Asymptotes and metaphors

Asymptotes and metaphors

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Asymptotes and metaphors teaching feminist theory
Gipson, Michael Eugene
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Dissertations, Academic -- Women's Studies -- Masters -- USF
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ABSTRACT: As we move through our daily lives, the cogency of the world shifts and changes. Many constructs exist to explain and account for how we view and interact with our environment. Education is where our understandings become formalized and are challenged. To this end, a plethora of pedagogical tools are made available to aid educators in illuminating the world(s) around and within each student. However, there is always room for new ways of presenting information, concepts, and ideas. I put forth the mathematical trope of asymptotes as a new pedagogical tool. Asymptotes, as metaphor, work as a pedagogical tool for their utility as both visual and conceptual space. Through highlighting how asymptotes can map conceptualizations of 'the body', be utilized as a means to build and comprehend theoretical inquiry, and reconceptualize difficult issues and concepts within Women's Studies and Feminist classrooms, I posit the asymptotes metaphor as both visual/conceptual space and pedagogical tool.
Thesis (M.A.)--University of South Florida, 2006.
Includes bibliographical references.
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by Michael Eugene Gipson.

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Asymptotes and metaphors :
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ABSTRACT: As we move through our daily lives, the cogency of the world shifts and changes. Many constructs exist to explain and account for how we view and interact with our environment. Education is where our understandings become formalized and are challenged. To this end, a plethora of pedagogical tools are made available to aid educators in illuminating the world(s) around and within each student. However, there is always room for new ways of presenting information, concepts, and ideas. I put forth the mathematical trope of asymptotes as a new pedagogical tool. Asymptotes, as metaphor, work as a pedagogical tool for their utility as both visual and conceptual space. Through highlighting how asymptotes can map conceptualizations of 'the body', be utilized as a means to build and comprehend theoretical inquiry, and reconceptualize difficult issues and concepts within Women's Studies and Feminist classrooms, I posit the asymptotes metaphor as both visual/conceptual space and pedagogical tool.
Thesis (M.A.)--University of South Florida, 2006.
Includes bibliographical references.
Text (Electronic thesis) in PDF format.
System requirements: World Wide Web browser and PDF reader.
Mode of access: World Wide Web.
Title from PDF of title page.
Document formatted into pages; contains 61 pages.
Adviser: Sara L. Crawley, Ph. D.
Pedagogical tools.
Dissertations, Academic
x Women's Studies
t USF Electronic Theses and Dissertations.
4 856


Asymptotes And Metaphors: Teaching Feminist Theory by Michael Eugene Gipson A thesis submitted in partial fulfillment of the requirements for the degree of Master of Arts Department of Women's Studies College of Arts and Sciences University of South Florida Major Professor: Sara L. Crawley Ph.D. Kennan Ferguson, Ph.D. Marilyn Myerson, Ph.D. Date of Approval: October 25, 2006 Keywords: bodies, education, gender, abject, pedagogical tools Copyright 2006 Michael E. Gipson


Dedication To my parents, Susan and Gene, who taught me that there are some things that are given, that others have to be earned, and th at the difference speaks volumes. I dedicate this work to you. Without your guidance and patience, both past and present, I would never have made it. All my love.


Acknowledgements I would like to send my heartfelt thanks to Dr DiPalmas Body Politics Class, Spring 2003, for their rousing discussi ons and engaging anec dotes. First, I must thank Dr. Caroline DiPalma whose humor, hear t, and green pen made this work truly possible. Thanks for your keen eye, dramatic intellect, and enduring patience. Thanks to the others who graciously read portions of this work and provided you input: Amy, David, Sam, Skip, Greg, and John, you all helped me pick apart my own ideas and find the important pieces often burie d. To my thesis committee, I didnt make it easy but some how you found a way and helped me get it done; thank you so much. And, finally, but definitely not least, to Yoli and Dale whose support and an e ndless streams of coffee truly saved my sanitycheers. Thanks again to everyone.


i Table of Contents List of Figures ii Abstract iii Asymptotes And Metaphors 1 Body as an Asymptote 5 Theory and Metaphor 19 Metaphor as Pedagogical Tool 34 Metaphors and Asymptotes 49 Bibliography 51


ii List of Figures Figure 1. X = 1 / X 7 Figure 2. The Theatre 22 Figure 3. Social World/Spatial 23 Figure 4. Social World/Conceptual 25 Figure 5. Binaries 27 Figure 6. Cyborgs 28 Figure 7. Oppositional Constructs 30 Figure 8. Mobile Subjectivities 32 Figure 9. Sex 37 Figure 10. Gender 38 Figure 11. Sex and Gender 39 Figure 12. Gay 42 Figure 13. Signs 43 Figure 14. Abjection 45 Figure 15. Abject 47


iii Asymptotes And Metaphors: Teaching Feminist Theory Michael Eugene Gipson ABSTRACT As we move through our daily lives, the c ogency of the world shifts and changes. Many constructs exist to explain and account for how we view and interact with our environment. Education is where our unde rstandings become formalized and are challenged. To this end, a plethora of pe dagogical tools are made available to aid educators in illuminating the world(s) around a nd within each student. However, there is always room for new ways of presenting info rmation, concepts, and ideas. I put forth the mathematical trope of asymptotes as a ne w pedagogical tool. As ymptotes, as metaphor, work as a pedagogical tool for their utility as both visual a nd conceptual space. Through highlighting how asymptotes can map conceptual izations of the body, be utilized as a means to build and comprehend theoretical i nquiry, and reconceptualize difficult issues and concepts within Womens Studies and Feminist classrooms, I posit the asymptotes metaphor as both visual/conceptual space and pedagogical tool.


1 Asymptotes and Metaphors The way(s) that we come to understand and make sense of the world around us is tied up in relational dynamics (metaphors and bi naries). Whether we interrogate, engage, or disconnect is bound to the different perceptio ns we have about the world and what we do or do not see based on the interconnecti ons and relationships we have made. This interrogation, engagement, or di sconnection could be seen or defined as an acquired ability or skill that is gained as we move through and interact with our environment. The ability to conceptualize, comprehend, and uti lize the multiple perceptions and the myriad of interconnections available, in the world, is important and essentia l in education and by extension the classroom. To nurture and inco rporate this ability pedagogically, educators work to shift and expand the perceptive lenses and options of our students, whether we wish to encourage critical thought, mental and emotional honest y, or the simple memorization of information. As educators, the goal and hope is that as the students leave our course(s), they will have more inform ation, skills, and options than when they arrived. In working to this end, we employ a multip licity of pedagogical tools and skills in the quest to engage and encour age each individual student. However, there is no singular magical method that will bring every student to class everyd ay eager and ready to learn. Rather, multiple styles of engagement and a plet hora of tools are utilized in the hope that some combination of these will reach the stud ents and connect them and the information,


