The Mathematics of Madness

“Madness” and “insanity” are the words most often deployed in descriptions of Hilda Hilst’s enigmatic novella, With My Dog-Eyes. It gives voice to “a mind unravelling,” writes Nick Lezard in The Guardian, “and through the gaps we see a horrified fascination with the body, a kind of carnal awareness of existential futility.” “[F]luid, shifting narration tells the story — if you can call it that — of mathematician and poet Amós Kéres’ descent into madness,” adds The Independent‘s Holly Williams, “mov[ing] rapidly between first person present tense, recalled memories, reported speech, and chunks of poetry; between absurdism, theory, fable and filth.” The novel “reads like a long poem,” Juan Vidal concurs in his review for NPR, “with utter insanity pervading each and every page. The vivid, disjointed prose mirrors the troubled mind of our protagonist… an expert in pure mathematics who is losing his grasp on reality.”

For me, however, the most captivating quality of With My Dog-Eyes is not the way in which Kéres’ burgeoning insanity leads his representations of events to become increasingly disjointed. That sort of thing has been done often enough before that it no longer bears remarking on. More captivating here is the way in which the novel’s structure projects a mind so fundamentally, inflexibly logical — so absolutely committed to mathematics — that when his reality begins to lose its logical underpinnings, when he ceases to grasp the causal connections between sequential experiences, Kéres mounts a resistance to insanity by seeking refuge in mathematical logic and marshalling his experiences into a form that follows its rules. Although this choice of form is to some extent suggestive of Kéres’ insanity, I was struck by how it also suggests his striving for coherence in the face of insanity — albeit a coherence that may likewise appear to be tainted by insanity insofar as the structure beneath the novella’s narrative surface is built upon an alternative to narrative logic.

“Poetry and mathematics,” Kéres muses, identifying his twin passions while recalling the onset of his insanity:

The black stone structure breaks and you see yourself in a saturation of lights, a clear-cut unhoped-for. A clear-cut unhoped-for was what he felt and understood at the top of that small hill. But he didn’t see shapes or lines, didn’t see contours or lights, he was invaded by colors, life, a flashless dazzling, dense, comely, a sunburst that was not fire. He was invaded by incommensurable meaning.

Kéres suffers from this event, of course, and begins to succumb to inexplicable lapses of time. While delivering a lecture on mathematics one day, he loses his train of thought and pauses for what he believes is only an instant. Later, though, he learns that his audience watched him staring into space for fifteen minutes before he returned to the task at hand — and worse than that, several students have complained to his superiors that such events are becoming fixtures of his classes. Rather than simply detailing Kéres’ lapses of time, however, With My Dog-Eyes as a whole is structured in a way that mimics their effects. Time and again events underway are cut off and interrupted by recollections of other, unrelated events, and these interruptions are in turn interrupted by yet other events, and even these interruptions of interruptions are themselves interrupted, until the narratorial focus snaps back to one or another of the previous recollections and the events therein resume or conclude as if they weren’t interrupted at all.

Mathematical Formulae

Disjointed, perhaps, but in another sense perhaps not. Although Kéres’ experience of madness no doubt disjoints his perception of reality, his recollection and articulation of that experience rejoints his reality along apparently mathematical lines. Every interruption of an event suggests some sort of association between that which is interrupted and that which interrupts. Moreover, every conclusion to an interrupted event delineates a boundary that encases all of the event’s associated interruptions no matter how disparate they may otherwise be. As a result, although the events detailed by Kéres appear to lack coherent narrative organization because they are presented achronologically and without any evident causal connections, a closer look at their structure reveals an attempt at mathematical organization instead. Sequences of interruptions constitute something akin to mathematical sets when bound together within broader events that receive a conclusion. Other events, outside of these sets, perform the role of functions when by modifying either an entire set or one of the events within it, and still other events that interlace the sets work to establish or modify the relations between several of them.

