Philip Acree Cavalier

Catawba College

Henry James’s Mathematics

My paper explores Henry James’s use of mathematical ideas in two of his early novels, The American and Washington Square. In Washington Square, Austin Sloper and Morris Townsend compete for the devotion of Sloper’s daughter Catherine.  The two men cast their desire to possess Catherine exclusively in terms of a mathematical problem that they must solve. In The American, Christopher Newman understands the process of becoming a cultured person as an arithmetical operation. Each painting, each sculpture, each church Newman sees, he adds to his sum; in a sense he is collecting experiences of viewing cultural objects without interpreting or distinguishing between those experiences. Newman discovers that the operation he employs fails him when confronted with culture and tradition. He starts to make aesthetic judgments by the end of the novel, but he cannot completely reform himself: in the novel’s last scene, Newman is guilty once again of trying to make certain behaviors add up in a way that is impossible. What he realizes is that he has miscalculated yet again. In both novels, the mathematical operations used by the central male characters fail because of those characters mismeasure and miscalculate. Before discussing the two novels in detail, I want to begin by identifying the most compelling feature of both arithmetic and geometry.

            For the purposes of this essay, arithmetic means essentially computation; James does not use arithmetic in the novels to refer to theories of numbers. Arithmetic is a concrete operation, one that refers specifically to the material world; it requires the presence of an object. In James’s hands, arithmetic often signals that a person who relies on solely on that operation to interpret the world is simple. James also suggests that characters of this sort are transparent, or at least completely legible to others. I will make the case later in the essay that Newman falls into the first category. But we see examples of both cases in the opening chapter of ­ The Bostonians, when Mrs. Luna meets Basil Ransom for the first time. We are told that “Mrs. Luna glanced at him from head to foot, and gave a little smiling sigh, as if he had been a long sum in addition. And, indeed, he was very long, Basil Ransom, and he even looked a little hard and discouraging, like a column of figures” (Bostonians 35). The relation between the two is arithmetical at first, suggesting that Mrs. Luna, on the one hand, is extremely naïve and incapable of understanding nuances and subtleties, while Basil, on the other, is transparent and unable to hide his Southern views. As the novel unfolds, both characterizations turn out to be true; what points to this conclusion is the fact that James casts the encounter between these two characters in terms of addition.

Geometry, by contrast, is abstract in that it does not require a specific object. As Jean Nicod explains it, the “universal aspect of geometry” is its “sequence of formal, and in a certain sense blind, reasonings, which draw their consequences from a group of premises formulated in terms of entities whose nature, being independent of the arguments, remain completely indeterminate” (Nicod 4). Arithmetic is a lower-order operation for James. It may be the principle operation in a capitalist business world, but it does not help one to make sense of cultural institutions or traditions, which cannot be quantified and added together to discover their value to an individual. Geometry, because it deals in abstractions and focuses on forms, offers a foundation for aesthetic judgments. And yet,  as James suggests in Washington Square, geometry carries with it the danger of turning people into abstractions, a move that makes it easier to manipulate them without any apparent consequences.

            In Washington Square, Austin Sloper and Morris Townsend transform the marriage plot into a mathematical problem that must be solved. The problem is an abstract one in so far as Catherine only functions as a variable in the problem; it is also a problem of geometry, in that Morris recognizes the necessity of maintaining a triangle in which Austin Sloper continues to act as one point, though a point at some distance from himself and Catherine. Ultimately, the two men struggle with each other; neither man cares much for Catherine, except as she affects the problem itself. They do not want to win Catherine but rather solve the problem that the other man creates.