2 concept(s), or text(s). Jyl Lynn Feldman encourages a reconcep tualization of the classroom from lecture hall to theatrical sp ace (2001); while, bell hooks reformulates it as the responsible engagement of mutual participants in the Er os of critical thought (1993). But, whatever conceptualiza tion of the educational dynamic we use, the exchange of knowledge remains central. This exchange of knowledge begins with our basic perceptions and conceptions about our environment and our selves. However, this is not entirely within our control. For example, the conceptualizations and understandings we have about our bodies is mediated via the available frameworks th rough which bodies can exist and be known. As such, the constructs and dynamics that su rround the epistemological and ontological reality of bodies is important. In Body as an Asymptote, I will illuminate the socially constructed nature of the body and how asymptotes work as a metaphor for the comprehension, engagement, and formula tion of this construction. From this metaphorical relation, I interconnect the func tion and value of meta phor in theoretical discussion. In Metaphor and Theory, I highlight the metaphorical nature of theoretical positing. Specifically, I will illuminate the ways that metaphor, my asymptotes metaphor included, functions as a means to conceptu alize, build, and interrogate theoretical discourse. I will focus on performance theory (specifically Irving Goffmans dramaturgy and Judith Butlers abject bodies), Donna Haraways Cyborg, and Kathy Fergusons Mobile Subjectivities as exemplars of the dive rse formulations and utilizations of metaphor. Mo reover, I will present metaphor as both foundation and tool for theoretical argumentation. Further, from this explicit positing, I will highlight how


3 metaphor works to put forth theoretical discourse and how it aids in the exchange of knowledge pedagogically. This pedagogical exchange of knowledge is especially important when engaging theoretical constructs/concepts and/or facilitating a dialogue in the classroom. In these cases, there may or may not be a singularly right or wrong answer(s); rather, there is an interplay of ideas and positions (a)effecting conceptual ization and understanding. To keep this dynamic from digressing into a fr eewheeling debate, we often employ different tools and frameworks to encourage the cogency of discussion and the interplay of ideas. Metaphor and/or metaphorical relations seem to be quite common. Metaphors allow us to interconnect and interrelate conc epts and ideas in a way that encourages more than the simple acquisition of information. Metaphor opens knowledge, the per ceptions of it, and its building process to engagement and contes tation. In short, metaphor is device(s) for understanding and experiencing one thing in terms of another (Lakoff and Johnson 1980). Metaphor, then, aids in the basic conception and comprehension of information, keeping in mind that personal levels of perception can and do impact what is seen or not. Therefore, metaphors and metaphorical inte rplay can be and have been used and formulated in a number of different ways. Ho wever, of most interest to me, and of importance in this work, is metaphor as peda gogical tool: specifical ly, the mathematical trope of asymptotes and their possible use as metaphor. I begin by positioning asymptotes as a meta phor parallel to feminist discussions of the epistemological and ontological constructions of bodies. From this positing of asymptotes as metaphor, I expand to illuminate how metaphors, my own included, make theoretical positing and argumentation compre hensible. Finally, I explicitly posit the


4 asymptotes metaphor as a pedagogical tool and implicitly present it as a visual and conceptual critique of Western binary opposition s. To reach this goal, we need to begin by understanding what asymptotes are, what they have to do with the knowing and being of bodies, and how the mathematical trope of asymptotes can be utilized as metaphor.


5 Body as an Asymptote What is the definition of body? In what way(s) does body relate to individuality? Within feminist theory te rms like body/ the body are quite common and over time become entrenched in the voca bulary, works, and concepts of many of us. However, when attempting to impart, share, and engage newcomers, to feminist theory, we often times have difficulty. It can s eem that aiding in the comprehension and utilization of theoretical concepts/constru cts is problematic at best and at least improbable. So, what do we do to remedy this gulf in understanding and usage? In my experience, I have found that ta ngibility is key. The presentation of something visual, something open to more se nsory connections and relationships, greatly increases the likelihood that students will conceptualize, comprehend, and utilize theoretical concepts. Like many of my students, when I be gan reading and working with theoretical concepts, I ha d an extremely difficult time understanding and connecting theoretical terms, concepts, and constructi ons leaving comprehension, legibility, and intelligibility seemingly impossible. But, what I needed, and eventually found, was a tangible piece, a visual something, that I co uld perceive, manipulate, and engage. I found asymptotes. Asymptotes, like many theoretica l concepts, are intangible; however, the rules for their existence, the space(s) they inhabit, the topography available for movement, and even the ways to see these invisible intangibles ar e all defined. In the end, it requires using what is s een to see the unseen. To this end, I started with the seen


6 and began my search. What follows is the theoretical and linguistic journey of the asymptote. I begin with something considered quite tangible the body. From this space of physicality, I will ente r the less concrete and more fluid theoretical realm. Through this movement, I will highlight the capabilities of asymptotes to work as metaphor. I do this to show that this tangible intangible can be utilized as a means of visualizing (making tangible) other theoretical concepts for comprehension and educational purposes. To begin, I will map and connect asymptotes and bodies. The body is represented and discussed in numerous ways within social, political, and medical contexts. It is described as a mirror, a cor poreal form with a fictive interiority, a social canvas, and so on. Th ese constructions are reified, critiqued, and shifted. Furthermore, many theorists note how the dichotomous and hierarchied systems available for the discussions of the body are re strictive and problematic (and destructive). Within this section, I will discuss some of the ways through which the understandings and conventions, related to the body, have been produced. Through the examination of these terrains of the body, I will illuminate the framework for an alternative mode of body knowledgeasymptote as a metaphor for th e conceptualization(s) of the body. This conceptualization of the body is in response to the vast field of critical lenses available for viewing bodies. To aid in fleshing out the conceptualization( s) of the body via asymptote, I will highlight some of th e parallels between the construction and presentation(s)of both. Additi onally, through the discussion of the connections between


7 asymptotes and bodies, I intend to erect three different constructi ons of the body as an asymptote: abject body 1 enframing the body, and telos body. What are asymptotes and how can they be used to discuss bodies? The asymptote 2 functions in such a fashion that there are poi nts (bodies) that matter, a la Judith Butler, and those that do not matter (a bjects). Additionally, this mathematical trope illuminates a key point within many theorists worksspecifically, that the telos 3 or ideal body, or the construction of it, is not attainable by any body. Moreover, the teleological body functions in a fashion similar to that of th e asymptote(s) that so me curving functions approach but never touch (attain) 4 A brief discussion of the relation between the graphic space in which asymptotes exist and the socio-medical-political dom ain(s) of bodies will aid in revealing the terrains I wish to traverse and link. Bodies and asymptotes are accorded th eir definitions, shapes, names, and spaces based on the fields they inhabit. Asymptot es exist within the frame of a graph and, relatedly, bodies exist within a given socio-historical te mporality. The graph and sociohistorical temporality both function to enfr ame what can and cannot be, i.e. what is legible and what is intel ligible (Brown 2001, Butler 1993, Foucault 1980). Specifically, these two frames define the te rrain in which bodies/asymptote s exist. For asymptotes, the graph defines where, how, and in which wa y(s) it may existbe namedvia the specific 1 These multiple constructions are built purposefully and in a fashion similar to Judith Butlers dual construction of abject in Butler, Judith (1998). How Bodies Come to Matter: An Interview with Judith Butler by Irene Costera Meijer and Baukje Prins in Signs Vol. 23, No. 2 Chicago, IL: University of Chicago Press. 275-286. 2 Asymptote: (noun) Mathematics a straight line approached by a given curve as one of the variables in the equation of the curve approaches infinity. Websters College Dictionary, 1991 edition. 3 My understanding of this is loosely informed by Aristotles construction. For more information see Aristotles Nicomachean Ethics Trans. Terence Irwin. 2nd ed. Indianapolis: Hackett, 1999. 325. 4 I would like to thank Carolyn Di Palma and Jennifer Germaine for their aid in helping to clarify my understandings of attainability.