Beyond serving as a mathematician’s account of his own descent into madness, then, With My Dog-Eyes also stands as Kéres’ attempt to reclaim his sanity by conforming his experiences to a non-narrative logic that may still enable him to make sense of them. This logic affords him a structural foundation on which to articulate his experiences and better equips him to literally commensurate the bursts of “incommensurable meaning” that afflict him. Of course, every narrative that surveys a life and takes stock of its significance is, in a sense, a narrative pegged to a mathematical formula, at least to the extent that it fixes some sort of value to the life in question by illustrating “what it all adds up to.” But while most works of that sort cleave to fairly linear formulae that are compatible with conventional narrative logic, With My Dog-Eyes employs a formula more appropriate to its narrator and his mathematical mind. The result is not the pure and simple chaos of a man’s reality falling apart: “a mind unravelling,” “a descent into madness,” “utter insanity pervading each and every page.” It is an experience of chaos relentlessly subjected to a system of order whose principles are not easily accommodated by the medium in which the experience is given expression.

Silence, True and Pure

Me and Ivy

Silence has shrouded this space for much of the last few months because, in my life offline, most of my recent thoughts have been bent around a different kind of silence, a silence true and pure. In April 2014, my wife and I became parents to a healthy and happy little girl named Ivy. Not quite six months later, however, Ivy underwent behavioural tests that showed some signs of hearing loss, and then, when she was exactly six months, specialised tests revealed that she is in fact profoundly deaf. She can’t hear sounds of any kind, not even at the volume of a close-range aircraft engine, and she suffers hearing loss so extreme that she may never be able to hear at all.

In coping with the failure of hearing aids, in anticipating the insertion of a cochlear implant, in working full-time and parenting while also learning how to respond to deafness in children and how to adjust our lives to meet the needs of a child with a severe disability, the stresses of the period following Ivy’s diagnosis have been monumental. But some of the most monumental stresses of all have come less from practical difficulties than from daily wrestling with a sense of long-term loss and the grief that attends it. To know that our daughter has no access to sound is to know that we may never be able to share with her so much of what we most appreciate in the world. For my wife, the greatest loss to Ivy is music in all its varieties. Coming from a family for whom music is the lingua franca of shared experience, it has been terrible for her to begin processing the knowledge that Ivy will in some sense be forever cut off, kept at a distance, from that part of her heritage.1 For me, of course, what seems to be lost is Ivy’s access to what I believe is the greatest of the pleasures of literature.

I was teaching The Scarlet Letter and Leaves of Grass when the results of Ivy’s tests came through and, at the same time, I was preparing to teach Gertrude Stein, Gary Lutz, Lydia Davis, and dozens of other writers who invest extraordinary energy in distinct, challenging, and versatile prose styles. I could not escape the obvious truth. So much of what literature means to me depends on being attuned to its prosody. So much of what makes it valuable for me resides in the harmonies and dissonances that develop and dissolve as the eye passes over a sentence, the succession of concordant and discordant intonations offered up by the author’s careful selection of words and by the equally careful positioning of those words in relation to one another. The value of prosody sings to me from the shelves full of books in my house and from every page of my own book, Blood and Bone, which was published when Ivy was just eight weeks old.

Language is the distillation of the constituent elements and concepts of the world, in all their overwhelming variety, into a system of symbols. For most people, at first, those symbols take the form of sound. Literature, then, is not a system of symbols constructed to represent the world, but a system of symbols constructed to represent other symbols, a lexical representation of the auditory symbols that are our primary means of referring to the world and of thereby representing it. Even though reading remains a “visual business,” as William H. Gass puts it, the writers whose work attracts me are those whose practices involve what Gass calls a sense of “the marvelous palpable quality of making words and sounding them.” Indeed, whether it be the work of Didion or Sontag, McCarthy or Murnane, Hemingway or Faulkner, Gaddis or Wallace, what resonates most powerfully with me is work in which each word seems to have been selected as much for its fixed referential qualities as for its atmospheric musicality, so that a carefully constructed tonal and prosodic soundtrack shadows the literal meaning of every sentence. But one need not turn to the writers above to seek out works in which prosody stands at the forefront of appreciable literary qualities. It’s there, too, at the forefront of just about every children’s book on the market — the majority of which make liberal use of qualities like alliteration and rhyme — so that Ivy’s deafness blocks her access to the pleasures of the literature available to her even at this early stage in her life. Will it hold other pleasures for her sometime further on? And equally, given the efforts now underway to facilitate Ivy’s acquisition of language, will literature come to hold for her distinct and unique pleasures that I can never access?

