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Stranger Relations: The Case forRebuilding Commonplaces betweenRhetoric and MathematicsG. Mitchell Reyesa

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To cite this article: G. Mitchell Reyes (2014) Stranger Relations: The Case for RebuildingCommonplaces between Rhetoric and Mathematics, Rhetoric Society Quarterly, 44:5, 470-491, DOI:10.1080/02773945.2014.965046

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Rhetoric Society QuarterlyVol. 44, No. 5, pp. 470–491

Review Essay

Stranger Relations: The Case forRebuilding Commonplaces betweenRhetoric and Mathematics

Pandora’s Hope: Essays on the Reality of Science Studies, by Bruno Latour.Cambridge, MA: Harvard University Press, 1999. 324 + x pp. $29.74 (paper).

Science in Action: How to Follow Scientists and Engineers through Society, byBruno Latour. Cambridge, MA: Harvard University Press, 1987. 274 pp. $27.55(paper).

Ad Infinitum: The Ghost in Turing’s Machine: Taking God Out of Mathematicsand Putting the Body Back in: An Essay in Corporeal Semiotics, by Brian Rotman.Stanford, CA: Stanford University Press, 1993. 203 + xi pp. $22.46 (paper).

Mathematics as Sign: Writing, Imagining, Counting, by Brian Rotman. Stanford,CA: Stanford University Press, 2000. 170 + x pp. $21.77 (paper).

Where Mathematics Comes From: How the Embodied Mind Brings Mathematicsinto Being, by George Lakoff and Rafael Núñez. New York: Basic Books, 2000.492 + xvii pp. $26.99 (paper).

Rhet-o-ric: language designed to have a persuasive or impressive effect on itsaudience, but often regarded as lacking in sincerity or meaningful content.

Math-e-mat-ics: the abstract science of number, quantity, and space.

—Oxford English Dictionary (OED)

The OED’s definitions of rhetoric and mathematics testify to an old and per-sistent polarization. Rhetoric—associated with the use of language to persuade,influence, and manipulate—plays the intellectual counterpart to mathematics—the search for abstract, pure, infallibly true relations between number, geometry,

Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/rrsq.

ISSN 0277-3945 (print)/ISSN 1930-322X (online) © 2014 The Rhetoric Society of America

DOI: 10.1080/02773945.2014.965046

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and space. This polarization, of course, has more authoritative advocates than anOxford dictionary. Bertrand Russell defined math as that which, “rightly viewed,possesses not only truth, but supreme beauty—a beauty cold and austere, like thatof sculpture, without appeal to any part of our weaker nature”; he later expandedhis apotheosis: “mathematics takes us still further from what is human, into theregion of absolute necessity, to which not only the actual world, but every possibleworld, must conform” (Russell, “The Study of Mathematics” 30–42). In contrast,Russell characterized rhetoric as “the appearance of great wisdom . . . [but] thereality of witchcraft” (Russell, Power 314). More recently, Phillip Davis and ReubenHersh give voice to the aporia between rhetoric and mathematics: “Mathematizationmeans formalization, casting the field of study [any field of study] into the axiomaticmode and thereby . . . purging it of the taint of rhetoric” (Descartes’ Dream 57). Oneneed not look far to find assertions about rhetoric and math that fall along theselines, scoring and then scoring deeper the chasm that renders them ever more dis-tant strangers. So opposed do these strangers appear today that many—both insidethe academy and out—see them as antithetical.

How did this come to pass? How did math become the “purest” countervailingforce to rhetoric—the former celebrated as the language of truth, the latter reducedto strategies of manipulation? And what are the consequences of the division—theestrangement—of rhetoric and mathematics, not just for our academic understand-ing of each but also for our views of their respective roles in society?

These are just some of the questions that scholars, in spite of conventionalwisdom, have recently begun to ask. They have done so because there are realrepercussions—intellectual, pedagogical, sociocultural—to maintaining the polar-ized status quo. Consider that mathematics, as a practice of writing, thinking, andarguing, is a whole realm of rhetorical action little understood by rhetorical scholars.Is it possible that within this realm one might find unique rhetorical practices thatcould expand and/or challenge our theories of rhetoric? Consider too that the polar-ization of rhetoric and math renders obscure a practice of writing/thinking thatonly seems to grow in influence each day. Is it in our interests as rhetorical scholarsto remain silent on this increasingly important discursive form, upon which mostforms of technoscience are based? Consider finally what sorts of interests might beinvested in maintaining the opposition. Might this dichotomy be one of the lastrefuges of Modernist thought, a refuge that scholars both inside and outside rhetor-ical studies began to attack in earnest in the 1980s and continue to challenge today?For these reasons and others we must reject conventional wisdom and enter theland of stranger relations, where we can detect the traces of an old alliance betweenrhetoric and math upended by the twin forces of Platonism and Modernism, expandour theories of rhetorical action, and begin to open the blackboxes of technoscience.

What is at stake in the campaign to rebuild commonplaces between rhetoric andmath? From the literature surveyed here, nothing less than a major transforma-tion in thinking about rhetoric, mathematics, and culture. Out of Bruno Latour’swork—especially Pandora’s Hope and Science in Action—we can locate an early

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moment of rupture between rhetoric and mathematics in Plato’s Gorgias even aswe build on his alternative actor-network approach. Out of Brian Rotman’s semi-otic analysis—progressively articulated in Signifying Nothing, Ad Infinitum, andMathematics as Sign—we can begin to see the deep seeded and often unconsciouscommitment to Platonic realism in contemporary mathematics, how it systemati-cally conceals the materiality of mathematical discourse, and how we can re-enliventhat materiality through semio-rhetorical analysis. And out of George Lakoff’sand Rafael Núñez’s Where Mathematics Comes From we learn of the conceptualmetaphors at the roots of mathematical thinking. We will use these books as coordi-nates for plotting a course toward more recent studies of rhetoric and mathematicsthat explicitly interrogate the role of rhetoric in mathematical practice.

Given this trajectory, the essay must follow a somewhat unconventional path.Instead of reviewing each book quasi-independently, I begin by analyzing the pri-mary forces polarizing rhetoric and math, which ultimately function as obstacles tothinking their imbrication. The essay then turns to the various circumventions ofthese obstacles developed in the books here reviewed. Our journey concludes withdiscussion of the connections between these books and scholarship within rhetor-ical studies as well as speculation about the possibilities for study of rhetoric andmathematics going forward.

Obstacles

Too many scholars to count have analyzed, critiqued, championed, and/or con-demned Gorgias, Plato’s famous polemic against rhetoric. Yet to my knowledge norhetorical scholar has noted the rhetoric of mathematics at the heart of Plato’s man-ifesto, a rhetoric of math that Bruno Latour masterfully illuminates in Pandora’sHope. In Gorgias, Latour claims, the movement of thought to underscore andcritique is not Plato’s explicit attacks on the Sophists nor his implicit use offalse binaries (instruction/persuasion, knowledge/opinion, Socrates/Callicles), butinstead a deeper movement in which the logos of geometry displaces the logos ofdemocracy. There, Latour argues, one finds the moment in which Plato transformsthe demos into an impossible monstrosity. To understand the estrangement betweenrhetoric and mathematics and the story of their polarization, then, we need go nofurther than a canonical text within our own discipline.

