An Imaginary, Ineffable God

Envisioning the reality of God in a complex universe.

Imaginary: Having existence only in the imagination; unreal.

René Descartes, my least favorite guy (well, okay, not really, but he did screw things up a bit for western philosophy and religion for a good long time) called the square root of a negative number “imaginary”. Imaginary numbers do not fit on a standard number line—they have no place on it, and therefore seemingly no place in the real, tangible world. And perhaps that’s fair enough. In the real, tangible world, I’ve so far never needed the square root of a negative number.

Still, at some point in the evolution of mathematics, the need arose for some sort of understanding of the square root of imaginary numbers, if for no other reason that mathematics must present itself as a complete philosophy, and as a complete philosophy has to account for things which can be conceived of, even if they have no practical purpose in the mundane lives of men. And yet clearly, these “imaginary” numbers exist because we encounter them here in this universe, even if they only exist as fleeting thoughts, fragments, blueprints for something else we do understand. And so Gottfried Leibniz, one of my favorite underdogs of history, wrote of the imaginary number and called it “the Divine Spirit” , “that amphibian between being and non-being.” And of these same numbers Leonhard Euler wrote, “…and of such numbers we may truly assert that they are neither nothing, nor greater than nothing, nor less than nothing, which necessarily constitutes them imaginary or impossible.”

…Or, you know, ineffable.

Ineffable: Incapable of being expressed; indescribable or unutterable.

Now of course in mathematics, we have a way around this because we can express imaginary numbers symbolically, and we have a “definition” of what such a number is. We can’t really talk about what an imaginary number is, not in the sense we can talk about other numbers, as representations of quantity. The best we can do is talk around them, explain them in terms of other things. Because though we have made allowances for them, they are nonsensical to us. Being and non-being.

Which, of course, is my understanding of God.

The question remained, though: how do we deal with imaginary numbers? How do we conceptually express their relationship to the “real” world? German mathematician Carl Friedrich Gauss came up with this brilliant solution: instead of a number line, he created a number grid, with an x and y axis. “Real” numbers went on the x axis, and “imaginary” numbers on the y. Thus the relationships between the numbers could be depicted and understood. Hence 2+i was written as a point +2, +1 on the grid, while 3-2i was a point +3, -2 on the grid. He called this grid the complex plane.

In this way, imaginary numbers have a relationship to the real world. They might not be in the world of man’s common experience, especially if that experience is overly linear. But a deeper, multidimensional view of numbers—of the universe—reveals these intricate relationships, and thus their “realness”. They “exist” because they stand in relation to that which I can see, feel, and know.

In a recent post in his blog, Patrick quotes Paul Tillich: “It would be a great victory for Christian apologetics if the words “God” and “existence” were very definitely separated except in the paradox of God becoming manifest under the conditions of existence, that is, in the Christological paradox. God does not exist. He is being—itself beyond essence and existence. Therefore, to argue that God exists is to deny him.” (Systematic Theology)

Perhaps it is strange for someone reared in the liberal arts to find such deep connection between God, spirit, and mathematics. But I am deeply moved by the idea of God’s non-existence in the sense of the non-existent imaginary number. I am moved by the notion that something may be removed from natural experience, arising only in contemplation of Mystery, and yet have a profound effect on the world. Perhaps my experience of math would not be less were I not introduced to imaginary numbers, but certainly knowing them has enriched my experience and understanding of the world. So it is with God, too. I can conceive of a world without God in it, but knowing God has certainly enriched my experience of life.

But it isn’t merely knowing about God that enriched me. It is knowing God. It is being able to stand in relation to God. It is one thing is to have a rough conception of God in a linear world where God has no real place; it is quite another to see the relationship etched in a complex plane, to make a place for God in His world as well as mine. That is where God becomes most real: when I see God not solely as something outside of myself, but as an eternal unfolding, a process, something both creating and created, of which I and all creation are absolutely a part. God is not so much being as action: God isn’t something that is so much as something that is becoming. I understand what the rabbis mean when they say God is a verb: God is the action of all the universe.

But my comparison between the ineffable and the imaginary eventually fails, for Tillich is right: God does not “exist”. God is existence. One of my most difficult problems early on in my study of Kabbalah was the question of creation. “But why?” I asked. “Why did God create in the first place?” Many of my peers tried to answer the question with Midrash and mythology, but I was deeply unsatisfied with all their answers until one day a young man said to me, “You want to know why but I’m afraid there is no why. Creation happened because God exists.”

I believe that.

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