Like Jews and Muslims, Christians are monotheists. In other words, they believe in the existence of precisely one God. Unlike other monotheists, however, Christians also believe that, while there exists just one God, He is three persons—Father, Son, and Holy Spirit. The belief that the one and only one God exists eternally as three persons is known as the doctrine of the Trinity, and it is this doctrine that plays an important role in Christian faith. In fact, the doctrine of the Incarnation—which says Jesus is God the Son becomes a man and thus both fully divine and fully human—assumes it. This latter doctrine lies at the very heart of Christian faith.
On it's face, however, the doctrine of The Trinity might appear to be a contradiction. One of the reasons why it appears so absurd is that God is beyond all of the 9 spacial dimensions and 1 time dimension that comprises our universe (26 spacial dimensions if String Theory turns out to be true). He's beyond all 10 (or 27, if string theory is confirmed) dimensions of our universe. What happens when we try to think of God in His triune being is that we try to conceive of the trinity in 3 dimensional space. We get the picture in our head of old man Yahweh sitting on the left hand side of Jesus with The Holy Spirit hovering above them. And we think "how can they be separate and yet be the same being? How can God be God and Jesus be God and The Holy Spirit be God all at the same time? This doesn't make any sense!" As I've already pointed out, whenever we try to concieve of God in His triune nature, we try to concieve of Him in 3 dimensions of space. This is a faulty way of trying to visualize The Holy Trinity because God is an extra-dimensional being, not a 3 dimensional one. This explains why we can't comprehend The Trinity.
But just because we can't comprehend beyond 3D doesn't mean it's irrational. For example, it's been pointed out by Hugh Ross and Neil Mammen that it can be mathematically proven that you can turn a basketball inside out in 4 dimensions of space without making a cut or a hole in the surface of the basketball. Even though it can be proven mathematically, it cannot be accurately visualized. Whenever I try to envision such a scenario, I inevitably have to make a cut in the basketball in order to turn it inside out.
Here's an analogy. Try to imagine a 2D world with a 3D creature hovering above the 2D world. The 2D people living in the 2D world. Now, let's say that you, the 3D creature entered into their world by putting your finger on the paper (which is the 2D creature's world). The 2D creature would then see your finger. You tell the 2D creature that this thing is call "a hand". If you put 3 fingers on the paper, the 2D creature would imagine that he's seeing 3 seperate entities. He would say "well, what do you know? 2 more hands showed up!" to which you would respond "No, this the same hand as you already saw. I just introduced you to 2 additional fingers which make up my hand. There's only one hand, but 3 fingers. These 3 separate fingers are joined together to make up my one hand." Now, to the 2D creature, this would appear absurd. Indeed, to the 2D person, you would sound like you're making theological contradictory double talk. But the only reason why it would sound that way to him is because it's impossible for him to visualize anything beyond the 2 dimensions of space that he experiences on a daily basis (he has no concept of up and down, only left and right). It's not a contradictory concept, just one that's impossible to concieve due to his limited-to-2D imagination. Whenever he tries to comprehend the three-fingers-one-hand concept, his head hurts and he just can't make any sense out of it. This is the same conundrum we face with the doctrine of The Trinity.
C.S Lewis, in his book "Mere Christianity", gave a similar analogy to help us understand why we can't understand the trinity. It too contained the fact that we're limited to imagining things to a maximum of 3 dimensions of space. He wrote "You know that in space you can move in three ways—to left or right, backwards or forwards, up or down. Every direction is either one of these three or a compromise between them. They are called the three Dimensions. Now notice this. If you are using only one dimension, you could draw only a straight line. If you are using two, you could draw a figure: say, a square. And a square is made up of four straight lines. Now a step further. If you have three dimensions, you can then build what we call a solid body: say, a cube —a thing like a dice or a lump of sugar. And a cube is made up of six squares. Do you see the point? A world of one dimension would be a straight line. In a two-dimensional world, you still get straight lines, but many lines make one figure. In a three- dimensional world, you still get figures but many figures make one solid body."
"In other words, as you advance to more real and more complicated levels, you do not leave behind you the things you found on the simpler levels: you still have them, but combined in new ways—in ways you could not imagine if you knew only the simpler levels. Now the Christian account of God involves just the same principle. The human level is a simple and rather empty level. On the human level one person is one being, and any two persons are two separate beings—just as, in two dimensions (say on a flat sheet of paper) one square is one figure, and any two squares are two separate figures. On the Divine level you still find personalities; but up there you find them combined in new ways which we, who do not live on that level, can. imagine. In God's dimension, so to speak, you find a be who is three Persons while remaining one Being, just is six squares while remaining one cube. Of course we cannot fully conceive a Being like that: just as, if we were so made that we perceived only two dimensions in space we could not properly imagine a cube. But we can get a sort of faint notion of it."
C.S Lewis goes on to say “And when we do, we are then, for the first time in our lives, getting some positive idea, however faint, of a super-personal—something more than a person. It thing we could never have guessed, and yet, once been told, one almost feels one ought to have be guess it because it fits in so well with all the things already.”
Now, no analogy is perfect. Nevertheless, I find it to be extraordinarily helpful. While it doesn't help us comprehend the Trinity in the least, it does help us to know why we can't comprehend it. And this is ok. We don't have to be able to comprehend The Holy Trinity in order to become Christians and to place our faith in Jesus Christ as Savior and Lord. What matters is whether the evidence is in favor of Christianity. I think it is (as I've pointed out in various posts in this blog). I may not be able to comprehend The Holy Trinity, but I DO apprehend it. Just as I haven't the faintest notion of how all the electronic parts of a computer work together in order to make a functioning computer, but I DO apprehend my computer indeed functions. In the same way, I accept that the doctrine of the trinity is true...even though it doesn't make a lot of sense to me because I can't possibly imagine phenomena beyond the 3 dimensions which I experience on a daily basis.