Plato’s is a rhetoric of mathematics. I emphasize the word “of” here becausePlato—like many philosophers since—took parts of an ancient Greek philosophyof math, tore them out of their context, and globalized them, imposing them onthe polis in the process. Or, as Latour puts it, “Socrates’ misrepresentation of theSophists depends on a category mistake. He applies to politics a ‘context of truth’that pertains to another realm” (Pandora’s Hope 247). The result is that the twogreat inventions of the Greeks, democracy and geometry, are forced to do battle, asif one must supersede the other. Carefully tracing Latour’s critique will help revealthe consequences of Plato’s dramatics for both rhetoric and math.

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Pandora’s Hope does not begin with Plato. Instead, the book sets itself theambitious task of establishing a research program for science studies that replacesModernist philosophies of science with what Latour calls “radical realism.” Radicalrealism’s first move—familiar to those acquainted with Latour’s work—is tosidestep the Modernist language of subjects and objects and focus instead on prac-tice. Only in painstakingly tracing scientific practice in an empirical way, arguesLatour, can scholars begin to escape the Modernist mythos of science and unveilwhat scientists and mathematicians actually do. True to these tenets, Latour dedi-cates the first half of the book to empirical case studies of science in action, fromwhich he teases out the empirical evidence to undermine conventional Modernistbeliefs about science while building an alternative theoretical vocabulary. Onlyafter marshaling these empirical studies against, in Latour’s words, “the Modernistsettlement” does he engage Plato and his rhetoric of mathematics.

And yet it is Plato’s rhetoric of math that is the beating heart of Modernism,of the desire to demarcate between science and non-science that gives rise to thescience wars, and of the twin fears of reality’s loss and mob rule that motivatesthe displacement of democracy. The good news, Latour argues, is that in Gorgiasone can still detect the ruins of the demos Plato so effectively destroyed: “To recon-struct the virtual image of the original Body Politic, we simply have to take positivelythe long list of negative remarks made by Plato: they show in reverse what ismissed when one converts what was, until then, the distributed knowledge of thewhole about the whole into an expert knowledge held by a few” (Latour, Pandora’sHope 237).

Prior to Plato, Latour claims, the social felicities necessary to a functioningdemocracy were held in high regard. Hints of them can be found in the dialogue:Rhetorical virtue, or the pluralistic ability to address the many and to listen to oth-ers, emerges through the character of Gorgias (452d–e); hints of the civic-mindeddesire to run a community well and the leadership qualities to do so emergesthrough Callicles (491a–b); and the courage required to deal with questions ofurgency in a context of uncertainty is revealed, if negatively, through Socrates (454e–455a), who argues one can best attend to the exigencies of politics with the didacticsand expertise of a professor. Latour’s response is incredulous:

Of course “it [politics] does not involve expertise,” of course “it lacks rationalunderstanding”; the whole dealing with the whole under the incredibly toughconstraints of the agora must decide in the dark and will be led by people asblind as themselves, without the benefit of proof, of hindsight, of foresight, ofrepetitive experiment, of progressive scaling up. In politics there is never a secondchance—only one, this occasion, this kairos. (Pandora’s Hope 242)

These conditions and the qualities needed to meet them are familiar to rhetoricalscholars, but it is their Platonic destruction to which we must attend. Latour pin-points the key moment in the debate between Socrates and Callicles, where Calliclesaccepts that it takes expertise to distinguish between good and bad pleasures

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(499e–500a). From there, argues Latour, the game is up: the distributed knowledgeof citizens figures as the darkness against which cuts the expert’s light. The people—slovenly, ignorant, easily manipulated—could not possibly distinguish between thegood and the bad because they do not know their essence. Thus all the ways andmeans the people use—oratory, plays, sculpture, music, architecture, assembly—togovern themselves, decide for themselves, represent themselves to themselves as acollective are rendered “habitudes”—blind forms leading the blind masses in a per-ilous darkness. The straw Callicles plays along. Yes the people are ignorant, yes theyare blind, and so they must be controlled by the strong: might makes right. However,and this is Latour’s real insight, Socrates and Callicles are in league together. Do notbe distracted by their difference of opinion cautions Latour—the former calling fora benevolent philosopher king and the latter defining politics as mere force—forthey both see the citizenry as blind and ignorant and both in different ways seek toundermine democratic practice.

Callicles’ strategy is rhetorical sleight-of-hand—create the appearance of democ-racy while using flattery to control the mob—while Socrates practices the art ofsubstitution; and it is through that art, Latour argues, that Plato’s rhetoric of math-ematics infiltrates the demos. Socrates’ response to Callicles reveals much in thisregard:

And wise men tell us, Callicles, that heaven and earth and gods and men are heldtogether by communion and friendship, orderliness, temperance, and justice; andthat is the reason, my friend, why they call the whole of this world by the nameof order [cosmos], not of disorder or dissoluteness. Now you . . . have failed toobserve the great power of geometrical equality amongst both gods and men:you hold that self-advantage is what one ought to practice, because you neglectgeometry. (Plato, Gorgias 507e–508a)

It is informative that Plato uses the Pythagorean term cosmos here, for it is thatphilosophy of mathematics he borrows from to reshape the demos. Out of that phi-losophy, Latour argues, Plato extracts the following principles, substituting themfor their democratic counterparts: for the democratic model of translation in whicheach citizen has the capacity to act—to interpret events and invent arguments toadvance their interests—he substitutes a geometric model of diffusion, where truthsare spread to the people and where citizens might even be forced, if necessary,“to adopt a course of action which would result in their becoming better people”(517c); for the democratic practice of collective demonstration in which the poliscan express itself to itself as a citizen-state he substitutes the logos of geometric equal-ity, which “requires a strict conformity to the model since what is in question isthe conservation of proportions through many different relations” (Pandora’s Hope248); and for the dynamic urgency of politics—and the invention of rhetorics equalto it—he substitutes the statics of an axiomatic mathematical model of language inwhich statements demonstrated as true become the benchmarks against which allothers are judged.

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Taken together, these principles render politics nothing more than an echo cham-ber and rhetoric nothing more than a tool for spreading the truths discovered byreal philosophers. In such a community, “every perturbation is judged a mistake,misrepresentation, misbehavior, betrayal” (249). It is easy to understand, from thisperspective, why Plato demonized sophistic rhetoric and those who practiced it; weare also beginning to see now that Plato’s arguments rested on a geometric logos,which has significant repercussions—within his thought and the thought of thoseinfluenced by him—for the prospects of rhetoric and democratic politics. As yet,however, we have not discussed the consequences of Plato’s rhetoric of mathematicsfor mathematics itself—we have not shown that it is in fact a rhetoric of math—northe ways scholars have recently attempted to circumvent the obstacles Plato put inplace to thinking rhetoric and math together. Doing so will offer several alternativesto Plato’s narrow views and open several new vistas of rhetorical inquiry.