My wife and I are in the midst of learning British Sign Language (BSL) so that we can pass it on to her. This is a difficult process because, whereas hearing children acquire language by environmental means, simply by being within earshot of spoken language on a regular basis, Ivy will acquire it only through bursts of direct visual contact with BSL practitioners. Nevertheless, with BSL as her native language, with the constituent elements and concepts of the world distilled into a system of symbols entailing bodily movement, written language will call to mind a complex of worldly referents and movement sensations where otherwise it would call to mind a complex of referents and sounds.2 If, for me, to read is to see a word written on the page and then, reflexively, to simultaneously grasp its referent and hear in my head the whisper of its sound, will Ivy’s reading involve grasping a referent while also feeling a ghostly motion passing through her fingers, her face, her torso and her arms? If written words transmit to me a sense of music unaccompanied by motion, will they transmit to Ivy something like a dance without a tune? What exactly will be, for her, the sensation that shadows their meaning? And if, someday, Ivy were to read the work of any of the writers named above, would she experience a sensation as pleasurable as the one I derive from their sound? She almost certainly wouldn’t. This is not to say that the sensation of movement in sign language cannot generate pleasure,3 but only that the above writers have arranged their words on the page so as to produce pleasure through sound without regard for signs. Additionally, since sign languages vary greatly from country to country and even amongst countries that share a spoken language, and since the grammatical structures of the sign languages of English-speaking countries tend to depart significantly from the structures of spoken English, chaos is the inevitable result of any attempt to sign a word-for-word translation of a sentence as written in English.

When it comes to novels, then, what possibilities exist for native signers? Is there anywhere a novel written so as to be instantly grammatically intelligible to them, independent of any habituation to the grammar of written English? Is there anywhere a novel whose prose, whose selection and sequencing of words, is directed towards producing pleasurable sensations of ghostly movements for signers rather than producing sensations of sounds? Is there a work whose every turn of phrase is intended not to appeal to those who can hear and to generate pleasure through prosodic musicality, but rather to appeal specifically to the deaf by pleasurably conducting the motions of a body accustomed to sign? Is the composition of such a work even possible? If so, what sorts of sensations would the reading of it produce in a person who reads the way I do?




1. While cochlear implants “have the potential to magnificently enhance the understanding and acquisition of spoken language,” as Gavin Francis observes in a recent article in the New York Review of Books, “15 to 20 percent of recipients gain little benefit from them and, contrary to some claims, they don’t reproduce normal hearing. Instead they transmit a simplified, broken-down representation of the acoustic world” which “one of the technology’s pioneers, Michael Merzenich, likens [to] ‘playing Chopin with your fist.’” Even in the best-case scenario, then, a full appreciation of music will probably remain inaccessible to Ivy.

2. As Susan Goldin-Meadow and Rachel Mayberry write, “To become readers, [hearing] children must learn the mapping between the spoken language they already know and printed words on a page. For English, as for most languages, that mapping is based on sound. Once children understand the underlying principles of the print-sound mapping… they can call upon their knowledge of their spoken language to facilitate the reading process,” such as when they are guided into ‘sounding out’ the letters of an unfamiliar word. But “deaf children are disadvantaged as potential readers on both of these counts — they do not have easy access to the phonological code and many do not know any language well.” Moreover, when “deaf readers translate [a written] sentence into [sign language],” they are continually at risk of finding the written sentence “relatively difficult to process,” and therefore unpleasant to read, because, among other reasons, “the signs in the translation [may be too] similar in form.”