            James introduces the geometrical nature of the Washington Square marriage plot in a conversation between Austin Sloper and his sister Marian Almond in the middle of the novel. Austin Sloper reports to his sister Marian Almond that he has become convinced that Catherine is not going to give in to his will by giving up Morris Townsend. Sloper tells his sister that Catherine is “going to drag out the engagement, in the hope of making me relent” (128). When Marian asks if Austin will relent, he replies, “Shall a geometrical proposition relent? I am not so superficial” (128). When Marian asks, in response to Austin’s comment about superficiality, whether geometry is about surfaces, Sloper replies that it “treats of [surfaces] profoundly. Catherine and her young man are my surfaces; I have taken their measure” (128). This exchange between Sloper and his sister suggests that Sloper is completely confident in his ability to determine what people are made of. He knows these two people-he has “measure[d]” them-and how they will behave. Whether or not Catherine eventually gives in, the way Sloper constructs the problem for his sister makes it abundantly clear that he believes that he can act in no other way. He is locked into a set of behaviors determined by the geometrical proposition he mentions. To change his behavior would not only mean acting illogically-it would constitute, of course, a break from the logic of his geometrical proof-but it would also be impossible. Sloper believes he can no more change his behavior once he has established the appropriate rules which govern the situation than he could change the laws of geometry. The problem is that, in order to make sure that geometry works, Sloper must measure things correctly. In this case, Sloper, and to a lesser extent Townsend, mismeasure Catherine Sloper’s surfaces.

            In the preface James wrote to his first novel Roderick Hudson, James reflects on the difficulty of imposing artificial limits on the subject of one’s novels. James asks the question, “Where, for the complete expression of one’s subject, does a particular relation stop-giving way to some other not concerned in that expression?” (Art 5).  In the paragraph that follows this question, James offers an answer that suggests something about the nature of the failure of Austin Sloper and Morris Townsend, despite the fact that James wrote these words more than 25 years after he had completed Washington Square. James asserts,

Really, universally, relations stop nowhere, and the exquisite problem of the artist is eternally but to draw, by a geometry of his own, the circle within which they shall happily appear to do so. He is in the perpetual predicament that the continuity of things is the whole matter, for him, of comedy or tragedy; that this continuity is never, by the space of an instant or an inch, broken, or that, to do anything at all, he has at once intensely to consult and intensely to ignore it. All of which will perhaps pass but for a supersubtle way of pointing the plain moral that a young embroiderer of the canvas of life soon began to work in terror, fairly, of the vast expanse of that surface. (Art 5)

The passage suggests that the act of novel-writing, and really of writing prose non-fiction of all kinds, begins with a basic geometrical operation: defining the circle of experience and relations that the writer will represent in the work. The tension James identifies here is between the need to believe completely that the geometry one has created is real, and the fact that one must refer to what happens beyond outside of the circumscribed world of the novel in order to make sense of the novel. But perhaps the most telling comment is when James refers to the “terror” he felt when he attempted to represent the “vast expanse of that surface.” What James implies here is the impossibility of represent that “vast expanse” completely or effectively. The anxiety James remembers is instructive when considering Austin Sloper: what makes him flawed is his inability to recognize the artificial nature of his categories and his limited knowledge of the “surfaces” he thinks he has measured. He believes, in a sense, that the “geometry of his own,” to borrow James’s phrase, is actually an absolute geometry.

            An important part of Sloper’s geometry is his classification of people. Sloper relies on categories of his own making in order to organize and understand his world; he sees types, not individuals. The forces that lead him to create categories are many: among them, the ever-encroaching city; his training as a physician; and his desire to protect a social elite from fortune-hunters and the newly-minted rich. Whatever forces cause him to create these categories, it is safe to say that without them, Austin would feel lost in the chaos. Sloper explains his “habit” of classifying people to Mrs. Montgomery, Townsend’s sister: “I am helped by a habit I have of dividing people into classes, into types. I may easily be mistaken about your brother as an individual, but his type is written on his whole person” (87). Sloper elaborates on this “type” by insisting that men like Townsend are determined “to accept nothing of life but its pleasures, and to secure these pleasures chiefly by aid of your complaisant sex. Young men of this class never do anything for themselves that they can get other people to do for them” (88). What is most revealing about Sloper’s statements is the fact that he clearly understands them as a necessary  part of negotiating a world that is full of potential con-men. But he also understands the men of Townsend’s class very well.