Circumventions

Plato’s machinations in Gorgias would be laughable if they were not so tragicallyinfluential. I need not rehearse for rhetorical scholars how Platonic thought wasextended, adapted, transformed, and hardened with the rise of Modernism, nor howit continues to haunt contemporary culture.1 Testifying to this continued influence,in mathematics what is today called “Platonic Realism” still enjoys a hegemonicposition. As Brian Rotman notes, “For most mathematicians (and, one can add,most scientists) mathematics is a Platonic science, the study of timeless entities, pureforms that are somehow or other simply ‘out there,’ preexistent objects independentof human volition or of any conceivable human activity” (Ad Infinitum 5). Rotman’swork figures as an early and sophisticated effort to develop an alternative to PlatonicRealism and thus serves as a productive point of departure for understanding howPlatonic thought gets rearticulated within modern mathematical discourse as wellas how it obscures the actual practice of mathematics.

The Semiotic Approach

The organizing principle of Platonic Realism is that mathematical objects exist inde-pendently and a priori of human cognition. Mathematical symbols are, accordingly,more or less adequate representations of ideal mathematical objects, and the pur-pose of doing mathematics is to discover “objective irrefutably-the-case descriptionsof some timeless, spaceless, subjectless realm of abstract ‘objects’” (Mathematics asSign 30). From this perspective, mathematical symbols should function as transpar-ent referents for real mathematical objects and their relationships and should haveno function beyond that: “Language, for the realist, arises and operates as a name

1Chaim Perelman’s work showed the Platonic roots of Modernist thought; see especially The Realm ofRhetoric. Latour’s work is strong in terms of Modernism’s impact on understandings of science.

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for the preexisting world. Such a view,” Rotman argues, creates “a bifurcation of lin-guistic activity into a primary act of reference—concerning what is ‘real,’ given ‘outthere’ within the prior world waiting to be labeled and denoted—and a subsidiaryact of describing, commenting on, and communicating about the objects named”(Mathematics as Sign 30). Thus the hard Platonic division between the work of rep-resentation and invention: when mathematicians scribble a proof that proves valid,they are not inventing; they are describing and discovering.

While this perspective may have some psychological benefits—enabling thoseoperating from within it to see their work as pure and absolute—it also has somereal deficits when it comes to understanding mathematical practice. Like the real-ist style so familiar to rhetorical scholars in other domains,2 mathematical realismimmediately denies the materiality of mathematical discourse. True mathematicalsymbols, formulae, and theorems are not interpretations or even representationsof an ideal mathematical reality for realists; they are transparent presentations that,taken together, “merely describe[] prior mental constructions appearing as presemi-otic events accessible only to private introspection” (Rotman, Mathematics as Sign29). But how, asks Rotman, can we account for the movement from mathematicalpractice to mathematical knowledge? By what means do mathematicians capturetheir supposedly presemiotic thoughts? And what is the mathematician’s relation-ship with the a priori realm of mathematical objects? Plato answers with referenceto the soul and a metaphysics of reincarnation; Gottlob Frege, one of the foundersof formal logic and a preeminent mathematical realist of the twentieth century, doesnot do much better:

The apprehension of a thought presupposes someone who apprehends it, whothinks it. He is the bearer of the thinking but not of the thought. Although thethought does not belong to the thinker’s consciousness yet something in his con-sciousness must be aimed at that thought. But this should not be confused withthe thought itself. (Frege, cited in Rotman, Mathematics as Sign 33)

For Frege there are objective, timeless thoughts and there are thinkers who can“apprehend” them, but the “something in his consciousness” that allows the finitehuman subject to access the infinite realm of absolute truth remains enigmatic.

For Frege and Plato and other mathematical realists, Rotman argues, the meansof production of mathematical knowledge are hidden because the constitutivework of the mathematical sign is systematically denied. Taken together, Rotman’sthree books—Signifying Nothing, Ad Infinitum, and Mathematics as Sign—figure asemiotic intervention into the space between rhetoric and mathematics that Platooriginally opened and that largely remains unexplored today.3 Building on CharlesSanders Pierce’s semiotic work, Rotman’s semiotics suggest that the first step tounderstanding math as a discursive practice is to ask how mathematical discourses

2See Robert Hariman; Reyes, “The Swift Boat Veterans for Truth.”3I draw mostly on Rotman’s more recent Mathematics as Sign because there one finds the clearest

articulation of his approach.

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subjectify those who practice them. When you do mathematics, in other words, whoare you? Two primary roles, Rotman argues, immediately emerge in mathematicaldiscourse: “the one who imagines (what Peirce simply calls the ‘self’ who conductsa reflective observation), which we shall call the Subject and the one who is imag-ined (the skeleton diagram and surrogate of this self), which we shall call the Agent”(Rotman, Mathematics as Sign 13).

Initially, the relationship between the Subject and the Agent appearsstraightforward—not unlike someone who uses a map, projecting an imaginary ver-sion of themselves into the mapped space; but unlike a map, mathematical signssignify a “purely imaginary territory” (14). This imagined space—and the differ-ences it introduces—is crucial to understanding mathematical practice: when onethinks mathematically (add all odd numbers between 1 and 100, for instance) onesimultaneously projects oneself into an imagined world (in our example, a worldwhere such “things” as numbers and number-lines “exist”) and then executes thenecessary operations. Crucially, however, this practice of thinking and imaginingand executing is, Rotman observes, constituted, buttressed, and reinforced by anequally important semiotic practice: “such creation cannot . . . be effected as purethinking: signifieds are inseparable from signifiers: in order to create fictions, theSubject scribbles” (Mathematics as Sign 14).

That scribbling—that material, corporeal, semiotic element of mathematicalpractice neglected by Platonists—becomes even more important when our math-ematical thinking moves from the finite (as in our previous example) to the infinite(add the series 1, 1/2, 1/4 . . .), for at that point we must not only project ourselves asa Subject into an imaginary mathematical world, we must also imagine an Agentunrestrained by “finitude and logical feasibility—he can perform infinite addi-tions, make infinitely many choices, search through an infinite array, operate withinnonexistent worlds” (14). Here the support of written signs becomes essential notsimply as a recording device for one’s a priori mathematical thoughts but as a meansof mathematical innovation: when we attempt to solve new or unfamiliar problems,for instance, we use signs to marshal our previous knowledge (both mathematicaland non-mathematical) and we use signs to create non-finite thought experimentsthat the Subject can, via the Agent, test.