3. In his recent book Far From the Tree, Andrew Solomon describes, with a sense of childlike wonder, watching the movements of a deaf woman who “manifests a pleasure in [her language] that only poets feel for English” through movements “so swift, crisp, and perfectly controlled that she seems to be arranging the air into a more acceptable shape.”


On Style

All works of art are founded on a certain distance from the lived reality which is represented. This ‘distance’ is, by definition, inhuman or impersonal to a certain degree; for in order to appear to us as art, the work must restrict sentimental intervention and emotional participation, which are functions of ‘closeness.’ It is the degree and manipulating of this distance, the conventions of distance, which constitute the style of the work. In the final analysis, ‘style’ is art. And art is nothing more or less than various modes of stylized, dehumanized representations. … Style is the principle of decision in a work of art, the signature of the artist’s will. And as the human will is capable of an indefinite number of stances, there are an indefinite number of possible styles for works of art. … To the extent that a work seems right, just, unimaginable otherwise (without loss or damage), what we are responding to is a quality of its style. The most attractive works of art are those which give us the illusion that the artist had no alternatives, so wholly centered is he in his style.

That’s Susan Sontag — who I could go on quoting ad infinitum — brought in here to speak to the takeaway paragraph in a great discussion between David Winters and Anthony Brown over at 3:AM Magazine. The subject is modernism, “then and now”:

David Winters: You mention Bernhard in the same breath as Lydia Davis, which I think is fruitful. What I mean here is that I read Bernhard for the same reasons I read some recent American writers. I want to say that I read for the style, but I don’t mean ‘style’ in the ‘superficial’ sense you astutely describe [in discussing “Peter Gay’s ‘modernism as style’ position”]. In the work of the writers I most admire, a style is always also a stance. That is, for them, a way of arranging words on the page is also a way of reaching a view of the world.

Gerald Murnane’s Show-and-Tell

Over at The Apiary, an artistic-archival project “specialising in films made about and in collaboration with musicians, theatre-makers, dancers and visual artists,” Marden Dean ventures into the fabled workspace of Gerald Murnane. Murnane has often spoken about his workspace, a bare office populated by dozens of filing cabinets in which he stores and catalogues every last note he has ever written on any subject whatsoever over the last forty or fifty years, but to my knowledge Dean is the first person ever to be allowed to enter and film Murnane’s little world. Some of the resultant images match up with Murnane’s own descriptions of his workspace, such as the typewriters atop the filing cabinets and the horse racing colours on the wall, but others took me by surprise. I always expected that Murnane organised all of his various notes in some sort of logical order, perhaps biographically or chronologically in accordance with whatever larger project he was working on at the time he wrote them. Not so. While he concedes that most of his notes are organised biographically, others are gathered together under more intriguing categories such as “IF I WERE A COWARD, I WOULD BURN THIS,” “WHAT I BELIEVE ABOVE ALL,” and “ENTER, WITH FLOURISH, H. FAWKNER.”

Speech and Stoner

Appreciations of John Williams’ Stoner have been floating around the blogosphere for a while now, thanks to John SelfdovegreyreaderEmmett Stinson and, more recently, D.G Myers and Rohan Maitzen, but another voice in praise of the novel can’t hurt. Stoner is a masterpiece. There’s no use festooning it with superlatives. They can’t convey how great it is. Read it!