equation that sets the rules/parameters for its shaping. The location of the curves in the figure below and those to follow are based on the mathematical principles of positive and negative. Figure 1 (below) contains a visual representation of this concept, wherein the grid of horizontal and vertical lines designate the terrain/domain in which the graphic presentation of a mathematical equation may exist (enter intelligibility). 5 For example, if the equation was Y = 1/ -X, then the curves would be in the empty quadrants and where the curves are now would be empty. 6 Similarly, the dynamics that are present within the socio-historical temporality define how, which, and what can be or are thought about bodies. Moreover, these dynamics, whether social, political, medical, or otherwise, affect the physical and epistemological terrains of bodies. In Sexing the Body: Gender Politics and the Construction of Sexuality, Anne Fausto-Sterling examines the ways that bodies are defined through and within social, political, and medical contexts (2000). She 5 Within the grid, the central vertical line is designated the y-axis and the central horizontal line the x-axis. The curves contained within the graph (now called a graph due to the inclusion of axis and increments) are representative of the following equation: y=1/x. To alleviate confusion, it should be remembered that the horizontal and vertical lines happen to occupy the same exact space the asymptotes for y=1/x do. However, while the xand y-axes are visible, the asymptotes are invisible. This is due asymptotes lines being both locations of infinitude and undefinablei.e. in the equation zero cannot ever be x, as zeroes cannot be denominators. Therefore, in this figure, as well as those to follow, the visual lines represent a dual conception: visible grid lines and invisible asymptotes. Thus, there is a continual slippery connection between the seen and unseen, not a designation of the asymptotes always having the exact same formulation in each positing. 8 6 Through the rest of this work, only the original two curves will be presented. This is done for two reasons: legibility (as words and concepts will be added later) and simplicity (as the figures can become too busy/ messy when several curves and words are present).


9 illuminates the terrain/grid of the body(s) and how the conceptualizations of this terrain affect physical bodiesi.e. how the discourse s in socio-medical politics affect the constructions (discursive) of and about th e corporeality of bodies Specifically, she examines the rules and systems that these discourses implement in relation to bodies. Socio-medical-political discour ses, and more explicitly the methods used, are critiqued for their ability and violence in affecting th e corporeality of the body. She posits that the rhetoric and practices used to designa te bodies affect no t only the physical body (e.g. intersexed bodies) but also the discour se(s) and modes of thought available for making bodies intelligible. The designati on of bodies allowed and/or knowable within socio-medical-political domain(s) relates to my former discussion of the visibility available for mathematical equations through th e interactions between the rhetorical and physical (re)presentations of different functions. 7 Fausto-Sterling wr ites: [p]eople of mixed sex [intersexed bodies] all but disappear ed, not because they had become rarer, but because scientific methods [socio-medical pol itics] classified them out of existence (2000, 39). In reference to Figure 1, this statem ent can be represente d in the interaction between the asymptotes and the hyperbolic curve. The asymptotes would represent intersexed bodies that lay outside of in telligibilityoutside of known socio-medicalpolitical intelligibility, which would be repres ented by the hyperbolic curve. My point is that this visual representati on of bodies outside intellig ibility highlights one of my 7 The point of importance to note here is that the location and number of asymptotes within the graph of a function are defined by a specific equation, which can and does shift. The basic formula for a hyperbolic function (which has asymptotes) is ax^2 + by^2 + cxy + dx + ey + f = 0 [a, b, c, d, e, and f can be any integer and thus greatly effect the shaping of the gr aph]. Hyperbola, n. Geom., a plane curve consisting of two separate, equal and similar, infinite branches, fo rmed by the intersection of a plane with both branches of a double cone (i.e. two similar cones on opposite sides of the same vertex). Oxford English Dictionary Online Oxford University Press, 2003. Hyperbolic, adj. 1. Rhet. Extravag ant, 2. Geom. A: Of, belonging to, or of the form or nature of a hyperbola. B: Applied to functions, operations, etc., having some relation to the hyperbola. Oxford English Dictionary Online, Oxford University Press, 2003.


10 specific constructions of body as an asymptot e, asymptotes as abject bodies. However, this dynamic of knowable and abject is not the only asymptotic 8 construction possible. When thinking of bodies, the concepts, names, definitions, and systems related to them are not as mutually exclusive as they initially appear to be. Bodies are influenced within present contextsyes, but contexts are connected to the socio-historical moments from which they emerged 9 For example, for people of th e twentieth-century the two-sex model 10 for defining bodies seems natural. However, this only appear s to be the case due to a few hundred years of social and poli tical discourse affecting the ways through and in which bodies are thought. Prior to the emergence (in a Foucauldian sense) of the two-sex model, however, a one-sex model for bodies was normative. 11 What is of interest in this shift, for my project, is how these tw o models framed the epistemological terrains for the discourses on bodies (Laqueur 1990). Expl icitly, these models mapped the terrains for the discussions of bodies and more im portantly defined the ways through which discussions of bodies could exist. These two points are very intriguing for their parallel position to the ways in which the specific e quation of a hyperbola de fines its existence i.e. how the equation(s) of a hyperbola a nd the related asymptotes frame the space possible for the hyperbolic curve (see footnot e 6). Laqueur notes how when the one-sex model was prominent the construction of body was based on a uniform and singular 8 Asymptotic: (adj.) Mathematics 1. of or pertaining to an asymptote. 2. (of a function) approaching a given value as an expression containing a variable tends to infinity. 3. coming into consideration as a variable approaches a limit, usu. infinity. Also, I use this term in a similar fashion to Michel Foucaults in History of Sexuality: An Introduction, Vol. 1. Vintage Books, Random House, Inc.: New York, 1978, 41. 9 For an in-depth discussion of emergence see Mi chel Foucault Nietzsche, Genealogy, History. The Foucault Reader. Edited Paul Rabinow. New York: Pantheon. 1984, 109133. 10 Laqueur makes this argument in Making Sex: Body and Gender from the Greeks to Freud. Cambridge, MA: Harvard University Press, 1990. 11 The telos position of male within the one-sex model and its shift to dominant and ideal within the twosex model will be discussed later.