Although we have only scratched the surface, two important rhetorical insightsemerge from Rotman’s work at this point: first, the structure of mathematical per-suasion within the practice of doing mathematics begins to take shape and, second,the forms mathematical discourse takes and their consequences begin to emerge.Let us deal with these in turn: If, as Rotman suggests, mathematics is a series ofthought experiments in which mathematicians imagine themselves into a mathe-matical world and, via inscription, make predictions that they test through theirimagined Agent, how are they persuaded (mathematicians would say compelled)to believe in the integrity of their testing? Unlike the physical sciences, mathemati-cians have no physical world with which to verify their predictions. By what meansare they compelled? By “observing” the “actions” of the imagined Agent projected

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into the already established mathematical world, Rotman argues, the Subject is per-suaded that the predictions within the thought experiment are probable. However,it is through a more rigorous proof procedure that mathematicians are persuaded ofa statement’s absolute truth. That proof procedure is composed of both fictive andlogical elements—the fictive figure of the imagined Agent and the logical force ofthe scribbling Subject. Each layer of a mathematical proof, Rotman claims, sustainsa dialectical tension between these elements even as each layer corresponds withthe scribbling and manipulating of written signs: “These manipulations form thesteps of the proof in its guise as a logical argument: any given step either is taken as apremise, an outright assumption about which it is agreed no persuasion is necessary,or is taken because it is a conclusion logically implied by a previous step” (17).

Yet this description of mathematical persuasion is inadequate, for animatingevery non-trivial mathematical proof is what Rotman calls a “leading principle,”an idea that motivates the logical minutiae of a proof: “Presented with a new proofor argument, the first question the mathematician . . . is likely to raise concerns‘motivation’: he will . . . seek the idea behind the proof . He will ask for the story thatis being told, the narrative through which the thought experiment or argument isorganized.” (18). Why, one might ask, are these ideas absent from the mathematicalproofs they animate? Because they exceed the strict boundaries of formal logical dis-course sanctioned within formal proofs (what Rotman calls “the Code”).4 Rotman’sargument here, and other scholars have made a similar point, is that one can know aproof, reproduce all the steps, even explain why those steps follow logically from oneanother, and yet fail to understand the meaning and significance of the proof.5 That isbecause meaning and significance come from “the idea behind the proof,” and thoseideas only exist semiotically in the “meta-Code,” that is, in the discursive formationsexcessive to formal logic. This aspect of mathematical practice forces Rotman to adda third figure to his semiotic model: the Person:

the Person constructs a narrative, the leading principle of an argument, in themeta-Code; this argument or proof takes the form of a thought experiment in theCode; in following the proof the Subject imagines his Agent to perform certainactions and observes the results; on the basis of these results . . . the Person is per-suaded that the assertion being proved—which is a prediction about the Subject’ssign activities—is to be believed. (Mathematics as Sign 35)

The Person—the actual corporeal, physical presence who scribbles and thinks,thinks and scribbles, and most importantly has access to the ideas in the meta-Code—names the motivational force behind formal mathematical proofs. Now wehave a more complete semiotic picture of mathematical persuasion.

4The issue of the relationship between informal and formal mathematical discourse, the discursive/argumentative strategies within each, and the rhetorical purposes of each remains an unexplored andpotentially rich area for rhetorical analysis. See the “Potentialities” section that follows.

5For others who make this argument see William P. Thurston; Lakoff and Núñez; Imre Lakatos.

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It is precisely the Person—who is finite, lives outside the formal mathemati-cal code, and has access to the ideas that motivate mathematical theorems andproofs—that Platonic realism denies. That denial brings us to our second rhetor-ical insight: although Platonism protects a faith in mathematics as absolute, it alsoshapes conventional mathematical discourse in profound ways. Consider the con-spicuous absence of indexical terms (“I,” “now,” “here”), for instance, in mostmathematical texts; or the omnipotent voice of command (the imperative mode);or the lack of contextual explanation of the concepts considered (Mathematics asSign 121). Each of these discursive characteristics echoes an investment in a Platonicworldview: the absence of pronouns reinforcing realism’s basic principle (math isabout real objects), the imperative mood aligning with a hierarchical theory ofForms, and the ahistorical style fitting with claims to transcendental truth. Yet ifone desires to communicate the actual practice of doing (rather than memorizingand regurgitating) math and hopes to offer an understanding of the meanings ofthe concepts mobilized in mathematical statements, then one needs to attend tothe creative, constitutive force of mathematical discourse that Platonic realism ren-ders invisible and that only now is beginning to come into view through Rotman’sanalyses.

For rhetorical scholars, the good news is that several old friends traffic withRotman’s reanimation of mathematical discourse: the meaning and significanceof a mathematical statement comes not from its infallibility—the establishment ofwhich is the purpose of formal logic—but from its meta-Code. Suddenly we seethat contextual knowledge—rhetorical, historical, sociopolitical—of mathematicalconcepts is central to understanding them, without which one can execute a prob-lem or a proof (as a computer might) and yet not have the slightest inkling of themeaning or purpose of that execution.6 Equally problematic, one who encountersPlatonically inspired mathematical discourse is likely to see it as an inert, abstract,rule-driven system of formal logic instead of a fascinating, evolving, contextuallysituated, creative practice of thinking and writing. The arts of mathematical innova-tion lie in the nexus between thinking/scribbling and the argumentation that these“thought-scribbles” give rise to within one’s mathematical community.7 And this,finally, is why I labeled Plato’s rhetoric a rhetoric of mathematics earlier in the essay:

6This is, of course, a major issue in the mathematics education literature, where studies of student perspec-tives on math reveal two consistent themes: students perceive math as (1) abstract and (2) rule-driven. Thepoint that we are building toward is that mathematics is not abstract or rule-driven by nature, but it can andoften is taught as an abstract form of logical (rule-driven) reasoning. This pedagogical approach, it has beenshown, does not allow the majority of students to identify with mathematics (see Boaler). Regarding computersand mathematics, an interesting phenomenon has emerged in the twenty-first century: powerful computersare analyzing enormous data sets and are producing complex mathematical formulas out of those data setsthat even the best mathematicians cannot understand—they know they work to predict certain phenomenain the data set but they cannot give meaning to those predictions. The fact that computers can generate novelmathematical formulae significantly undermines the Platonic view of mathematics. See Rotman, Mathematicsas Sign, 126–128.

7Lakatos’s work reveals the importance of historical context and the dynamics of argumentation inmathematical innovation. See Lakatos, Proofs and Refutations.

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it shrouds many of the most fascinating aspects of mathematical practice behind ametaphysical veil that is both damaging—to math, to rhetoric, to politics—and,Rotman shows us, unnecessary.