During his first interview with Morris Townsend, Sloper explains why he disapproves of Townsend as a suitor. Morris has anticipated Sloper by asserting, “I am poor,” to which Sloper responds,

That has a harsh sound . . . but it is about the truth-speaking of you strictly as a son-in-law. Your absence of means, of a profession, of visible resources or prospects, places you in a category from which it would be imprudent for me to select a husband for my daughter, who is a weak young woman with a large fortune. In any other capacity, I am perfectly prepared to like you. (74-5)

Sloper works from two different categories here: the category of the poor young man trying to marry a soon-to-be-rich young woman; and the weak young woman with a large fortune who cannot protect herself or her possessions from fortune-hunters. Sloper suggests that he is not opposed to either category-he does not make value judgments about either, or at least not about Morris’ type (his treatment of Catherine implies some value judgments). The problem lies in uniting these two categories. What Sloper suggests is that the proposition that a man from Townsend’s category and a woman from Catherine’s could marry for reasons unrelated to the inheritance is a patently false proposition. Sloper thinks his role is to show both of them that the proposition is false and therefore impossible. The problem is that Sloper’s faith in his ability to place people in the right category is almost completely absolute. He admits that he may be wrong one time out of one hundred, but that is surely not a reason, in his mind, to abandon the process of classifying people. His faith in his categories is akin to his faith in science, medicine, and reason generally; and yet, his faith in medicine and science did not enable him to prevent the deaths of two of his family members. It might be fair to say that his faith in his own categories and types leads to an estrangement from his daughter that represents at least the death of their relationship.

            If Austin Sloper understands Morris Townsend as a danger type and the problem of getting rid of him as a geometrical one, Morris Townsend also understands his attempt to win Catherine’s fortune mathematically. In a chapter that shows Morris considering his options about Catherine, we see that Morris wrestles with the different variables of the problem and looks for ways to insure that he does not wind up with a wife who is unattractive and poor as the solution. Such a solution would represent a defeat for Morris, who confesses to Catherine later in the novel, “I don’t like to be beaten” (160). Townsend understands the terms of the problem according to the following propositions:

1.      That Catherine is a fixed variable: she will be constant and loyal to him;

2.      That Morris could marry her regardless of whether or not Sloper leaves his money to Catherine;

3.      That she will bring with her at least $10,000 per annum, money over which her father has no control;

4.      That Morris thinks he is “worth” more than $10,000 per annum;

5.      That he might wind up with no money at all if he does not marry Catherine;

6.      That, ultimately, Austin Sloper’s actions are the unknown variable.

Given these propositions, Morris Townsend has to solve the problem by working out what Sloper would do if Townsend and Catherine married. “Doctor Sloper’s opposition was the unknown quantity in the problem he had to work out,” the narrator informs us; “The natural way to work it out was by marrying Catherine; but in mathematics there are many shortcuts, and Morris was not without hope that he should yet discover one” (134). Ultimately Morris concludes that Sloper “will never give us a penny; I regard that as mathematically proved” (170). From this point in the novel, Morris acts only to extricate himself from the situation, which requires him to act toward Catherine with “a sort of calculated brutality” (175). By the end of the chapter, Morris is gone; once he has solved the problem by figuring out Austin Sloper-and doing it accurately-Townsend retreats. Once the mathematical problem is solved, the marriage plot is effectively concluded.

