Syzygy

Six is a ‘perfect number’ – it’s the sum of its divisors, 3, 2 and 1 – and it’s favoured for that reason by Azarya Sheiner, a six-year-old mathematical genius who is the central attractor, but not the protagonist, of Rebecca Goldstein’s new novel, 36 Arguments for the Existence of God. Twenty-eight is the next perfect number (divisors 14, 7, 4, 2, 1), and 28 arguments for the existence of God might have been more than enough. But 36 is a perfect number of perfect numbers: a perfect square, and it’s twice 18, a deeply lucky number according to the Kabbalistic ‘gematria’ system of assigning numerical values to Hebrew letters (the letters of chai, the Hebrew for ‘life’, have a joint value of 18). There are in addition 36 tzadikim or righteous ones alive on earth at any time, according to Jewish mystical tradition, the Lamed Vavniks (lamed is the letter ל, numerical value 30, vav is the letter ך, numerical value 6). The world will come to an end, it’s said, if their number ever drops below 36.

If you want to know more, ask Jonas Elijah Klapper né Klepfish, the second main attractor, the second of the four people who have to be brought into syzygy for the sake of the book’s central scene. He’s a ‘Jewish walrus’, born poor on the Lower East Side, who has a preposterous appetite for high culture, and a rather specious way of locating 36 in his own name. He’s the head and sole member of the Department of Faith, Literature and Values at Frankfurter University, 12 miles ‘downriver’ (upriver?) from Harvard: a vatic, monstrous man, super-Bloomian, a Bocca della Verità ‘mashing his chin down towards his chest, so that his jowls fanned out like an Elizabethan ruff’, his facial expressions extravagant, as in a silent movie. Professor Klapper says gorgeous things. He has a weakness for fast food. There is a depth of sadness in his eye. He’s a considerable creation, not the less so for being a type.

The third party is Goldstein’s protagonist, Cass Seltzer. Seltzer isn’t a genius (unlike most of Goldstein’s protagonists) but orbits in an irregular, lemniscate fashion between Azarya and Klapper, who are. He’s a psychologist of religion at Frankfurter, the author of a recent bestseller, The Varieties of Religious Illusion, which contains 36 arguments for the existence of God, reproduced verbatim, along with their rebuttals, as the appendix to Goldstein’s 36 Arguments. Seltzer is a mild presence, his type ‘fundamental niceness’. He’s known among the ‘new atheists’ of our day (Hitchens, Dawkins et al) as ‘the atheist with a soul’; unhappily divorced, he has recently been restored by a new lover, the fierce and mildly prosopagnosic Lucinda Mandelbaum.

Mandelbaum isn’t one of the central four characters and is absent for most of the novel, but she’s a classic Goldstein creation, bursting with brain chic. She’s the author of Mathematical Foundations of Game Theory with Applications to the Behavioural Sciences; she’s famous for discovering a non-Nash equilibrium (‘the Mandelbaum Equilibrium’); she’s beautiful, known as the ‘Goddess of Game Theory’. She thinks, to her cost, that most things in life are a zero-sum game, and she has – as she leans over you – brandy-glass breasts.* She has invented a new verb, ‘to fang’. To fang someone in debate – her speciality – ‘is to pose a question from which the questioned can’t recover. You could see the stun, the realisation of helplessness setting in.’

Then, out of the past, bounds Roz Margolis, the fourth figure, tall, glad, strong, an anthropologist specialising in the Amazon, her breasts womanly but not further specified, her ‘upper lip sweetened by all the laughter it had laughed’. She has founded a new non-profit organisation, the Immortality Foundation, to conquer ageing, and it seems to be working for her. She marks another position on Goldstein’s map of ideas: what’s the relation between religion and the desire for immortality? If immortality were given on earth, how much religion would remain?

Each of the 36 chapters of 36 Arguments has an argument for a title, and Margolis arrives, likeably, in Chapter 4, ‘The Argument from the Irrepressible Past’. The narrative obliges, shifting back 20 years to 1988, when Klapper ruled at Frankfurter and Seltzer was a member of his novitiate (i.e. one of his PhD students). Klapper, or ‘the Klap’, is interested in the gematria value (36) of Seltzer’s Jewish forename (Chaim) and in the fact that Seltzer’s mother grew up in an Orthodox Jewish community that she later left (like Goldstein herself). He learns, with exophthalmic excitement, that Seltzer is related to the spiritual leader or ‘Rebbe’ of this sect, the ‘New Valdeners’, who left their home town of Valden in Hungary in 1939 and founded ‘New Walden’, a shtetl 40 miles upriver from New York City on the west bank of the Hudson (modelled on New Square, Rockland County).