More than its perfect prose, tone, characterisation, and narrative momentum, what impressed me about Stoner was the subtlety of its self-awareness. I expected a reprise of the startling but unwavering realism of Williams’ previous novel, Butcher’s Crossing, which is arguably one of the half-dozen or so truly outstanding New Westerns and which offered me my first taste of Williams’ work. What I found instead was a work of literature that acknowledged and justified its own literariness right from the very first page, and continued to do so throughout:

William Stoner entered the University of Missouri as a freshman in the year 1910. … Eight years later, during the height of World War I, he received his Doctor of Philosophy degree and accepted an instructorship at the same University, where he taught until his death in 1956. He did not rise above the rank of assistant professor, and few students remembered him with any sharpness after they had taken his courses. When he died his colleagues made a memorial contribution of a medieval manuscript to the University library. This manuscript may still be found in the Rare Books Collection, bearing the inscription: “Presented to the Library of the University of Missouri, in memory of William Stoner, Department of English. By his colleagues.”

An occasional student who comes upon the name may wonder idly who William Stoner was, but he seldom pursues his curiosity beyond a casual question. Stoner’s colleagues, who held him in no particular esteem when he was alive, speak of him rarely now; to the older ones, his name is a reminder of the end that awaits them all, and to the younger ones it is merely a sound which evokes no sense of the past and no identity with which they can associate themselves or their careers.

That’s how the novel opens. Straight away it marks out its literary territory. On the one hand, by noting the inadequacy of the sole surviving written record of the life of William Stoner, it implies that what is required is something like itself: an account of Stoner’s life that is both more elaborate and more specific than what currently exists. On the other hand, by noting the “casual” questioning of Stoner’s life and the variations in the verbal accounts offered in response, it implies also that what is required is not only a more elaborate and specific account but, crucially, a written one. What Stoner wants, from its very first page, is an account of Stoner’s life that becomes more elaborate and specific the more it both supersedes the inadequate written record in the University of Missouri library and militates against the transience and ambiguities of speech as an alternative means of superseding that record. Time and again throughout Stoner, as the novel goes about setting the record straight, it casts speech as an act through which its task might be accomplished if only speech was not so capable of misdirection via rhetorical seduction, distraction, and outright deception.

Here, for instance, is the young Stoner’s adviser, Archer Sloane, whose speech mannerisms seduce Stoner into devoting himself to the study of literature:

The instructor was a man of middle age, in his early fifties; his name was Archer Sloane, and he came to his task of teaching with a seeming disdain and contempt, as if he perceived between his knowledge and what he could say a gulf so profound that he would make no effort to close it. … His voice was flat and dry, and it came through barely moving lips without expression or intonation; but his long thin fingers moved with grace and persuasion, as if giving to the words a shape that his voice could not.

And here is Stoner’s first contact with the woman who will become his loveless wife — who will eventually do everything in her power to ruin him — as she, too, seduces him with words, and less with the words she actually speaks than with the simple act of speaking:

Stoner had turned back when she began to speak, and he looked at her with an amazement that did not show on his face. Her eyes were fixed straight before her, her face was blank, and her lips moved as if, without understanding, she read from an invisible book. He walked slowly across the room and sat down beside her. She did not seem to notice him; her eyes remained fixed straight ahead, and she continued to tell him about herself, as he had asked her to do. … And [later] something unsuspected within her, some instinct, made her call him back when he started to go out the door, made her speak quickly and desperately, as she had never spoken before, and as she would never speak again.

And here is Stoner’s first in-depth encounter with Charles Walker, the arrogant student who will destroy Stoner’s professional life just as Stoner’s wife destroys his life at home:

[Walker’s] voice rose and fell, his right hand went out with its fingers curled supplicatingly upward, and his body swayed to the rhythm of his words; his eyes rolled slightly upward, as if he were making an invocation. … Walker’s voice dropped to a conversational level, and he addressed the back wall of the room in a tone that was calm and equable with reason. …

Anger, simple and dull, rose within Stoner [when he realised the extent of Walker’s intellectual vapidity], overwhelming the complexity of feeling he had had at the beginning of the paper. His immediate impulse was to rise, to cut short the farce that was developing; he knew that if he did not stop Walker at once he would have to let him go on for as long as he wanted to talk. … He had waited too long to interrupt, and Walker was rushing impetuously through what he had to say. …

After he became used to his anger Stoner found a reluctant and perverse admiration stealing over him. However florid and imprecise, the man’s powers of rhetoric and invention were dismayingly impressive [and] Stoner became aware that he was in the presence of a bluff so colossal that he had no ready means of dealing with it.