            James seems to embed geometrical principles into the structure of the novel itself. The novel’s title is unique among James’s novels because it identifies a particular location, Washington Square, which is also a geometric figure. James introduces geometry in chapter 21 of the novel; he shows Morris Townsend apparently resigning himself to the fact that it is “mathematically proven” that Austin Sloper will never give Catherine any money if she marries Morris in chapter 28; and he stages Catherine’s final rejection of Townsend-an act that indicates Morris misjudged Catherine-in the novel’s final chapter, chapter 35. These events occur, in other words, in chapters 21 of 35; 28 of 35; and 35 of 35. We can take the lowest common denominator in each case and come up with 3/5, 4/5 and 5/5; to simplify further, we get the numbers 3, 4 and 5. These numbers are significant because they constitute the lengths of the sides of the smallest triangle in which all the sides are whole numbers. The ratio suggests wholeness, balance, and proportion. In a novel in which James scrutinizes the triangular relations between Sloper, Catherine, and Morris-a relation that is always on the verge of becoming a square with Aunt Lavinia as its fourth point-it seems to be more than mere coincidence that the structure of the novel itself bears traces of geometric figures. Washington Square is a novel about the geometrical nature of relations, and also about the dangers of having absolute faith in the geometry of one’s own making.

 

The American opens with Christopher Newman lounging on a divan at the Louvre, overheated and exhausted from his day of looking at the museum’s collection. He is overwhelmed by the abstract nature of the activity in which he is engaged. Looking at art yields for Newman no tangible result because he lacks the mental operation that would enable him to make sense of the sensory experiences of the day. “Long, lean, and muscular,” as James describes him, Newman “suggests the sort of vigour that is commonly known as ‘toughness’” (17). But Newman’s toughness is only of a certain kind; it does not serve him well as he navigates his way through this major cultural institution. He has followed his Badeker-his map of culture-and seen all the paintings that that guidebook indicates are important. But it leaves Newman with nothing more than an “aesthetic headache” (17). Indeed, James tells us that while Newman’s “physiognomy would have sufficiently indicated that he was a shrewd and capable fellow, and in truth he had often sat up all night over a bristling bundle of accounts, and heard the cock crow without a yawn . . . . Raphael and Titian and Rubens were a new kind of arithmetic, and they inspired our friend, for the first time in his life, with a vague self-mistrust” (17). What we know first about Christopher Newman-before we know any of the circumstances that enabled him to get to the Louvre on this particular day in May 1868-is that art both confuses him and seems to have an overpowering affect on him physically. At least initially, Newman lacks a kind of cultural stamina, which he develops to a certain degree during the course of the novel. But the main problem here, and the problem at the novel’s center, is cast in terms of mathematics: Newman understands the mathematics of business, but not that of culture.

            There is a telling shift of emphasis in this first chapter: James begins with a portrait of the tourist exhausted by observing art and ends with the same tourist revivified when he can turn art into a business proposition. Newman shifts his attention from the paintings in the Louvre collection to the copy of one of those paintings, by Murillo, being executed by Noemie Nioche. Newman stands over Noemie’s work, inspecting it silently. When he finally speaks to her, his first question is one word: “Combien?” Newman’s one-word question signals an important shift from the abstract world of art appreciation to the concrete, market-bound world of art collection. In the former, the elements of the painting add up, in Newman’s mind, to nothing. Or rather, they do not add up because he does not understand the operation of culture well enough to know how to evaluate them. In the latter case, however, Newman can make sense of collecting because he can understand art in terms of business transactions. I should note here that “collectio” was, at one time, used interchangeably with “sum”; collecting art, then, implies an arithmetical relation. The value of the copy he wishes to buy no longer depends entirely on abstract notions of taste and aesthetics. Value is determined, instead, by the market for the copy, and in this case, by Newman’s desire as the consumer to possess the painting. Newman may not understand how to read this new kind of market, and he may wind up overvaluing the product, but he understands that, even in its most complicated form, any market is a series of calculations.

The word “combien” reveals Newman’s critical capacity: he judges based only on a system whose logic is perfectly clear to him-market economy-but cannot make aesthetic judgments. In bargaining with the Nioches for the copies Noemie is to provide, Newman can calculate the value of the art he possesses. He begins with a certain amount of money, y, and spends x amount on Noemie’s copies. He returns to America possessing art in tangible form, whose value equals y - x. The role of collecting enables Newman to control the act of looking at art, because he can possess the artwork and determine its value concretely and on his own. Determining whether or not his judgments are sound, or to put it differently, whether or not he has been swindled, does not factor into Newman’s equation.