A visit is arranged, and the scene is set for the novel’s central event. Klapper, Seltzer and Margolis meet the child Azarya, the Rebbe’s only son and successor, blond, blue-eyed, brilliant, ignorant of the outside world. Azarya is enchanted by numbers, which he calls maloychim, ‘angels’, and in particular by ‘special’ numbers: prime numbers, perfect numbers, squares, cubes. He has understood many of their properties; his powers seem to match those of the young Gauss. He throws off a version of Russell’s paradox in a teasing aside to his father. He gives Roz a drawing to take away, a puzzling pattern of numerals. She works out that it represents factorials and constitutes a proof that the nth difference of xⁿ is n!

An unthinking question from Klapper triggers Azarya into a proof that there is no highest prime number. He recites his proof (a variant of Euclid’s) poetically and blissfully to the assembled male New Valdeners during a ceremony. Seltzer attends, suffering ‘sensory assault’ on entering the synagogue from

the contained roar of the vast boiling sea of black, which gradually individuated into discrete men, hundreds rising steeply to the rafters in tiered waves from the small cleared centre … It was the homogeneity of the Valdeners’ appearance and the synchronisation of their motion that liquefied them, the individuating features smoothed away by the identical beards and the payess and kaputas and shtreimlach [sidelocks, kaftans, fur hats], undulating waves made up of Valdeners swaying in unison in great sweeping arcs in time to the powerful surge of their song …

The rows and rows of Valdeners were jumping, like one large organism they rose upward and returned to earth in perfect unity … Ever since the Ba’al Shem Tov, the master of the Good Name, rebelled against the intellectualised strain of Judaism prevailing in his day, the Hasidim have cultivated a worship of the divine that is experiential, sensual, ecstatic. This is why they dance. This is why they sing. But the Valdeners of New Walden possessed a path to ecstasy that was theirs alone, and it was obvious on every face up and down the tiers. The Rebbe’s son was their ecstasy … In every row, in every tier, in the whole assembled crush of Valdeners, carried on cantillated waves of explosive love, blasted with their gratitude for having been born Valdeners.

Here, at the age of six, Azarya is happy. Growing up, he is mortally oppressed by the New Valdeners’ expectations. ‘Every time I hear how they call me, Azarya ha-kodesh, Azarya the holy one, it sounds like shovels of dirt on a coffin.’ At 16 he goes out into the world and decides to become a mathematician at MIT but his father dies suddenly, and his choice changes: leave New Walden altogether or become the new Rebbe. The book returns to 2008 and Azarya’s decision is unfolded, along with much else, notably a roaring debate about the existence of God between Seltzer and a flinty Christian in Harvard Memorial Church.

Goldstein trained as a philosopher (she has taught at Columbia, Rutgers, Harvard, Brandeis and Trinity College Hartford). Her books hug the East Coast strip bounded by Princeton in the south (where she earned her PhD under Thomas Nagel) and Boston in the north. She has what Hobbes called libido sciendi. She’s absorbed by the relation between emotion and intellect, and in particular by genius. The off-chart mathematician Noam Himmel opens her first novel, The Mind-Body Problem. William James and his sister Alice feature in The Dark Sister (1991), a book Iris Murdoch called ‘brilliantly ingenious, beautifully written and thoroughly alarming’. More recently, the physicist Samuel Mallach appears in Properties of Light (2000); Gödel and Spinoza are the focus of her non-fiction works Incompleteness: The Proof and Paradox of Kurt Gödel (2005) and Betraying Spinoza: The Renegade Jew Who Gave Us Modernity (2006). Klapper is, so far, the closest she has come to the arts.