And here is Walker again, delivering a presentation followed by a question and answer session that has been scripted by his supervisor, Hollis Lomax, precisely in order to distract Walker’s listeners from noticing his limited intellectual capabilities:

Walker’s presentation was lucid, forthright, and intelligent; at times it was almost brilliant. Lomax was right; if the dissertation fulfilled its promise, it would be brilliant. Hope, warm and exhilarating, rushed upon [Stoner], and he leaned forward attentively.

Walker talked upon the subject of his dissertation for perhaps ten minutes and then abruptly stopped. Quickly Lomax asked another question, and Walker responded at once. … Walker’s voice continued, fluent and sure of itself, the words emerging from his rapidly moving mouth almost as if — Stoner started, and the hope that had begun in him died as abruptly as it had been born. … Lomax finished his questioning, and Holland began. It was, Stoner admitted, a masterful performance; unobtrusively, with great charm and good humor, Lomax managed it all. … He rephrased [other listeners’] questions… changing them so that the original intent was lost in the elucidation. He engaged Walker in what seemed to be elaborately theoretical arguments, although he did most of the talking. And finally… he cut into [other listeners’] questions with questions of his own that led Walker where he wanted him to go.

During this time Stoner did not speak. He listened to the talk that swirled around him. … He was waiting to do what he knew he had to do, and he was waiting with a dread and an anger and a sorrow that grew more intense with every minute that passed.

At one point, when Lomax threatens to charge Stoner with professional misconduct and construes actual events in a way that makes them appear sinister, Stoner cries out: “How you make it sound! Sure, everything you say is fact, but none of it is true. Not the way you say it.” And later, when Stoner’s retirement dinner offers him an opportunity to publicly construe events however he pleases, he is rendered powerless by his inability to speak:

As the applause dwindled someone in the audience shouted in a thin voice: “Speech!” Someone else took up the call, and the word was murmured here and there. …

[Stoner] got to his feet, and realized that he had nothing to say. He was silent for a long time as he looked from face to face. He heard his voice issue flatly. “I have taught…” he said. He began again. “I have taught at this University for nearly forty years. I do not know what I would have done if I had not been a teacher. If I had not taught, I might have–” He paused, as if distracted. Then he said, with a finality, “I want to thank you all for letting me teach.”

And finally, at the end of his life, Stoner receives news of Katherine Driscoll, the colleague and lover he was forced to abandon when their affair jeopardised both of their careers, and this last encounter with Katherine affirms the strength of the written word:

In the early spring of 1949 he received a circular from the press of a large eastern university; it announced the publication of Katherine’s book, and gave a few words about the author. … He got a copy of the book as soon as he could. When he held it in his hands his fingers seemed to come alive; they trembled so that he could scarcely open it. He turned the first few pages and saw the dedication: “To W.S.”

His eyes blurred, and for a long time he sat without moving. Then he shook his head, returned to the book, and did not put it down until he had read it through. … The prose was graceful, and its passion was masked by a coolness and clarity of intelligence. It was herself he saw in what he read, he realized; and he marveled at how truly he could see her even now.

Whether or not he can “truly” see her is, of course, an open question, and is just one aspect of the broader question of whether or not the written word is in fact more capable than speech of conveying the “truth” of a human life via the elaboration and specification of circumstantial detail. But with its continual ambivalence towards speech, Stoner seems to me to close off that broad open question in favour of the written word and thus in favour of richly detailed humanist realism as the literary mode best suited to its purposes — although, unusually for that sort of realism, it senses its own lack of intrinsic authority and works hard to accrue and justify it.