Dostoyevsky on the Problems of Evil and Geometry

Theology

Written by Mitch Stokes

Saturday, 19 December 2009 14:00

In The Brothers Karamazov, nineteenth century Russian novelist Fyodor Dostoyevsky parallels the problem of evil with the discovery of non-Euclidean geometry. Despite the naturalness with which evil and mathematics go together, Dostoyevskys discussion of mathematics is still surprising. His point isnt that mathematics causes human suffering, as true as that might be. Hes showing us, rather, one of the reasons the problem of evil is the most powerful objection to the existence of God; namely, it forces us to lay aside our preconceived notions of whats reasonable, something were loath to do. But the problem of evil isnt an intellectual problem or at least not primarily intellectual. Rather, its in part a problem stemming from mistaken loyalties. So too, the problem of geometry.One of the novels characters, Ivan Karamazov, is an astute intellectual who in many ways represents modernism (a version of rationalism), where reason claims our ultimate devotion. In a crucial conversation with his younger brother, Alyosha, Ivan divulges his beliefs about God. He begins with geometry, of all things. Ivan believes that reason constrains God to create the cosmos according to ordinary, Euclidean geometry. (Euclidean geometry is the geometry that Euclid presents in his famous book the Elements, the geometry most of us learned in high school.) But, Ivan says,there were and are even now geometers and philosophers, even some of the most outstanding among them, who doubt that the whole universe, or, even more broadly, the whole of being, was created purely in accordance with Euclidean geometry.The problem, according to Ivan, is that the real world may not be Euclidean, but non-Euclidean. That is, physical space doesnt answer to all the truths of ordinary Euclidean geometry. In real life, for example, parallel lines can meet! (Einsteins general theory of relativity later seemed to confirm this possibility.)Ivan responds with disgust to this prospect: Let the lines even meet before my own eyes, I shall look and say, yes, they meet, and still I will not accept it. Its not that Ivan would deny the fact that the lines meet. The problem is that their convergence would be repugnant. If, against all reason, parallel lines can meet, then space is just as twisted as the humans who inhabit it. By Ivans lights, even if God has made the world in a non-Euclidean fashion, he shouldnt have.Speaking of twisted humans, it similarly seems to Ivan that God shouldnt have allowed the occurrence of wanton evil. The existence of a perfectly good, all-knowing, and all-powerful God seems according to Ivans reasoning incongruous with the existence of horrific suffering. Again, its not the fact of suffering that Ivan denies that much is all too obvious its just that the fact is unacceptable, inappropriate, just plain wrong. It flies in the face of reason. So Ivan resists God, despite believing that He exists. Hes like the demons, who believe but swear fealty elsewhere. Ivan defers to what he can understand, to what seems reasonable. In this sense he is a modernist, and in this sense he is an idolater.Dostoyevskys pairing of mathematics and evil in this way, however, really does seem odd. Were aware that theres a problem of evil; but that someone would suggest theres an analogous problem of geometry strikes us as improper, insensitive even. Human suffering analogous to a mathematical discovery? Tell that to people in genuine pain. But modernists saw the discovery of non-Euclidean geometry as a bona fide crisis. Their fundamental belief that human reason is the ultimate epistemic authority was based on mans mathematical successes, in particular, on the legacy of Euclids Elements. Since its appearance around 300 BC, the Elements has prodded the Wests search for intellectual certainty. And the confidence it created in mathematics and reason was rewarded by the scientific revolution, a revolution that fulfilled Platos dream of mathematically describing the cosmos, thereby inaugurating the Enlightenment.But in the 1800s, a previously unthinkable mathematical theory (one in which parallel lines can meet and the sum of the interior angles of a triangle arent 180 degrees) suggested that this unqualified allegiance to the Elements and therefore to reason was misguided. Through non-Euclidean geometry, mathematics had begun to undermine itself and so, in effect, reason toppled its own rule. This is modernists problem of geometry. It tends to undermine belief in reason not unlike the way the problem of evil undermines belief in God.This is some of the background to Ivans struggle. In spite of Ivans allegiance to reason, the discovery (invention?) of non-Euclidean geometry caused Ivan to question his loyalties. He says that reason our reason at least is fundamentally Euclidean (Dostoyevsky is alluding here to a view held by the Enlightenment philosopher, Immanuel Kant). And because our reason is Euclidean, its hobbled. So Ivan is torn; whos to be trusted? The existence of non-Euclidean geometry is a mathematical discovery a discovery of reason. Reason at one time told us that the world was Euclidean. Now it tells us, all apologies, that it was wrong. Ivan despairs, eventually going mad.Ivans struggle mirrors the Wests. Since before Plato, the West held reason in high esteem. (The modernist spirit is not, therefore, modern after all.) But then just when the Enlightenment was hitting its stride reason threw itself into doubt with non-Euclidean geometry. This discovery is one of the main causes of postmodernisms suspicion of reason.But much of Dostoyevskys commentary here would be lost on us without an appreciation of the non-Euclidean revolution. And this is but one example of how widespread mathematics influence is. Not putting too fine a point on it, mathematics is important. But merely being able to do mathematics is insufficient, primarily because theres much more to understanding mathematics than recipes and formulas. To be sure, mathematics is a powerful means for describing, predicting, and controlling the physical world. But its study is also required for understanding culture. To allude to Kant: calculation without understanding is empty, understanding without calculation is impossible. Our problem with geometry is not the modernists; our problem is that we dont understand it.

http://www.credenda.org/index.php/Theology/dostoyevsky-on-the-problems-of-evil-and-geometry.html (07.08.2015)