I’ve been reading some classic literature lately and was interested to see mathematics show up two of these works.
Last week I read Voltaire’s Candide (1759). One of the main characters is the ridiculous Dr. Pangloss, who subscribes to Leibniz’s philosophy of optimism (or Voltaire’s take on optimism). Leibniz believed in a good and omnipotent God who created “the best of all possible worlds” and Voltaire pokes fun at this belief by making Dr. Pangloss and the other characters suffer miserably despite their optimism.
Although Voltaire does not mention Leibniz’s mathematics, math does show up later when Voltaire’s takes a jab at Parisian scientists in Chapter XXII:
Candide stayed in Bordeaux no longer than was necessary for the selling of a few of the pebbles of El Dorado, and for hiring a good chaise to hold two passengers; for he could not travel without his Philosopher Martin. He was only vexed at parting with his sheep, which he left to the Bordeaux Academy of Sciences, who set as a subject for that year’s prize, “to find why this sheep’s wool was red;” and the prize was awarded to a learned man of the North, who demonstrated by A plus B minus C divided by Z, that the sheep must be red, and die of the rot.
Right now I’m reading Fyodor Dostoyevsky’s The Brothers Karamazov (1880). Today I read Part II, Book V, Chapter 3, in which Ivan Karamazov mentions non-Euclidean geometry. I’ve reproduced the entire paragraph below and have highlighted the relevant passage.
“Joking? I was told at the elder’s yesterday that I was joking. You know, dear boy, there was an old sinner in the eighteenth century who declared that, if there were no God, he would have to be invented. S’il n’existait pas Dieu, il faudrait l’inventer. And man has actually invented God. And what’s strange, what would be marvellous, is not that God should really exist; the marvel is that such an idea, the idea of the necessity of God, could enter the head of such a savage, vicious beast as man. So holy it is, so touching, so wise and so great a credit it does to man. As for me, I’ve long resolved not to think whether man created God or God man. And I won’t go through all the axioms laid down by Russian boys on that subject, all derived from European hypotheses; for what’s a hypothesis there is an axiom with the Russian boy, and not only with the boys but with their teachers too, for our Russian professors are often just the same boys themselves. And so I omit all the hypotheses. For what are we aiming at now? I am trying to explain as quickly as possible my essential nature, that is what manner of man I am, what I believe in, and for what I hope, that’s it, isn’t it? And therefore I tell you that I accept God simply. But you must note this: if God exists and if He really did create the world, then, as we all know, He created it according to the geometry of Euclid and the human mind with the conception of only three dimensions in space. Yet there have been and still are geometricians and philosophers, and even some of the most distinguished, who doubt whether the whole universe, or to speak more widely, the whole of being, was only created in Euclid’s geometry; they even dare to dream that two parallel lines, which according to Euclid can never meet on earth, may meet somewhere in infinity. I have come to the conclusion that, since I can’t understand even that, I can’t expect to understand about God. I acknowledge humbly that I have no faculty for settling such questions, I have a Euclidian earthly mind, and how could I solve problems that are not of this world? And I advise you never to think about it either, my dear Alyosha, especially about God, whether He exists or not. All such questions are utterly inappropriate for a mind created with an idea of only three dimensions. And so I accept God and am glad to, and what’s more, I accept His wisdom, His purpose which are utterly beyond our ken; I believe in the underlying order and the meaning of life; I believe in the eternal harmony in which they say we shall one day be blended. I believe in the Word to Which the universe is striving, and Which Itself was ‘with God,’ and Which Itself is God and so on, and so on, to infinity. There are all sorts of phrases for it. I seem to be on the right path, don’t I’? Yet would you believe it, in the final result I don’t accept this world of God’s, and, although I know it exists, I don’t accept it at all. It’s not that I don’t accept God, you must understand, it’s the world created by Him I don’t and cannot accept. Let me make it plain. I believe like a child that suffering will be healed and made up for, that all the humiliating absurdity of human contradictions will vanish like a pitiful mirage, like the despicable fabrication of the impotent and infinitely small Euclidian mind of man, that in the world’s finale, at the moment of eternal harmony, something so precious will come to pass that it will suffice for all hearts, for the comforting of all resentments, for the atonement of all the crimes of humanity, of all the blood they’ve shed; that it will make it not only possible to forgive but to justify all that has happened with men — but thought all that may come to pass, I don’t accept it. I won’t accept it. Even if parallel lines do meet and I see it myself, I shall see it and say that they’ve met, but still I won’t accept it. That’s what’s at the root of me, Alyosha; that’s my creed. I am in earnest in what I say. I began our talk as stupidly as I could on purpose, but I’ve led up to my confession, for that’s all you want. You didn’t want to hear about God, but only to know what the brother you love lives by. And so I’ve told you.”
There is a brief discussion of this passage on the Mathematical Fiction website.