11 idealthe adult, citizen male. He points out that as the two-sex model gained prominence, the modality of bodies shifted to include a dual construction for bodies. Moreover, Laqueur illustrates how this modal shift affected the rh etoric and physicality of bodies. Specifically, this shif t was a splitting of the telos body into two interdependent bodies. This interdependence is due to the conceptual mode, normative social dynamics, that posited the male body (formerly at the t op of the telos) as positive and the female body as negativeexplicitly a negated body in so much as this body was lacking and therefore less than. In relation to the hyperbolic curve and its asymptotes, the curves in Figure 1 could be said to represent the one-sex model in th e sense that this curve has not been shifted specifically this hyperbolas asymptotes are on the xand yaxes. But, this same figure could be said to represent the two-sex model, as well, for the two curves contained therein are exact copies of each other. The reason that these curves can be representative of the two-sex model is through the functi oning of attributesin this case numbers. When positive numbers (attributes) are used (defined) the curve is contained within the upper right corner of the graph, this space contains only positive x and y values. 12 However, if negative numbers (attributes) ar e used (defined) the curve is contained within the lower right corner which cont ains only negative x and y values. This conceptualization of Laqueurs argument and Figure 1 is important because of the specific designation of spaces (epistemologies ) I am attempting to make. Explicitly, within Laqueurs work, he is illustrating how the designations inclusions, and exclusions 12 This positive/ negative relation is important because of the hierarchical nature of binaries. This power/value differential is always at play, implicitly and explicitly. However, the progression through the figures to come should not be concep tualized as being based solely on this differential. Rather, they should be viewed in relation to the explicit discussions tied to each and the way(s) that these are grouped together.


12 within the oneand two-sex models acted as frames through which the discourses, conceptualizations, and corpor ealities of bodies came to and could exist. Similarly, in Figure 1, the asymptotes (x and y axes) frame the space available for the curves. To expand this idea of frames and their affect s on bodies, Geoffrey Bowker and Susan L. Stars discussions of tuberc ulosis in Of Tuberculosis and Trajectories and racial classifications in The Case of Race Classifications and Reclassification under Apartheid are very useful. Through the analyses of cla ssificatory systems and their affects, Bowker and Star illustrate the ways these systems frame iden tity and the subject body. When analyzing the affects of tuberculin diagnosis, they not e that once a person became a patient with tuberculosis, the ways available to describe, relate, identify, and so on the person became framed within the context of the tuberculosis diagnosis. It was extremely difficult, if not impossible, to step outside of or remove th e frame of disease. To be exact, when the person was a patient they were defined by their diagnosis. Moreover, even after they left the hospital (if they survived) the person was related to as having had tuberculosisi.e. once a person was framed by the diagnosis that frame forever altered the means available for viewing/knowing them as an in dividual (2000). However, this distinctive shift in subjection has quite a different affect when Bowker and Stars theoretical lens centers on race instead of disease. In The Case of Race Classification and Reclassification under Apartheid, they illumi nate the shifting and blurring that occurred when the conceptions of subject, body, and race intersected. Specifically, they noted how the production and implementation of more disc rete and fortified ra cial classifications made it possible for ones identity to b ecome completely shifted by not only the


13 system/state but by ones self 13 (2000). These permeable and sh iftable classifications are important in relation to the forming of bodies. Pointedly, the mobility and porous designations of subject and body illustrate how frames, whether medical, political, or social, only appear natural due to their genera l status of invisibilit y. Moreover, it is this hidden frame that allows for the appearance of natural-nesswhi ch designates legible and intelligible bodies. Formerly, I noted how asymptotes and socio-medical-political discourses define and contain the episte mologies and ontologies of the body, which appeared to be discrete and i mmutable. However, in this sec tion I have attempted to show how these constructs can be reinterpreted. Specifi cally, though bodies can be epistemically and ontologically defined by r ace, disease, socio-medical-political, and so on, discourseslike hyperbolas by asymptotesthe se frames that signify bodies are not immobile and static: rather, they can and do shift and change. Thus, consistent with Foucault, I argue that enframing the body a nd the subject is not a singular event or emergence; rather, it is an affective process. Further, this enframing the body is the second asymptote-body construction I wished to posit. However, the affective process on and mobility of the subject-body is the third body as asymptote construct I feel needs to be illuminated further to connect this metaphor and c onceptualizations of the body. What designates an acceptable, and more importantly attainable, body is defined by the specific socio-historical temporality in which the question is posed. As noted formerly, Laqueurs work Making Sex is an intensive critical analysis of the shift from what he calls a one-sex to two-sex model. W ithin the one-sex model, the position of male 13 For a specific example see the case of Jazz musician Vic Wilkinson on page 205 of Bowker and Stars The Case of Race Classification an d Reclassification under Apartheid. Sorting Things Out: Classification and its Consequences (Inside Technology).


14 at the top of the telos 14 is what I wish to focus on momentarily for it may allow the answering of several questions. How is it the construction of telos is built on the assumption that the top is attainable when so fe w are ever actually at the top, if at all? In what ways is this seemingly unattainable top of the telos related to the position of one construction of abject as outsi de the discursive frame? If telos is in actuality an unattainable position and instead functions as a site of conve rgence, then how could this telos be seen as an ever-shi fting goal? In what ways are the power dynamics embedded in the telos of equal, and in some cases more, importance than the telos itself? Though it appears that these are a vast range of questi ons, I believe that thes e questions can be at least tied together through the affective pr ocess in the shift from a one-sex to two-sex model. A key point within the one-sex model cons truct is that the ma le position/body at the top of the telos is attainable. However, when we look back at recorded history some interesting questions arise. One, if this position is attainable (supposedly) by anyone (male) then why would concerns about race and class become so problematic as we progress (temporally) forward toward the pres ent day? And, two, when the male at the top of the telos shifted to dominant within the two-sex model, what was the impact on the relationship between men and women and with in these new categorizations? These two questions are interrelated through power. Michel Foucault note d that power is pervasive, active, and inescapable (1990, 1995). The male po sition at the top of the telos in the onesex model requires the use and consolidation of power. Those few males (white, citizen, 14 This positioning of the male teleological body and the attainability of telos is discussed in a similar style to that of the gender py ramids of Kate Bornstein in My Gender Workbook: How to Become the Kind of Man or Woman You Always Thought You Could Beor Something Else Entirely (1998) New York, NY: Routledge.


15 elite, etc.) who it could be argued existed, as the embodiment of the top of the telos, would have had to embody the ideological constructions of what male-ness or masculinity was at the time. Thus, temporality would have and has had a great influence on the construction of what traits and/or ch aracteristics would designate the top of the telos. Further, as we progress (temporall y) through history, the constructions and dynamics interacting on the telos would change and shift. Furthermore, as the shift from the different constructions of telos occurred, and eventually the shift to the two-sex model, we could upon inspection possibly recogn ize the mutability of borders that would have allowed previous abjects to enter intel ligibility. Moreover, as these new intelligibles entered discourse the constr uctions of what was normativ e and/or ideal would have shifted, eventually, affecting the interpolations of the telos. To reconnect this concept to Foucaults positing, the will to power would have been greatly influential in these shifts in the telos because as individuals enter intelligibility they could be said to gain a degree of power that their formerly abject position did not possess. These shifts in pow er are important for they highlight an important point. The un-attainability of the t op of the telos has everything to do with the ideological constructions of the body in that position. Specifically, this position, I believe, can never actually contain a corporeal body instead an ideolo gical construct of one. What does this mean for the shift from the one-sex model with male at the top of the telos to the two-sex model where male is dominant? Pointedly, that there is not a corporeal body that in actuality matches the ideologically c onstructed one; instead, there are always and