            In the first half of the novel, Newman applies his business arithmetic to the task of accumulating cultural capital, and Newman seems to think it is working. But in the second half of the novel, Newman comes to find out that his calculations have all been wrong. Newman, the self-made man who might have stepped out of a Horatio Alger novel, discovers that approaching culture arithmetically does not work. After Newman realizes that his arithmetic has failed him, he suffers a crisis of identity as well. In order to understand why, it is worth pausing briefly to consider the ways in which the novel critiques Alger’s success story formula.

            The short version of the Horatio Alger success story is this: a poor boy living on the streets overcomes his hardships and prospers because of hard work, perseverance, and honesty. The most compelling aspect of Alger’s novels, for my purposes, is the way in which the pages of the novel become one long arithmetic problem. In Ragged Dick, for instance, Dick opens a savings account halfway through the novel and puts $5 in it. Ten pages later, Dick adds another $2.50 to it; he now has $7.50 in savings. Fifteen pages after that, we find out that Dick now has $18.90, which grows to $117 in nine months. The arithmetic ends when the novel does, not before. In other words, Alger structures his novel in such a way that the arithmetic is constantly in the foreground. Dick’s role (and Dick is interchangeable with Alger’s other boy heroes) is simply to initiate the arithmetic. Dick’s identity depends on the amount of money he has in his pocket or in his savings account; he succeeds because the people he encounters recognize value in an identity that is determined arithmetically through accumulation of capital. When he has no money and owns nothing, however, he is invisible. He has no identity in the world of capital (a strong work ethic and perseverance, qualities Dick possesses, do not amount to anything on their own; they are simply indicators of the likelihood that the person will later gain an identity by accumulating wealth). 

Newman, in a sense, is an extension of the Alger hero, but when he moves into in Parisian high society, which is to say in a world that revolves around cultural capital, he discovers that the Alger success story is actually seen as a sign of inferiority. Newman tells Urbain de Bellegarde in the middle of the novel that he has had only one interest: “my specialty has been to make the largest possible fortune in the shortest possible time” (124). The defining feature of his identity has been his ability to accumulate wealth in an accelerated fashion. In the eyes of Urbain and his mother, there is nothing valuable or laudable in such an identity; more precisely, the Bellegardes are blind to such people. And more generally, Newman’s experiences throughout the novel in Europe tend either to demonstrate the meaninglessness of that identity, or to continue to undermine it in Newman’s own mind. Indeed, by the end of the novel, that identity seems to have been almost completely effaced. Newman, we are told, “was able to conceive that a man might be too commercial,” and later that if “his commercial imagination was dead, he felt no contempt for the surviving actualities begotten by it” (301-2). The novel undoes the Alger myth by showing that the kind of arithmetic that Ragged Dick and Newman have thrived on fails in the face of culture. Long before Newman realizes this, however, he spends his time in Europe trying to make the cultural sights of Europe add up to a sum that would represent a fortune in cultural capital.

The most explicit example of Newman’s attempt at cultural arithmetic occurs during Newman’s first visit to the Bellegarde mansion to see Claire de Cintre. Newman converses with Claire’s younger brother Valentin, who is curious about the rich American. In the course of the conversation, Valentin asks Newman “Are you interested in architecture?” Newman’s response is strangely indirect; he explains, “Well, I took the trouble, this summer . . . to examine-as well as I can calculate-some four hundred and seventy churches. Do you call that interested?” (83). While on the face of it Newman’s response-and particularly his final question-might appear silly or even sarcastic, the question is an honest one. The whole form his response takes is once again indicative of the kind of mathematical limits Newman faces. He can “calculate” the number of churches he has seen in the summer; this operation is very similar to the arithmetic that led him to compile a fortune. While contemplating the results of his travels after his travelling companion Babcock leaves him, Newman comes to realize that “he had spent his years in the unremitting effort to add thousands to thousands, and, now that he stood well outside of it, the business of money-getting appeared extremely dry and sterile” (75). Newman has spent his summer travelling around Europe in order to engage in basically the same operation using different materials: instead of adding “thousands to thousands,” Newman is adding churches to churches. But Newman doesn’t know exactly what to think about this accumulation of church visits. In fact, Newman seems to lack a vocabulary to articulate his experiences: he doesn’t even know whether his calculation qualifies him as interested or something else.