An attentive reader might reasonably ask at this point, but how does Rotmanexplain mathematics’ usefulness in the physical sciences? To parrot the physicistEugene Wigner, how can one explain the “unreasonable effectiveness of mathe-matics” without reference to the a priori? Math’s effectiveness is only “mysterious,”Rotman rejoins, if one already sees with Platonic eyes, that is, sees a world wherefinite humans have access to and can discover eternal truths and where the Personand the meta-Code critical to mathematical practice are invisible. Rotman’s alterna-tive proposition: “mathematical objects are not so much ‘discovered out there’ as‘created in here,’ where ‘here’ means the cultural circulation, exchange, and inter-pretation of signs within an historically created and socially constrained discourse”(Ad Infinitum 140). This does not amount, Rotman emphasizes, to a reductive socialconstructivism; instead there is “a twofold movement between mathematical signi-fieds and the world” (141). Each constitutes and is shaped by the other in an evolvingseries of transformations: “mathematical signifieds themselves owe their origin toempirical, material features of the world” and the world, especially the techno-scientific world of late capitalism, owes its warp and woof to the forms mathematicalsignifieds often give to it.8

The semiotic program Rotman initiates is sophisticated and productive, devel-oping a semiotic theory of mathematical practice that reveals the structure ofmathematical persuasion, offering a grounded, non-metaphysical account of maththat challenges Platonic realism, and opening a whole realm of symbolic actionto rhetorical analysis. And yet, Rotman’s approach, like any analytic, has limita-tions. Rotman’s work has many fascinating rhetorical implications, but often thoseimplications are left undeveloped. His description of mathematical statements aspredictions, for example, suggests mathematical discourse might be largely deliber-ative in character; but analysis of this possibility is absent from his work. Likewise,Rotman shows that mathematical meaning comes—through the Person—from themeta-Code external to formal mathematical discourse, but what are the analyticstrategies available to scholars—short of talking to “the Person”—to tease out thedifferent ways meanings get produced in mathematics, to study how they circulate,and to analyze how they influence mathematical practice? Perhaps a result of hisintense focus on mathematical signs is a certain kind of shortsightedness when itcomes to larger macro-rhetorical questions. Fortunately for our story, other schol-ars have begun to address some of these broader issues, building on and extendingRotman’s work.

8For insightful accounts of the emergence of Greek geometry and its debt to empirical, material features ofthe world see Michel Serres; Reviel Netz.

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The Cognitive-Metaphorical Approach

Were it not for a shared interest in mathematics, Lakoff and Núñez’s WhereMathematics Comes From could not be more different from Rotman’s work. In theirbook one finds a more quotidian style, one less given to philosophical polemics;and while they have an interesting way of sidestepping Platonic realism, unlikeRotman they do not appear compelled to challenge it directly. Likewise, theirmethod of reading mathematical discourse—a combination of linguistics, cognitivescience, and metaphoric analysis familiar to readers of Lakoff’s previous work—putsRotman’s semiotic approach in sharp relief if only for its seemingly linear execution.And yet several affinities emerge: both show an inclination towards close analysis ofmathematical discourse, both have an abiding interest in the ideas that motivatemathematics, and both conclude that mathematical practice cannot be accountedfor from a strict Platonic perspective. Their differences, however, are conspicuous,and in attending to them we can glimpse the complexity of the relationship betweenrhetoric and math. It is not so much that their projects are incommensurate. Therelevant distinction, rather, comes from how each conceives of the production ofmathematical meaning.

Where Mathematics Comes From represents an ambitious effort to begin a newarea of study the authors call “mathematical idea analysis.” They immediately settheir project apart from Rotman’s: “The intellectual content of mathematics liesin its ideas,” they claim, “not in the symbols themselves” (xi). Thus for Lakoffand Núñez any account of the origins and practices of mathematics must attendto mathematical ideas; and if those ideas emerge from human cognition, as theyargue, then a cognitive scientific approach should shed considerable light on howmathematics begins, functions, and is understood.

“What,” Lakoff and Núñez ask, “is the cognitive structure of sophisticated math-ematical ideas?” They posit three findings from cognitive science as essential toaddressing this question: the first, “the embodied mind,” comes from researchshowing that sensory experiences structure human concepts; the second, “thecognitive unconscious,” suggests that most human thought is unconscious—“notrepressed in the Freudian sense but simply inaccessible to direct conscious intro-spection” (5); the third, “the conceptual metaphor,” names the mechanism bywhich humans understand abstract concepts through more concrete ones. Withthese three findings, Lakoff and Núñez attempt to explain how abstract, highlyformalized mathematical ideas emerge, build on each other, and hold meaningfor those who understand them. Absent from all the research on mathematics,they contend, is analysis of the ideas implicit in equations, the ways mathemati-cal ideas are weaved together in mathematical statements, and why the veracity of amathematical statement comes from those ideas and their interdependence.

One can hardly speak of mathematical ideas, of course, without encounteringthe Platonic view, and so Lakoff and Núñez do, however briefly. In contrast toRotman’s impassioned challenge, theirs is an agnostic approach: “The question of

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the existence of a Platonic mathematics cannot be addressed scientifically. At best,it can only be a matter of faith, much like faith in a God. . . . Science alone canneither prove nor disprove the existence of a Platonic mathematics, just as it cannotprove or disprove the existence of a God” (Where Mathematics Comes From 2). Laterthey clarify that the only mathematics they are interested in is “humanly created andhumanly conceptualized mathematics,” that, because human mathematics is “con-ceptualized by human beings using the brain’s cognitive mechanisms,” questionsabout the nature of human mathematics are scientific questions, and, finally, if onebelieves mathematics to exist a priori the burden of proof lies with that person toprove it scientifically (Where Mathematics Comes From 2–3).

Sidestepping Platonic realism in this way has some disadvantages. WhereMathematics Comes From is, for example, less alive to Platonic realism’s widespreadinfluence and continued hegemony. More importantly, we hear Rotman shout fromthe other room, the work, perhaps less reflexive due to lack of engagement, allowscertain Platonic tendencies to slip in through the backdoor. While these critiquesbear consideration, and we will return to them to be sure, their overemphasis mighteclipse the great advantage of this approach: their argument makes strategic useof the logic of science—falsifiability—to undermine the claims of Platonic realismeven as it legitimizes what is, at bottom, a metaphorical analysis of mathematicaldiscourse.

The most insightful moments in Lakoff’s and Núñez’s treatise, those which setthe book apart, emerge through mathematical metaphor analysis. “Many of theconfusions, enigmas, and seeming paradoxes of mathematics,” they suggest, “arisebecause conceptual metaphors that are part of mathematics are not recognized asmetaphors but are taken as literal” (6). Deliteralizing those metaphors will thus helpclarify some of the conflicts associated with mathematics, but, they caution, doing sowill not eliminate mathematics’ metaphorical content: “Conceptual metaphor . . .

[enables] us to reason about one kind of thing as if it were another. This means thatmetaphor is . . . a grounded, inference-preserving cross-domain mapping—a neuralmechanism that allows us to use the inferential structure of one conceptual domain(say, geometry) to reason about another (say, arithmetic)” (6). Sophisticated math-ematical ideas, Lakoff and Núñez argue, often weave several conceptual metaphorstogether; only through metaphoric analysis, then, can we begin to reveal their highlycomplex conceptual content.

Let us consider an accessible but still interesting example. The Cartesian-coordinate plane—a symbolic apparatus that marks for many the beginning ofModernism—had a profound impact on mathematics, science, and culture, andholds together a blend of metaphors crucial to understanding its conceptual force(Figure 1).