16 only approximations of that ideal 15 And, what of the telos and the asymptote? What is the connection? The telos of bodies, whic h contains the epistemic and ontologic constructions, is still functional within th e two-sex model because it designates the ideal forms that bodies should or can take. An d, the telos relates to (is related through) the conjunction of abject bodies, enframe d bodies, and the affective process of approximationwhich due to socio-histori cal temporalities will shift and change. Perhaps, some more tangible example of my meaning and constructions will aid in highlighting the connections I wish to make. The influence of the supposed attainabl e telos can be seen today within a number of realms. Dan Edelmans The Thin Red Line: Social Power and The Open Body illustrates the ways that the ideologica l constructions of the body influence the corporeality of them. In his discussion of Bodybuilding/Shaping, Edelman points out how the will to power, internalized identifica tion with the ideal, abject epistemologies, and personal frame of reference all influence the cor poreality of bodies. Specifically, he notes that bodybuilding requires the control ling of the body (will to power) to alter it progressively towards a specific goal (internaliz ed ideal, social norm). Further, he notes how the individuals understanding (frame) of their body influences their acce ptance or denial (abjection) of some bodies and/or personal body topography (2000). In his discussion of Cosmetic Surgery, Edelma n expands the idea of the body is the inscribed surface of events (Foucault, 1984) to the literal and explic it enactment of this process of inscription (2000, abstract). Edel man illustrates how the process of cosmetic surgery is a convergence of several id eologies: the will to powerover the body, 15 This concept is informed by Judith Bu tlers construction of performativity in Bodies That Matter: On the Discursive Limits of Sex. New York: Routledge, 1993.


17 internalization of idealthus the need for cosmetic surger y, abjectiondenial of some types of embodiment as acceptable, and the socio-normative frame of beauty. In both of these discussions, Edelman high lights what I call an affective process of approximation. Within these discussions, bodies are affected by inte rnalized ideals, the need/desire to match or approximate the idea ls, abjection in the se nse that the body is a terrain to be adjusted, cut, reshaped, or reinterpreted, and framed by social norms and ideals that designate acceptable and unaccepta ble bodies. Furthermore, the ideological body that is being approximated, the top of the telos, is never actually achieved. Thus, as individual bodies approximate the top of the telos they could be seen as acting similarly to the way that the hyperbola continually appr oaches an asymptote but never achieves it. Moreover, since both the hyperbola and bodies could be said to approach infinitude hyperbolas can have an infinite number of integers and never touch the asymptote (remembering that in the figure the axes a nd the asymptotes occupy the same space and are never touched by the curves, only approached ), and the ideologica l body at the top of the telos (telos body) will continually shif t due to the changing socio-historical temporality within which it is definedthen th e asymptote and the telos could be said to be the infinite that the hyperbola and bodies attempt to reach but never attain. Through the connections of bodies and asym ptotes, I have attempted to illuminate a terrain from which to attain an understand ing of the epistemologies and ontologies of the body. I positioned the mathematical trope of asymptotes as a metaphor for conceptualizing the ways that bodies are thought about, pres ented, and allowed to be. From the topographic terrain of bodies and math ematical trope of asymptotes, I wish to


18 extend this conceptualization of metaphor and engage the interactions of metaphor and theory or theoretical discourse.


19 Theory and Metaphor In discussions of theory and metaphor, it is important to clarify and note some specific conceptual and terminological definitio ns and connections. First, if I am talking or writing about a theory or theoretical idea, model, construct, and so on, then I need to be cognizant that theories encapsulate and designate a specific set of dynamics and/or relationships that are dependent on an order/system of understanding, meaning, and value, be it multi-variant/ multidimensiona l or linear. These dynamics, relationships, orders, and systems generally rely on a singular focus/ intent and understanding. From within this space or dynamic, my second point emerges. Representations, and the meanings and values attached to them, are often intentionally or unintentionally metaphorical in nature. In Metaphors We Live By, George Lakoff and Mark Johnson note we often experience and understand things in terms of others, wh ich allows us to transfer/ borrow meaning(s) from other realms of interpretation [perception?] (1980). For example, if I wish to study or understand contemplation I could approach it from several angles. As a behavioral psychologist, I could catalog and conceptualize a series or sequence of behaviors that ar e intrinsic to contemplati on. As a sociologist, I could focus on how the contemplation affects the socio-personal relationships between individuals and/or designated groups. As there are a considerable number of available theoretical frameworks, tests, methods, and systems to look at contemplation, a multitude of understandings, definitions, and ar guments could be made; but, at the base


20 of all these lies a system of relation that inte rconnects object, subject, meaning and value. This is where metaphor lives. 16 Metaphor weaves physicality, concept, and value together in contingent understandings. Metaphor, the n, is a means to comprehend, engage and/or formulate an understanding of something thr ough the re-presentation of connections and meanings. And, this is where metaphor can aid in theoretical discussion, in comprehension, and conceptualization. Thr ough this chapter, I will show how my metaphor of the asymptote works to not only undergird theory, but how it can aid in argumentation and comprehension. I begin with a look at performance theoryexplicitly Irving Goffmans dramaturgy and Judith Butlers abject bodies where metaphor or representation works to concep tualize, argue, and define th eoretical constructs while mapping shifts in meaning and to conceptualize the shifting interactive domain of the social world. Next, I focus on D. Haraways Cyborg to highlight how metaphors and the asymptote are not simple re-presentations ; rather, they are cen ters or nexuses of meaning where multiple (often contentious) c onceptualizations and perceptions can meet in a relational paradigm. Finally, I highlight Kathy Fergusons Mobile Subjectivities as a means to conceptualize metaphors and as ymptotes as mutable, multiplicitious 16 The study of this falls under the broad rubric of semioticsthe study of signs. A brief discussion of semiotics will be dealt with in Metaphor as Pedagog ical Tool; however, for a good starting point and background on semiotics see the following works: Browning, F. 1994. The Culture of Desire: Paradox and Perversity in Bay Lives Today. New York, NY: Bay Pressa di scussion of the impacts and interconnections of naming, iconography, and identity. Butler, J. 1993. Bodies That Matter: On the Discursive Limits of Sex. New York, NY: Routledgea discussion of the interactions and affects of language, identity, agency, and socio-political applicability. Dyer, R. 1977. Stereotyping in The Columbia Reader on Lesbian and Gay Men in Media, Society, and Politics. Edited by Gross, L. and Woods, J. D. New York, NY: Columbia University Pr essan examination of language, identity, and social dynamics. Foucault, M. 1980. Two Lectures in Power/Knowledge: Selected Interviews and Other Writings 1972-1977. Edited and Translated by Colin Gordon. New York, NY: Pantheon. 78-109a discussion of the interplay between language, knowledge, and society. Irigaray, L. 1985. This Sex Which Is Not One. Translated by Gillian C. Gill. Ithaca, NY: Corne ll University Pressan examination of language as it relates to legibility, intelligibility, and socio-political dynamics. This is by no means an exhaustive list, these works inform this work however contai n discussions that are beyond the scope of it.