Goldstein’s conceits are sweet in the street sense. They aren’t just one-liners, they have body. Her books are stuffed with Judaica, sacred and secular, always carefully explained. They lay out a great range of witticisms, echoes and allusions that require considerable background knowledge, and contain jokes and themes that are likely to remain obscure to those who haven’t done philosophy. Seltzer periodically experiences himself in a way described by Nagel in The View from Nowhere (1986), from which Goldstein quotes. As we try to achieve a fully objective conception of the world, Nagel says,

each of us, reflecting … must admit that one very large fact seems to have been omitted from its description: the fact that a particular person in it is himself. What kind of fact is that? What kind of fact is it – if it is a fact – that I am Thomas Nagel? How can I be a particular person? … It can seem that as far as what I really am is concerned, any relation I may have to TN or any other objectively specified person must be accidental and arbitrary. I may occupy TN or see the world through the eyes of TN, but I can’t be TN. I can’t be a mere person … The experiences and the perspective of TN with which I am directly presented are not the point of view of the true self, for the true self has no point of view … Something essential about me has nothing to do with my perspective and position in the world.

‘Unless you have had this thought yourself,’ Nagel writes, ‘it will probably seem obscure, but I hope to make it clearer.’ I find it obscure, but Nagel and Seltzer are not alone. When I gave this passage to a seminar at New York University, and asked whether anyone felt they knew what Nagel and Seltzer were talking about, a third were bewildered, a third were unsure or undecided, but a third judged that they’d had experience of exactly the same kind.

Goldstein’s novels are also, with the usual provisos, romans à clef. Daniel Korper, an expert lover in The Mind-Body Problem who identifies the ‘curve from the waist out to the hips’ as the most moving curve in a woman’s body (unmindful, perhaps, of the evolutionary energy behind this emotion), is widely held to have acquired descriptive details from two Princeton philosophers. Mallach, the physicist in Properties of Light, shares many ideas with David Bohm. Klapper, who thinks ‘Goethe … settled for being a genius’ and could have gone further, has, like Bloom (Harold, not Allan), an eidetic memory. And if Goldstein is caught up in the erotics of mental power, so the female protagonist in The Mind-Body Problem thinks (as her best friend observes) that ‘the male sexual organ is the brain.’

Perhaps the genius in Goldstein is a secular surrogate for a Rebbe, dreamed by an epikoros, a renegade from Orthodoxy. If so, the loop closes in this book: the genius becomes the Rebbe. Nietzsche says of philosophy that ‘one builds one’s philosophy like a beaver, one is forced to and does not know it,’ and perhaps the same is true of novelists. Some will be impatient with what feels mechanical, a matter of flat-pack assembly, in Goldstein’s composition; the gearing of the book can be felt as it operates. There are moments of descriptive overload, and 36 Arguments is to a remarkable degree a matter of surfaces, even when it discusses inmost things. But it’s also 400 pages of smarts. There are thousands of neat things, from the Bellovian point about the soul-information carried in a person’s upper lip to Klapper’s discussion of Arnold’s ‘Dover Beach’ – a poem that has now, after McEwan’s Saturday, made two full appearances in fiction in five years. There are strong minor characters: Seltzer’s fierce French ex-wife, with ‘starved-wolf’ eyes; Shimmy Baumzer, ex-kibbutznik, president of Frankfurter, operator; Sy Auerbach, Seltzer’s New York literary agent, who has ‘an agenda that goes beyond putting the “antic” back in “pedantic” and the “earning” back in “learning”’: he wants a new kind of public intellectual, bypassing the old-timers who don’t know ‘their asses from their amygdalas’.

There remains the 50-page appendix, which contains Seltzer’s 36 arguments for the existence of God, each with its rebuttal. It opens with the big three, the Cosmological Argument, the Ontological Argument and the Argument from Design (strictly speaking the Argument to Design), all refuted by Kant, although not as neatly as by Hume before him. It unravels through the obscene (no. 25, the Argument from Suffering) and the contemptible (no. 31, Pascal’s Wager) to the absurd (no. 36, the Argument from the Abundance of Arguments). Seltzer seems to think that the arguments are all ‘formally constructed in the preferred analytic style, premises parading with military precision, and every shirking presupposition and sketchy implication forced out into the open and subjected to rigorous inspection’. One trusts that Goldstein doesn’t agree, or that her appendix isn’t the same as Seltzer’s, because the arguments are a mess, thick with enthymeme, which isn’t a herb for remembrance. They couldn’t have been properly set out, in fact; the appendix would have been insufferably long. As it stands it is to be read lightly, in a spirit of sporting irritation and expostulation.