One of the basic conceptual metaphors involved in Descartes’ seventeenth-century invention—what Lakoff and Núñez call the “category is container”metaphor—transforms number into space; that is, before one can conceive of aCartesian plane one must accept (perhaps unconsciously) the metaphor that maps

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Figure 1 2-dimensional Cartesian-coordinate plane.

the category “numbers” onto the spatial representation “number line.” The “num-ber line” becomes the container for the category “numbers.” To that metaphor, onethen weds the “geometric figures are objects in space” metaphor that is the basisof the Euclidean plane (and Platonic metaphysics). This metaphorical blend (“TheCartesian Plane blend”) achieves a simple but powerful alchemy: it enables one tosimultaneously arithmetize space and spatialize algebra. Suddenly mathematicians“can geometrically visualize functions and equations in geometric terms, and alsoconceptualize geometric curves and figures in algebraic terms” (385). The Cartesianplane thus becomes an efficient means of transformation, for it not only allows func-tions to be visualized geometrically and geometry to be figured arithmetically, it alsoenables all manner of previously non-mathematical phenomena (terrain, motion,rates of change, weather) to be mathematized; that is, filtered and transformed andmapped into a mathematical space constituted by conceptual metaphors.9

Such work marks an exciting moment of possibility: Lakoff’s and Núñez’sresearch performs a mode of analysis of mathematics whose roots lie in rhetori-cal studies. Furthermore, this kind of analysis, they argue, is not merely possible butnecessary if one wants to understand the meaning of mathematical statements. Theimplications ripple across many shores. One wonders, building on their provocativeclaims, how other tropological forms function within mathematical discourse, towhat extent polysemy plays a role in historical moments of crisis and shift in math-ematical practice, and in what ways the arts of mathematical invention might belinked to novel metaphorical thinking.

9To the skeptical reader who thinks math is only metaphorical at the basic level: Nearly half of WhereMathematics Comes From addresses more complex mathematics, offering analyses of the concept of infinityand of Euler’s classic equation eπ i = −1. A full treatment of these analyses is beyond the scope of this essay.

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Provocative as their work is, however, we must temper any enthusiasm with asober recognition of the book’s shortcomings. In spite of their attention to thegreat variety of conceptual metaphors within mathematics, a dangerous reductivismsurfaces in their work. Take, for example, their analysis of infinity. Few conceptsin mathematics have had a more profound influence and few could match thehistorical variety of formal symbolics through which infinity has been thoughtand mobilized. Lakoff and Núñez dedicate a whole section of their book to theconceptual metaphors that “govern” the meaning of infinity. And yet their ownconceptual methodology, which seems intractably tied to the hierarchical logic ofa concrete/abstract binary, forces them to argue in an essentialist fashion that thereis one most-originary metaphor of infinity (“The Basic Metaphor of Infinity”) onwhich all other mathematical thought of the infinite is based. If this kind of hier-archical reductivism does not sit well with you, you are in good company: manymathematicians have decried the flattening out of important conceptual diversitythat Lakoff’s and Núñez’s work eschews (see Schiralli and Sinclair, “A ConstructiveResponse” 84). Importantly, however, mathematicians have not rejected their con-ceptual metaphor analysis altogether. We can, I think, take the strongest elements oftheir approach without burdening ourselves with their penchant for origins.

Even after that culling process, though, questions persist. Like Rotman, Lakoff’sand Núñez’s mode of analysis affects a micro-view of mathematics. One wondersover the yet broader issues that their analyses help us to understand but fail toaddress: What of the mathematization of the human experience gathering momen-tum in the twenty-first century, tied as it is to a positive feedback loop in whichmathematics makes the technologies possible that amplify the need for math-ematization? And how does mathematics extend out beyond itself to shape oursociocultural worlds? For answers to these questions we must return to Latour.

The Actor-Network Approach

Increasing attention to Latour can be seen across rhetorical studies. Yet no bookof Latour’s offers more to rhetoric than Science in Action. Unlike Rotman, Lakoff,and Núñez, Latour’s book is a study in contrasts. Whereas the books above attenddirectly to mathematics as a discourse which can and should be read—that is,analyzed for the ways in which meaning and ideas flow through its symbolicforms—Science in Action positions mathematics within an extended investigationof technoscience. While the reading of mathematics is crucial, it cannot and shouldnot, Latour argues, be separated from the networked assemblages that mathematicsboth serves and makes possible.

“Every time you hear about a successful application of a science,” Latour declares,“look for the progressive extension of a network” (249). With this as his guidingprinciple, where, he asks, should we begin an investigation of science and technol-ogy? Not with the black boxes—the finished products. The dynamic practices ofargument and controversy crucial to hardening and polishing a scientific claim into

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a “finding” takes place long before it is ready for public consumption: “Our entryinto science and technology will be through the back door of science in the mak-ing, not through the more grandiose entrance of ready made science” (4). As all ofLatour’s work suggests, only in the practices of scientific invention will we be able tosee what scientists and mathematicians actually do and escape the Modernist mythosof big-S “Science.”

Toward that end, the first section of Science in Action, titled “From Weaker toStronger Rhetoric,” examines the twin forces that steel scientific claims: researcharticles and laboratories. There Latour finds, contrary to popular belief, not theabsence of controversy but instead its amplification. New scientific claims gothrough a rigorous, labor intensive rhetorical regimen before they are declared factor fiction: counterarguments are raised, alternative explanations offered, laborato-ries mobilized, evidence marshaled, modalities disputed. What is surprising is notthe process so much as its implications. As one delves into scientific invention,Latour notes, rhetoric becomes more, not less, important. That is simply because asone goes deeper the controversies and debates often proliferate. Equally important, ascientific claim “by itself . . . is neither a fact nor a fiction; it is made so by others, lateron” (25). Scientific claims are considered true or valid or factual, in other words,by virtue of the networks to which they are associated; by virtue of who or whattakes them up and how. If they stood alone they would be soft; instead they rallyan assemblage of humans and nonhumans to their aid; they rhetorically mobilize acollective (61).10

The majority of the book elaborates on these points with intricate studies of theactors and networks assembled, linked, and associated in the practices of scientificinvention: Diesel building the first engine of his namesake, Lyell inventing the disci-pline of geology, Pasteur in the lab articulating microbes. Latour uses these examplesand more to build a methodology and an accompanying vocabulary for analysis ofscientific practice. His exploration of scientific invention eventually brings him tothe shores of mathematics.

Latour is interested not so much in mathematics as in the networks math makespossible. Like Newton, who wrote the Calculus to solve problems in physics, onemight say Latour engages mathematics by necessity rather than inclination. For ashe explores scientific invention—follows Pasteur, examines Edison, retraces Lyell—an inexorable pattern emerges: each time these actors need to harden their claimsto defend themselves, they turn to mathematics as a means of generating, mobi-lizing, and concentrating data: “Numbers are one of the many ways to sum up, tosummarize, to totalize. . . . The phrase ‘1,456,239 babies’ is no more made of cry-ing babies than the word ‘dog’ is a barking dog. Nevertheless, once tallied in thecensus, the phrase establishes some relations between the demographers’ office andthe crying babies of the land” (234). The demographers’ office, one center of cal-culation among many, uses numbers to “know” a population. But the power of

10Rhetoric of science scholars have extended Latour’s argument in various ways. The number of scholars istoo long to list here but one might profitably begin with John A. Lynch and Chantal Benoit-Barné.