21 conceptions for the comprehension, engageme nt, and discussion of social constructs, while acknowledging the need for situational so lidity and fixity. In the discussions to follow, it must be understood that I approach these works from the position that metaphor (with all its semiotic twists and turns) forms the grounding framework for perception and communication 17 As such, I have conceptualized th e theorists positings as metaphorical in nature; although, the theorists themselv es may or may not agree with this conceptualization. All the worlds a stage, And all the men and wome n merely players: They have their exits and their entrances. 18 This statement illuminates several of the dynamics at play in performance theory. Here, I outline first Goffmans notion of drama turgy because he explicitly utilizes the performance metaphor. I, then, shift to a di scussion of Butlers abject bodies (Butler 1993, Goffman 1959). Performance involves a set of designated statements, behaviors, and socially staged intenti ons. The performance of these occurs within a spacethe socialand in line with the statement above, occurs everywhere. A nd, this performance is bound by rules of conduct, expectation and execution (Goffman 1959). To start, imagine sitting in a theater. 19 On stage, a scene (location) is set, an actor enters, and the show begins. In this space, there are several assumptions the actor(s) and audience agree 17 See Lakoff and Johnsons Metaphors We Live By (Chicago: University of Chicago Press, 1980) for the positing of how this conceptualization of metaphor as foundational dynamic works and its (probable) implications. 18 Shakespeare, W. (1936) As You Like It, in The Complete Works of William Shakespeare : The Cambridge Edition Text edited by William A. Wright. Garden City, New York: Ga rden City Publishing Co., Inc. Act II, vii, 40-43. 19 I am starting with a framework more inline with Goffman to build the conceptual space for Butlers positing.


upon. For the actor(s), (1) the presentation or act occurs within the confines of the stage (generally), (2) the location, time, date and so on are put forth as the world that the actors character inhabits, (3) the events, behaviors, conversations, etc. may (not) extend past the stage 20 (4) the character presented may (not) put forth the individual actors person/self, (5) the reality of the world on stage exists only as long as the actor(s) and the audience continue to accept it as such. For the audience, (1) realitys rules of behavior, language, physics and so on are in suspension for the duration of the play/scene, (2) the existence of the audience may (not) be included in the play/scene 21 (3) the events, behaviors, comments, etc. occur in the world set forth not reality, and (4) the agreement that the play/scene may include or exclude the audience based on rules set by the script. With these points in mind, Goffmans dramaturgy requires only the expansion of the concept from the confines of the theatre to the social world or everyday reality. This seemingly difficult shift, in essence, is quite simple. The differences between Figure 2: The Theatre (above) and Figure 3: The Social World (below) are rather obvious but an explanation will prove helpful. 22 20 This will depend on whether the scene/play uses what is termed open or closed sets, specifically, is the edge of the stage an open space or a closed space/wall. 21 Comments, behaviors, or responses that include the audience in the plays process, plot, events, and so on. These are distinct from the breaking of character where the actor becomes her/himself that is not part of the play/scene.


In the first defining of performance, the space/location and rules were designated as theater based (See Figure 2: The Theatre, above). In this conception, the actor(s) and audience were given specific domains and rules. The actor occupies the stage and the audience watches the show. Similar to Figure 1: Y = 1 / X (pg 3), Figure 2: The Theatre contains all of the concomitant pieces for asymptotes. However, here, rather than bodies, per se, being the focus, a set of relations is posited: Actor-stage, actor-audience, audience seating, and actor/audience-theater. The edge of the stage and audience seating are both explicitly delineated by the curves. The theatre is the overall available space. And, the asymptotes (xand y-axes) are the tacit agreements of actor(s) and audience. In the most general sense, this is the dynamic of the theatre. However, Goffmans dramaturgy, though similar in dynamic, is actually a metaphorical extension of theatrical space into the social world. Goffmans dramaturgy occurs (takes place) in the social world, a world bound by power/discourse, inclusions/exclusions, and legibility/intelligibility. In Figure 3: Social World/Spatial (right), the same lines and curves are shown, however some labels and dynamics are different. The actor is now an individual and the audience is a collection of other individuals in the social world. The dynamics have shifted from the rules of the theatre to the social norms for language, behavior, value, etc. But, where Figure 2: The Theatre presents a model of tacit agreement, Figure 3: The Social World/Spatial re23


24 presents this as an implicit and explicit se t of relationships. The individual (unlike the actor) does not have an exact sc ript to follow; instead, he/she has a fluid system of rules of conduct/behavior, language identification, and so on. Goffman posits that several simultaneous dynamics are active in the social world. One, an individual in the social world is and can only be designated as such for as long as he/she remains legible and intelligible within it. Two, the social world is built through a reiterative set of inclusions and exclusions which simultaneously mark what will and will not be the stuff of the object to which we then refer (Butler, 1993)i .e. what is part of the social world is known through not only what is included but what is excluded as well. Three, the reiterative process, in the social world, is power for it both persists and enforces the norm while at the same time opens the norm to disruption and contestation. And, four, the individual is the actor and the audi ence, in social space, because the social encapsulates both the conception of the i ndividual and the conn ective dynamic(s) between the individual, othe r individuals, and the social world. By extension, the conception of the individual exists both as an internal matrix and as an external space (Butler, 1993). To concentrate on how Goffmans performance metaphor may inform gender analysis, a reconceptua lization of the social world is necessary to shift from Goffmans construct of dramatur gy to Butlers abject bodies. The reconceptualization of the social world requires, not the eclipsing of the physical person by presentation or performan ce, rather, a change in perspective. Specifically, there are three ar eas that need to be highlighted, which I designate as: inclusion/exclusion, power/discourse, and legibility/intelligib ility. As the individual is both in and of the social world, the norms (b e they behavioral, linguistic, emotive, etc)


are at the same time internal and external to the individual. Thus, the conceptualization and value of these becomes central, due to the impact that discourse and power have on the individual and the social world. Therefore, the construction of Figure 3: The Social World-Spatial does not present a fully comprehensible positing of Butlers performativity(as it does for Goffmans dramaturgy), rather Figure 4: The Social World-Conceptual is more functional. In Figure 4 (right), the curves represent the extremity of the positively/negatively valued norms within the social. Specifically, these curves denote the limit of what is legible and intelligible in social space. For example, an individual could identify him/herself as a student, sibling, worker, thief, or murderer and so on because these have an identifiable value and meaning; however this same individual could not identify as banana, hat, sword, etc. in social space. This is due to the conceptualization of what individual means and the terms and concepts available. 22 Therefore, the space outside of the curves denotes and forms the discursive limit for legibility and intelligibility. To be precise, it works as an unchartable region of abjects, a region of abjection 23 which is only understandable as 25 22 I am cognizant of Judith Butlers argumentation about agency, however I am not including here due to space and focus constraints. For a great introduction to her discussion of agency see: Butler, J. (1997) Imitation and Gender Insubordination in The Second Wave: A Reader in Feminist Theory, edited by Linda Nicholson (New York: Routledge, 300-315). 23 Abject/Abjection though related to Butlers performativity is not dealt with here because (1) this discussion is vast and a work in and of itself and (2) it will be discussed in the next chapter as an example of some complex and theoretically difficult topics in teaching feminist theory and how the asymptote metaphor works for pedagogical purposes.


