimensional space of Flatland—so too was God somewhat “bound” by His attempt to be with us. By becoming man in Jesus, but retaining His Godhood outside of our world, Jesus was bound by everything that binds men—time and space, biological growth and maturity, illness and death, emotion and suffering, and entropy (decay). This is how He can both simultaneously be God, and yet not know everything that God knows (“only the Father in heaven knows…”).


To summarize, I think it best when thinking of God that we remember that the early Christians were very careful to say that Jesus, God, and the Spirit are all consubstantial—of the same substance. Just as a cylinder is all one substance with three faces, so too is God one substance with three Persons.

If we think of God that way, we find many of our problems with Trinitarianism and Scripture going away. We understand how God can be three-in-one; we understand how Jesus can be both God and man simultaneously; we understand how Jesus was bound by His manhood for our sakes.

So all of this helps explain who God is, and how He became man.

Do not forget why He became man.

Why did He do it? Why restrict Himself at all for us—people who have either ignored Him, or yelled at Him, or rebelled against Him throughout history? Because of His love for us, undeserved and unending. He humbled Himself for our sake, coming down to our level, meeting with us, so that He could build for us a path back to Him for eternity.

This is what the season of Christmas is about. The resurrection of Jesus, which we celebrate at Easter, is an amazing miracle. I can’t help but think, though, that God-becoming-man remains the most astounding thing He ever did for us.

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