The basic problem Newman faces is that he does not have the tools-mathematical and verbal-to help him to interpret his cultural experiences. James makes this abundantly clear when he shows Newman, accused by Babcock of being incapable of drawing any conclusions about what he had seen, trying to list some:

Could he not scrape together a few conclusions? Baden-Baden was the prettiest place he had seen yet, and orchestral music in the evening, under the stars, was decidedly a great institution. This was one of his conclusions! But he went on to reflect that he had done very wisely to pull up stakes and come abroad: this seeing of the world was a very interesting thing. He had learned a great deal; he couldn’t say just what, but he had it there under his hat-band. He had done what he wanted; he had seen the great things, and he had given his mind a chance to ‘improve,’ if it would. (74)

Newman’s inability to make any distinctions about culture, beyond the most basic ones, does not lead him to doubt the value of his experiences in Europe. On the contrary, Newman believes fully that he has stored the material he needs in his mind and will be able to do something with it later. In a strange way, this reflects once again the logic of Newman’s capitalist arithmetic: like the capital he accumulated during the three years after the Civil War that enables him to travel now, Newman thinks he is accumulating cultural capital for use at a later time. Unlike Babcock, who “delighted in aesthetic analysis, and received peculiar impressions from everything he saw,” Newman enjoys everything equally and receives no impression (69).  But again this is completely consistent. Newman did not need to make distinctions about whether he liked a particular thousand dollars more than a different thousand dollars; every thousand dollars brings an equal amount of enjoyment because it ­adds to his fortune. So, too, with churches, or buildings, or paintings-they merely represent numbers that he can enjoy because they are included in a set of calculations that, he thinks, must lead to cultural wealth.

I would argue that one major problem Newman encounters repeatedly is his inability to recognize the geometric principles that influence and determine the structure of the buildings and churches, and the composition of paintings and sculptures, he views. He is incapable of seeing cathedrals and churches as unified pieces of art. Newman has moments when certain buildings strike him for no obvious reason; apparently Gothic architecture is one form that interests him. In his book The Gothic Cathedral: Origins of Gothic Architecture and the Medieval Concept of Order, Otto von Simson explains that “In Gothic architecture, whatever its technical shortcomings may have been, the distinction between form and function, the independence of form from function, have vanished . . . . Gothic architecture was created . . . in response to a powerful demand for an architecture particularly attuned to religious experience” (10). The Gothic cathedral communicates its message not only through the sculptures, stained-glass windows, and other ornaments, but also in the very structure of the space itself, which is designed to communicate harmony through proportion. “The aesthetic values of Gothic architecture,” von Simson asserts elsewhere, “are to a surprising extent linear values. Volumes are reduced to lines, lines that appear in the definite configurations of geometrical figures” (8). We see an example of Newman’s interest in Gothic architecture when he visits Brussels at the start of his tour around Europe. Newman is “greatly struck with the beautiful Gothic tower of the Hotel de Ville, and wonder[s] whether it would not be possible to ‘get up’ something like it in San Francisco” (66). As in the opening scene at the Louvre, Newman can only engage art by imagining possessing a copy of the thing that attracts him. We get no insight into what Newman finds compelling about the tower, but we do know that we should question his judgment: we are told that Newman’s “perception of the difference between good architecture and bad was not acute, and that he might sometimes have been seen gazing with culpable serenity at inferior productions. Ugly churches were part of his pastime in Europe, as well as beautiful ones” (68). The problem, for Newman, is that he is blind to the geometrical principles that would enable him to make distinctions between, for example, different Gothic structures. “His mind,” as Babcock finds in the brief period during which they travel together, “could no more hold principles than a sieve can hold water”; nonetheless, Newman “admired principles extremely” (70). Admiring them or not, without principles Newman cannot evaluate the success of the Gothic tower he sees by comparing its structure to the geometrical principles that Gothic architects and builders espoused. All Newman can do is look at the object, enjoy it, and try to add it (or an image of it) to his collection of “art” objects.