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mathematizing a population does not lie in the numbers themselves; it lies in theconcentration of diverse phenomena—age, gender, wealth, religious affiliation—into one form: “Were we to follow how the instruments in the laboratories writedown the Great Book of Nature in geometrical and mathematical forms,” Latourdeclares, “we might be able to understand why forms take so much precedence. Incentres of calculation, you obtain paper forms from totally unrelated realms butwith the same shape (the same Cartesian coordinates and the same functions, forinstance). This means that transversal connections are going to be established inaddition to all the vertical associations made by the cascade of rewriting” (244).This also means that mathematization is a process of rewriting, of transforming theworld into mathematics—into the language of form.

Mathematics, Latour contends, underwrites the worlds of capital and techno-science not because it is true in some transcendental sense but because it enhancescapacities to mobilize traces, stabilize relations, and accelerate combinations.Exploration of the East Pacific in the eighteenth century illustrates his point. WhenLapérouse first visited what was then called Segalien in 1787, Latour observes, hewas weak. He had no knowledge of the land, the navigable straights, or the points ofdanger; he was dependant on his native guides. Yet a decade later he was stronger—no longer dependant on those same guides. What changed in those ten years? Themodalities of number and calculation combined with the Cartesian-coordinate sys-tem allowed explorers to extract and mobilize traces through the use of log books;those traces, slowly and painstakingly gathered in far away centers of calculation,enabled the production of navigational maps; those maps facilitated flows of capital,extraction of resources, exploitation of peoples.

Latour’s point? These mathematical modalities enable powerful forms of controlfrom a distance. Unlike our previous authors, the question of interest for Latouris not epistemological (about knowledge) nor hermeneutical (about meaning) butalways sociopolitical (about power): “how to act at a distance on unfamiliar events,places and people? Answer: by somehow bringing home these events, places, andpeople” (223). Mathematics in all its diverse forms is a powerful vehicle, collapsingdistance by mobilizing traces, transforming particularities of difference into stablesimilarities of form, and, because of that formal coherence, encouraging associa-tions and combinations between phenomena that, left in the world, would appearto have no relation whatsoever.

Equations only further enhance these qualities; they are both results of data col-lected and amplifiers of patterns and relationships between traces. We need notglorify equations—they are no different than other tools (graphs, tables, lists) usedto mobilize data—but merely recognize what they do, namely, “accelerate the mobil-ity of the traces still further. In effect, equations are subsets of translations andshould be studied like all the other translations” (238–239). When Edison struggledto invent the incandescent high-resistance lamp, for example, he used equations(Joule’s law, Ohm’s law) not because they would transport him to an abstract realmof pure truth but because they helped him draw together into one form the many

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heterogeneous constraints he faced. Concentrated into a few equations, Edison wasmore easily able to see those constraints and their relations. As important, he wasable to manipulate those equations so as to test each constraint and reveal whichone was the weakest. Equations, then, are important not because they are true butbecause they are “the sum of . . . mobilizations, evaluations, tests, and ties. They tellus what is associated with what; they define the nature of the relation; finally, theyoften express a measure of the resistance of each association to disruption. . . . Theyare . . . the true heart of the scientific networks, more important to observe, studyand interpret than facts or mechanisms, because they draw all of them togetherinside the centres of calculation” (240–241).

Potentialities

Latour’s arguments, when combined with the work of Rotman, Lakoff, and Núñez,bolster the case for developing links between rhetoric and math. Far from the lan-guage of pure reason, through Latour we begin to see mathematics as the web thatweaves the world of technoscience, as a discourse that rewrites the networks it rep-resents, and as a vehicle that concentrates power. Mathematics, then, is inherentlypublic and political—all the more so for the efforts that seek to insulate it fromthese very domains. Mathematics must be understood in light of the networks andrelations it renders, the ways it simultaneously concentrates and conceals power,the means by which it translates the objects of its gaze, the productive metaphor-ical structures it uses, and who we become when we do math. Each book we havereviewed suggests the viability and the benefits of critical rhetorical study of math-ematics; each book also calls for more sustained inquiry. Rhetorical scholars canand should bring their distinctive insights to bear on such an enterprise. A few havestarted to do just that, challenging the orthodox division between rhetoric and mathwhile offering fascinating case studies thought-provoking both for their content andtheir potential.

Giovanna Cifoletti’s work brings to the study of rhetoric and math a crucialemphasis on the historical and contextual. In the archives she recovers an old andlong forgotten alignment between the two that was alive and well as late as the six-teenth century. In those decades prior to the Modernist shift, Cifoletti argues, onefinds “a time for which today’s opposition between the two cultures was not yetvalid” (“Mathematics and Rhetoric” 376). In part a consequence of how rhetoricwas conceptualized during the Renaissance—not as mere ornamentation but “as anart of thinking” fundamental to many intellectual pursuits (“From Valla to Viète”392)—rhetoric and mathematics could and did profitably intertwine. Rejectingthe Modernist distinction between style and content, Cifoletti closely examineshow stylistic differences in mathematical presentations in sixteenth-century textsinfluenced mathematical innovation. Her conclusions: the rhetorical modalities ofmathematical presentation fundamentally impact mathematical invention; atten-tion to these rhetorical dimensions of math aids in our historical understanding

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of how math evolved; and our contemporary estrangement between rhetoric andmath is neither necessary nor inevitable—it is a strategic, historical, discursiveconstruction.

My own work on the Calculus of the seventeenth century builds on and extendsCifoletti’s work (Reyes, “The Rhetoric in Mathematics”). There I wanted to showthat mathematics is rhetorical not merely when mathematicians argue or when oth-ers make use of mathematics for nonmathematical reasons, but more fundamentallyat the level of the invention of concepts. There are, in other words, at least twoforms of rhetorical action associated with mathematics: situational rhetoric, whichis widely recognized and studied in our journals; and constitutive rhetoric, which isless commonly attended to but critical for understanding mathematical invention.11

My study closely examined the discourses through which the Calculus was articu-lated and assembled in the seventeenth century, finding at the heart of the Calculusa concept—the infinitesimal—that violated the rules of Euclidean geometry dom-inant at the time. These transgressions gave rise not only to controversy withinscientific and mathematical circles but also to a series of arguments that constitutedthe infinitesimal—a concept that, by its nature, could not be verified empirically norwithin the constraints of seventeenth-century mathematics. Rhetorical argumentwas the infinitesimal’s sole champion.

