In this season of The Cosmic Library, you’ve heard us discuss how Fyodor Dostoevsky's Karamazov brothers converge, even as they're on seemingly distinct tracks. And the novel directs attention to convergences in surprising ways: at one point, for example, Ivan Karamazov alludes to non-Euclidean geometry in which parallel lines meet—in which otherwise separate things join.  It doesn't just happen mathematically, or philosophically: dreams, too, can bring the novel’s characters toward convergence. Robin Feuer Miller, Dostoevsky scholar, says here: “Dreams that characters have are as important to them, in the long run, and as illuminating to them in the long run, as any philosophical ideas that they might embrace.” Math and dreams both offer means by which alternative ways of thinking can be accessed, and by which separations might get resolved or reconsidered. Mathematician and science journalist Paulina Rowińska says in this episode, “Math is much richer than what we learn in school. And the key point, that’s also relevant to Dostoevsky, is that math is also relative, as with Euclidean/non-Euclidean.” Different geometries, different philosophies, and different states of consciousness all offer ways for characters to think differently, and change, and collide in The Brothers Karamazov. No single system seems victorious here, but the process that moves through system after system—or character after character—works with irresistibly vital, dramatic force. Guests for this season of The Cosmic Library: Garth Risk Hallberg, author of the novel City on Fire Andrew Martin, author of the story collection Cool for America Hearty White, host of Miracle Nutrition on WFMU Paulina Rowińska, author of Mapmatics Robin Feuer Miller, professor of Russian literature at Brandeis University and author of The Brothers Karamazov: Worlds of the Novel   Katherine Bowers, professor of Russian literature at the University of British Columbia and author of Writing Fear: Russian Realism and the Gothic Learn more about your ad choices. Visit megaphone.fm/adchoices