26 that which is beyond social cogency. This as ymptotical relation is important because, whether we focus on Figure 2, 3, or 4, the performativity/ performan ce metaphor (like the asymptote) opens social space and concep tualization to theo retical inquiry and engagement. However, this multiplicitious abi lity of metaphor (and asymptote) is not its only function or value. Metaphor can also act as a nexus or ce nter point for a variety of theoretical and conceptual id eas, dynamics and systems. Metaphors allow for the mapping of shifts or changes in meaning and/or value. They, also, serve as centers for the illumina tion of conceptual/theo retical interconnection and nexuses for multiple dynamics and syst ems of meaning. Donna Haraways Cyborg works to highlight how oppositional construc tions and systems of thought are actually interdependent conceptualizations built of exclusion and elision. Cyborg accomplishes this through its function as metaphor and nexus. This metaphorical action offers a different conceptualization of self, soci ality, and meaning at tribution. Haraways Cyborg is constructed with several ideas and dynamics interconnected: (1) cyborgs are hybrid beings, (2) these hybrids are built of multiple systems of meaning and value, and (3) the hybridization that is the cyborg opens the way for us to move beyond the dualisms in Western tradition. (Haraway, 1985) Bu t, to more fully explain this metaphor as nexus/center, a more specific and cohe sive delving into Haraways concept is essential, for the Cyborg exists betweeni.e it is a third space in a world of pairs. Haraways cyborg exists between and at the boundaries of science fiction (the imaginary or conceptual) and so cial reality (the real or physical)where these fade or meld into each other (1985). It is here that the distinctions between them present as an


optical illusion(s) (1985). 24 This fading/melding/between space(s) is where the cyborg metaphor opens dualities to interrogation and engagement. Haraway points out three major components of social reality (understanding these as gendered): human/ animal, natural (organic)/man-made (machine), and physical/non-physical 25 (1985). These formulations construct a series of bounded distinctions present within the personal, social, and medical/scientific world. This splitting of the world, through these forms, builds and encourages a perception that is hierarchical and absolute in nature. Figure 5: Binaries (right) show how this splitting confines perceptions and conceptions: human distinct from animal, organic from man-made and so on. However, the cyborg is posited to breaking these distinctions. Specifically, because [t]he cyborg is resolutely committed to partiality, irony, intimacy, and perversity, there must be a programmatic rejection of the heroic human myths of Origin and End (Haraway, 1985)meaning that as the distinctions between blur the traditional conceptions of identity become untenable. So, if the boundaries between human and animal, natural and man-made, etc. are fading and/or melding, then the standard constructions and understandings must be changed. Thus, the cyborg as a kind of 27 24 As noted in the first section, Body as an Asymptote, the asymptotes are also optical illusions in that the horizontal and vertical lines are the graphic space for the curves, while simultaneously occupying the space of the invisible asymptotes. 25 Haraway does not see these as distinctly separate, however she does acknowledge these as being perceived this way.


disassembled and reassembled, postmodern collective and personal self sits in the nexus of several conceptual and perceptual dynamics. (Haraway, 1985) The cyborgs occupation of multi-layered dynamics allows for the asymptotic bridging of conceptual frameworks and meanings. Haraways conception of cyborg maps the seemingly disjointed chain of perceptual illusions and simultaneously offers a way out. Haraway highlights the need to give up or move past dualistic, mutually exclusive patterns of conceptualization and organization. Instead of looking for disconnection, explicit differentiation, and/or concrete proof, we should be looking toward and striving for recognition of connection, the ambiguity of differences, and signals/signs. (Haraway, 1985) Haraway offers some rather compelling examples to illuminate problems in dualistic thinkings exclusionary dynamics and how this process elides the relationship between the parts of the binary. By separating human from animal, human-animal from machine, and the physical from the non-physical, Haraway posits that we have limited our ability to conceptualize, comprehend, and change or escape destructive ways of thinking and even being. The cyborg metaphor works as a bridge to do this because it attempts to find a common language in which all resistance to instrumental [social] control disappears and all heterogeneity can be submitted to disassembly, reassembly, investment, and exchange. (Haraway, 1985) But, rather than be caught in another set of binaries, the cyborg 28


29 metaphor follows an asymptotic path. The cyborg occupies no distinct position or location, rather it functions as a nexus fo r different discursive communities, bringing these together in conversation while incor porating, informing, and recontextualizing each. In Figure 6: Cyborgs (above), a few ex amples of what cyborg incorporates, as nexus, are shown as lying be tween the curves. These curves, as noted for Figure 5: Binaries, are the policed bounda ries that the social worl d see as necessary. The Cyborg sits in a position similar to that of asymptotes. And, like asymptotes, instead of explicitly leaving or falling into the binari es, Haraways cyborg functions between, at the edges of, and bridges these offering a ne w way to conceptualize, understand, and be. The cyborg shows how metaphor can function, not just as a map of shifts or simple replacement of concept for concept, but as a nexus or central point for relationships in meaning, value, and understanding. In contrast, Kathy Fergusons Mobile Subjectivities illumina tes how metaphors are not only representations or interconnections rather they can also be mu lti-conceptual, multi-definitional constructs for formulating and weaving fluidic and amorphous theoretical models. Kathy Fergusons Mobile Subjectivities illuminates the cont entious utility of metaphor to conceptualize. Mobile Subj ectivities, though theoretically tied to identification and/or selfhood, highlight how metaphors can function in multiplicity without losing cohesion. Fergusons metaphor is not simply a new representation or a system of connections; it is too concrete and dirty to claim innocence too much inprocess to claim closure, too interdepende nt to claim fixed bounda ries. Unstable but potent, diverse but not incomprehensible mobile subjectivities [can] play across terrainsrefusing stable memberships while insisting on affiliations. (Ferguson, 1993)


The use of metaphor, by Ferguson, encourages theoretical constructs to be about more than epistemology, ontology, or both; her metaphor puts forth a conception of theory that exceeds physical, linguistic, and emotive paradigms without eliding or excluding the personal or social value they may have. Fergusons Mobile Subjectivities (as a reconceptualizing metaphor for self) highlight a topography without concretizing a terrain. This seemingly fluidic solid presents metaphor in its most base and potent form. This conception of the mobile subjectivities (metaphor) enables it to shift from representation to representation and connection to connection without becoming mired in discursive power dynamics; the ability to do this lies within its conceptual and active formulation. By delving into this amorphous construction, it becomes possible to see how Fergusons metaphor maps, without graphing in permanence, a terrain that is generally outside of legibility and intelligibility (as defined by social normativity). Ferguson begins by problematizing the different ways through and in which we conceptualize, understand, and value the solidity of the boundaries between the personal, social, and/or political, interconnectedness and separation, the local and the global, and the singular and the multiple. It has been taught that these are each separate, definable, and discrete concepts. For example, the personal, the social, and the political are conceptualized as separate 30