            The only time in the novel when we get an extended look at Newman in a church occurs when he goes to the Carmelite convent where Claire lives after deciding she could not go through with the marriage. What we discover is a basic problem in the way Newman experiences churches: he sees only fragments of the whole that is intended to make an impression on the church-goer. As the chapter begins, Newman is standing outside the convent getting “what comfort he [can] in staring at the blank outer wall of Madame de Cintre’s present residence” (275). He returns a few days later, on Sunday morning, to attend mass. Once inside, and before mass begins, Newman goes up to the iron screen that divides the Carmelite nuns from the gathering congregation, and tries to see through it to the other side: “Newman fastened his eyes on the screen behind the altar. That was the convent, the real convent, the place where she was. But he could see nothing; no light came through the crevices. He got up and approached the partition very gently, trying to look through. But behind it there was darkness, with nothing stirring” (276). Newman sees the screen as the thing which separates the “real” convent from the outside world, but of course this gets it wrong-if the screen functions in that way, then why is it that access to the chapel is only possible on Sunday mornings? The screen separates one part of the mass from the other, but the two parts of the chapel-public and private-are both parts that make up the whole which is supposed to constitute a religious experience for those present. Later in the service, when the Carmelite nuns begin their chant, Newman tries to pick out one voice from the whole choir: “He listened for Madame de Cintre’s voice, and in the very heart of the tuneless harmony he imagined he made it out” (277). What these passages suggest is that Newman does not recognize the harmony created by the parts of the choir, or by the parts of the chapel, or even by the parts of the service. He is, we might say, unable to read the language of the form of the church service and the structure of the chapel itself. This inability to read that language suggests that Newman, even at this late point in the novel, is still essentially culturally illiterate. 

            In Newman’s case, his inability to interpret accurately cultural signs leads him, at the end of the novel, to make his greatest miscalculation: he throws the note that contains information about the Bellegardes’ secret into the fire instead of using it against them. Newman destroys the note because he believes he has succeeded in frightening the Bellegardes by making them think he might expose them. Satisfied by this measure of revenge, Newman has no more need for the evidence. But Mrs. Tristram, who is with him at the moment that he burns the note, tells Newman that he failed to accomplished what he thought he had and gives her reading of the Bellegardes’ behavior: “My impression would be that since, as you say, they defied you, it was because they believed that, after all, you would never really come to the point. Their confidence, after counsel taken of each other, was not in their innocence, nor in their talent for bluffing things off; it was in your remarkable good nature! You see they were right” (The American 309). The novel ends with Newman looking at the burned-up note, realizing that he has lost his chance to get revenge. Not only has Newman miscalculated how the Bellegardes would  respond, but perhaps even more galling is the fact that he has proven as difficult to figure as a “long sum in addition.”

            It is important to note that James does not end the novel by showing us an innocent character, turned cynical, vowing to fight the people who have done him wrong on their own terms (as we see with Eugene at the end of Pere Goriot).  Nor does he end it by showing the humiliated character returning to the provinces (such as perhaps Robin in Hawthorne’s “My Kinsman Major Molineux”). Instead, James chooses to end the novel at the moment of Newman’s greatest miscalculation; he does so also at the end of Washington Square, when Townsend storms out after his failed attempt to rekindle Catherine’s interest. In the latter case, the miscalculation is as much Lavinia’s as Townsend’s; but the fact remains that in each of these cases, James seems to draw attention to the mathematical failures of the characters.