These studies of rhetoric within mathematics are complemented by a relative pro-liferation of recent rhetorical studies of mathematization in other domains. JessicaMudry’s excellent study of the quantification of food in Measured Meals (2009), forexample, examines the impacts of that phenomenon on contemporary perceptionsof health and nutrition. With Mudry’s emphasis on “a discourse of quantification,itself, as a stylistic device that tropes and refigures the objects it describes” (8) sheextends the constitutive analytic paradigm even as she shows the tropological forceof quantification to transform qualities into quantities, humans into incompletesubjects, and food into a commensurable form of capital. Jordynn Jack’s Scienceon the Home Front (2009), which examines what I think of as the horizon of judg-ment (the premises, assumptions, decisions) that governed calculations of safety atthe Hanford site of the Manhattan Project, likewise extends our understanding ofthe constitutive potentialities of quantification. Jack shows how quantification bothpromoted and reinforced a form of technical rationality that allowed the scientiststo dissociate their work from broader ethical questions, thereby severely constrain-ing discussion of human and environmental health issues. Finally, James Wynn’srecently published Evolution by the Numbers (2012) traces the rise of math in thebiological sciences, teasing out the topoi of mathematical arguments and how theyslowly transformed the concept of evolution and rewrote biological epistemology.12

11Analysis of rhetoric as constitutive has increased in many areas of rhetorical studies but remainsa minority approach to the study of mathematical discourse. I develop this point in “The Rhetoric inMathematics.”

12These works build of course on previous scholarship on mathematics as deployed in other domains,including especially the domains of economics and statistics.

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These studies are important for their insights into their particular historical andrhetorical contexts of focus and for their challenge to the contemporary estrange-ment between rhetoric and math. The books reviewed here, when combined withthese studies, compose an emergent body of research, but they also signal a chal-lenge to rhetorical scholars. Are we willing to question the priority of alphabeticspeech so apparent in our journals? If we are indeed a field that studies symbolicaction, should we not attend to all symbolic action, both alphabetic and numeric? Iwould like to suggest in closing that if we answer affirmatively we actually advanceour interests in several ways.

It is in our interests to attend to the numeric as critical informants, that is, asthose who can offer critical insight into the deployment of mathematics in mat-ters of public concern. Our unique contribution comes from an interest not merelyin the micro issues of utility and instrumentality but more crucially from ourmacro understanding of math as a discursive form with historical specificity, onethat maintains networks, concentrates power, subjectifies its subjects, constructs amathematical gaze, influences, enhances, and sometimes displaces political judg-ment. Ours would not be an effort to reduce mathematics to rhetoric, but rather toenhance understanding of math as a discursive formation that enables, strength-ens, weakens, and creates relations between humans and nonhumans. Mathematicsis a socializing force that can articulate nonhumans into sociability with humansand thus radically transform collectives. In order to attend to these new, complex,and fast changing collectives we will need not only to trace the materiality of math-ematical discourse but also transform our own traditional humanistic theories ofrhetoric.

We stand to benefit from the study of mathematical discourse, then, not just ascritics but also as theorists. Our theories of rhetoric understandably emerge—givenour history—from practices of persuasion within the domains of orality and lit-eracy. They are accordingly human-centric, placing human agency at the center ofcritical-theoretical attention, focusing on the “personas” of a text or set of texts, ana-lyzing the “motives” underlying symbolic action, celebrating the rhetorical prowessof particular authors, and the list goes on. A turn to mathematical discourse chal-lenges such critical affinities: math, as Latour suggests, weaves networks of humansand non-humans together into ever more complex collectives. To attend to math-ematical discourse on its own terms, then, requires us to transgress the borders ofhumanism so that we can incorporate non-humans into our analyses. This is alreadyhappening in many corners of rhetorical studies, but perhaps math will push us yetfarther outside our alphabetic comfort zones to the edges of the symbolic, wherehumans and nonhumans meet.

Today, on the cusp of big data and the advance of mathematization, we will needto broaden our attention to numeracy if we hope to continue to adequately accountfor public discourse and political decision-making. And already we can see howthe works here offer new vistas for theoretical advance. Rotman’s semiotic theorycan and should be extended through our rich corpus of scholarship on discourse

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and argumentation (what to make of math’s deliberative inclinations, for example);Lakoff’s and Núñez’s work on metaphor can and should be extended by attention toother mathematical tropes (especially metonymy); Latour’s reconceptualization ofscientific and mathematical practice can and should be brought to bear on our ownideas in studies of the rhetoric of science (which has already begun). We are likely tofind, too, that in attending to mathematical discourse certain practices or conceptsunique to mathematical thought bear fruit when cross-pollinated with traditionalrhetorical theories.13

Whatever the direction this research takes, we now know that to engage in it isto undermine one of the fundamental pillars of alliance between Platonism andModernism, we can now see how the work thus far produced weaves together,and we can envision the variety and potential of future studies in the border-lands between rhetoric and math. To read mathematics in the ways detailed hereis not only to render the politics of math visible but, perhaps more important, tocomplicate our notions of what mathematics and rhetoric are in the process.

G. Mitchell ReyesLewis & Clark College

References

Benoit-Barné, Chantal. “Socio-Technical Deliberation About Free and Open Source Software:Accounting for the Status of Artifacts in Public Life.” Quarterly Journal Of Speech 93.2(2007): 211–235. Print.

Boaler, Jo. “Mathematics from Another World: Traditional Communities and the Alienation ofLearners.” Journal of Mathematical Behavior 18 (2000): 379–397. Print.

Cifoletti, Giovana. “From Valla to Viète: The Rhetorical Reform of Logic and Its Use in EarlyModern Algebra.” Early Science and Medicine 11.4 (2006): 390–423. Print.

———. “Mathematics and Rhetoric. Introduction.” Early Science and Medicine 11.4 (2006):369–389. Print.

Davis, Phillip J. and Reuben Hersh. Descartes Dream: The World According to Mathematics.Mineola, NY: Courier Dover Publications, 2005. Print.

Hariman, Robert. Political Style: The Artistry of Power. Chicago: University of Chicago Press, 1995.Print.

Jack, Jordynn. Science on the Home Front: American Women Scientists in World War II. Urbana, IL:University of Illinois Press, 2009. Print.

Lakatos, Imre. Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge, UK:Cambridge University Press, 1976. Print.

Lakoff, George, and Rafael E. Núñez. Where Mathematics Comes from: How the EmbodiedMindBrings Mathematics into Being. New York: Basic Books, 2000. Print.

Latour, Bruno. Pandora’s Hope: Essays on the Reality of Science Studies. Cambridge, MA: HarvardUniversity Press, 1999. Print.

13Bernhard Riemann’s concept of manifold, for example, comes to mind as a potentially beneficial way toadvance our thinking about polysemy and subjectivity, for it emphasizes not only the discrete differentiationsof meaning and identity but also their layered and continuous features. See Arkady Plotnitsky.

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———. Science in Action: How to Follow Scientists and Engineers through Society. Cambridge, MA:Harvard University Press, 1987. Print.

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