In one of my classes we’re about halfway through The Brothers Karamazov, and we had an interesting conversation yesterday in which we tried to sort through what Ivan means when he says he has a “Euclidean mind.” One of my students rightly pointed out that my own explanation of the phrase did not seem to fit all his uses of it. So I came home and wrote up some thoughts that I emailed to the class. This is what I wrote to them.

Here’s how Ivan introduces the concept of a “Euclidean” mind:

… it is not for me to understand about God. I humbly confess that I do not have any ability to resolve such questions, I have a Euclidean mind, an earthly mind, and therefore it is not for us to resolve things that are not of this world. And I advise you never to think about it, Alyosha my friend, and most especially about whether God exists or not. All such questions are completely unsuitable to a mind created with a concept of only three dimensions. And so, I accept God, not only willingly, but moreover I also accept his wisdom and his purpose, which are completely unknown to us….

That is: because our minds are earthly we cannot understand anything about God, since God is by definition trans-earthly. Therefore the only option is accept, by an act of will I suppose, what we cannot possibly understand.

So Ivan says

“I accept God” “I also accept his wisdom and purpose” “I do not accept this world of God’s”

Now, at first this seems nonsensical to me. If you do not accept the world that God created then how can you claim to accept “his wisdom and purpose”? But I think he means this: I know that God is God and I am not, I agree in principle that He is infinitely good and in comparison with him I am just a bedbug, but still, with my Euclidean mind — the mind God gave me, by the way — I look at the way children suffer in this world and I say: No thanks. I can’t accept that and I don’t want to accept that.

Then, at the end of his discourse, he comes back to the “Euclidean” theme and reaffirms some of his points made earlier — but adds some confusing ones:

I am a bedbug, and I confess in all humility that I can understand nothing of why it’s all arranged as it is. So people themselves are to blame: they were given paradise, they wanted freedom, and stole fire from heaven, knowing that they would become unhappy — so why pity them? Oh, with my pathetic, earthly, Euclidean mind, I know only that there is suffering, that none are to blame, that all things follow simply and directly one from another, that everything flows and finds its level — but that is all just Euclidean gibberish, of course I know that, and of course I cannot consent to live by it! What do I care that none are to blame and that I know it — I need retribution, otherwise I will destroy myself.

He goes on for some time in this way. The more I think about it the more confused I get. Some of it I can make no sense of at all: I have no idea what he means when he says “everything flows and finds its level.” But as far as I can tell he’s saying three chief things here:

Christianity teaches that “people themselves are to blame” for rebelling against God; But with his Euclidean mind he can only see that, thanks to the way God chose to make the world, “there is suffering” for which “none [that is, none of us human beings] are to blame”; Nevertheless, even if no human being is to blame, “I need retribution, otherwise I will destroy myself.”

So who will be the object of his retribution? We find out in the story he goes on to tell, the story of the Grand Inquisitor: the Son of God will be the one he punishes.

Ivan has a very complicated relationship to what he thinks Catholicism is: he believes it to be a power-hungry politically-motivated corruption of the Gospel, a network of manipulators using the appeal of Christianity to accomplish their own ends — but that’s precisely what he would do in the same circumstances, because he wants retribution here and now, not in some imagined hereafter. If Ivan could have been anything he wanted to be, he probably would have been a great Renaissance Pope: corrupt by the standards of the Gospel, but effective in worldly terms.

What Ivan tries to avoid seeing, what he can’t quite face or reckon with, is what we learn from Alyosha and Zosima: that God explicitly offers Himself to be the object of our retribution. “No one takes [my life] from me, but I lay it down of my own accord. I have power to lay it down, and I have power to take it again; this charge I have received from my Father” (John 10:18).