31 because of the perceived realms they occupy with personal in opposition to social/political. Figure 7: Oppositional Constructs (a bove) highlights the discrete compartmentalization of the dynamics Fer guson problematizes. She posits that to continue this line of understanding excludes the experiential components each has. This seeming mutual exclusivity is based on the conception and va lue placed on discretion, compartmentalization, and opposition. To counter point this natural tendency, Ferguson purposely positions Mobile Subjectivities between, through, and in tandem with these dualistic constructions. The positing of Mobile Subjectivities in flux, affords this metaphor the option of strategic positionality. (Ferguson, 1993) This occurs through the metaphorical action of language, specifically, both terms in her me taphor are fluid in conception. Mobile, in this case, holds the themes of movement/ action, object, and locus in tandem. While subjectivities encourages multiplicity and contextualization. This amorphous fluctuating dynamic allots this metaphor a greater range of interaction and c onnection. To clarify, back in Figure 1: Y=1/X (pg 3), I show curves as well as points along or within them. This visualization shows curves, segments of these, and points. The mutative and connective dynamic contained therein is the starting point of the metaphor for Ferguson. In the definition Ferguson gives for Mobile Subjectivities, she illuminates how the conceptualization and value of constructs need not be solid and fixed. Rather, she seems to advocate a dynamic and position of semi-permanence. To accomplish this, she puts forth four contextual and interactive formulations: temporality, relationship, irony, and ambiguity. Ferguson writes:


Mobile subjectivities are temporal, moving across and along axes of power (which are themselves in motion) without fully residing in them. They are relational, produced through shifting yet enduring encounters and connection, never fully captured by them. They are ambiguous: messy and multiple, unstable but persevering. They are ironic, attentive to the manyness of things. They respect the local, tend toward the specific, but without eliminating the cosmopolitan. They are politically difficult in their refusal to stick consistently to one stable identify claim; yet they are politically advantageous because they are less pressed to police their boundaries, more able to negotiate respectfully with contentious others. (Ferguson, 1993) This positing locates mobile subjectivities between, across, and within the dualities for it relies on context, content, and intent. This allows Fergusons metaphor to be a fluidic solid with multiple singularities. What this means is that the Mobile Subjectivities metaphor occupies a range of locations and interacts with many dynamics simultaneously. In Figure 8: Mobile Subjectivities (right), Fergusons metaphor is both curve and asymptote. Mobile subjectivities can enter legibility and intelligibility (curve and points) but does not require these (asymptote) to continue to act. This functionality of Fergusons Mobile Subjectivities allows her metaphor to remain metaphorical (fluid, dynamic, unstable) without giving up form and action. Specifically, Mobile Subjectivities exists in both interstitial and emergent spaces allowing it to enter into or be part of the curves, escape from and contest these same positions (asymptotes), and work to bridge/connect the curves (bridging the curves and/or eliding the asymptotes). 32


33 Through this chapter, I have highlighted the interactive nature of metaphor in connection with theoretical conc epts. Metaphor is oft times s een as a replacement for or elision of some thing/concept/dynamic. Inst ead, metaphors offer a different presentation, view, or formulation to aid in comprehensi on. Perfromance theory utilizes metaphor as a way to contextualize the shifting and interact ive domain of the social world. Haraways Cyborg posits metaphor as a nexus or center, where multiple (often contentious) conceptualizations and formulations can meet in a relational paradigm. And, Fergusons Mobile Subjectivities encourages the am orphous and mutable essence of metaphors, while acknowledging the need for solidity and fixity within specific locations, dynamics, and systems. Through, these I have attempte d to show how my asymptote works, not only to map argumentation, but as a metaphor capable of many things, yet not explicitly tied to any. This formulation of the asymptote metaphor highlights the functionality of metaphors in general; and, at the same ti me, encourages their continued use for theoretical and conceptual purposes. And, through this chapter, I have implicitly illuminated another function of my asymptotes metaphor: metaphor as explanation or for explanatory purposes. However, the asymptot es metaphor can also be utilized as a pedagogical tool.


34 Metaphor as Pedagogical Tool Ive read this three times and I just dont get it. This is a statement I have heard innumerable times. And, I think: how am I going to guide this student to or aid him/her in finding an answer(s)? In many cases, I find that the transition from the concepts written in articles, books, etc. to th e understanding or incorporating of this information into the mind is not always an easy one. Further, it is oft times not a question of comprehension or ability, rather one of c onnection and bridging. So, findi ng the signposts and/or map(s) of the conceptual/theoretical framework or argu ment is essential. Now, this is rarely a singular or simple task. Instead, multiple atte mpts are more common. Further, there tends to be metaphor(s) or sets of metaphorical connections that work as both signpost and map. I continually notice that the metaphors that work best (for me) are those that include and utilize conceptual, visual and performative dynamics. Jyl Lynn Feldman argues, good pedagogy, is up close and personal, rather than intimidating and detached and that the bounda ries between personal space and national state must be collapsed. (2001) In Never a dull moment: Teaching and the Art of Performance-Feminism Takes Center Stage she posits a performative pedagogy, formulated of visual, visceral, and interactive components. Performative pedagogy is utilized and presented as both t ool and style. It consists of an equilateral triangle of three parts: spectacle, spectator, and spect acular. (2001) She argues that we need to reconceptualize the students as spectators and the professor as performer/ producer of


35 spectacle (2001). Then everything, from normal discussions to explosions, disruptions, and/or departures becomes a spectacular, pedagogical fireworks displayan event to watch, appreciate, applaud in all its colorful, insightful splendor. (2001) She is arguing that it is not enough to change the way we teachi.e. find a new approach rather, we need to change the way we think about teaching and what it means to teach. bell hooks extends this rec onceptualization of the e ducational paradigm through her argument for an engaged pedagogy (1994). In Teaching to Transgress: Education as the Practice of Freedom she posits engaged pedagogy as means to re-integrate and encourage critical thinking, responsibility, and participation in the classroom and pedagogical paradigm. hooks argues that the ol d educational paradigm build of/on the separation of mind and body, the disconnection of theory and practice, and the absence of Eros 26 is no longer working. Ideally, educati on should be a place where the need for diverse teaching methods and styl es would be valued, encourag ed, [and] seen as essential to learning. (hooks, 1994) To break away from the old normative process, hooks points out that without the capacity to think critically a bout our selves and our lives, none of us would be able to move forward, to change, to grow. (1994) Furthe r, there should be a celebration, a sharing, a passionate exchange of ideas. Moreover, as we share this passion of ideas, learning, and engagement, students be gin to respond and this response (positive and/or negative) draws the students inthe y begin to participate. Through this participation, students begin to feel, and maybe even see themse lves as part of a learning community. And, as their attachments to and confidence in the learning community grows, they begin to find a sense of mutual responsibility for its growth and development. 26 Erospassion and lovea force that provides an epistemological ground informing how we know what we know and invigorating class discussion and exciting the critical imagination (hooks, 1993).


36 By extension, as the students become more engaged and involved, the classroom becomes a field of possibility. (hooks 1994) Like Feldman, hooks notes that any pedagogical approach should engage and encourage the students whether we view education in terms of theatrical interaction and display or a passionate engagement of critical thinking. Both hooks and Feldman, agr ee that all pedagogical approaches need a multiplicity of tools so that the classroom dyna mic does not stagnate. Within this context, I put forth the asymptotes metaphor as a new pedagogical tool for its potential to encourage critical thinking, participation, and discussion. To explain, detail, and highlight the asymptotes metaphor as pedagogical t ool, I will focus on three commonly difficult concepts for students in Wo mens Studies and Feminist Theory classrooms: gender, semiotics, and abject. This is by no means an exhaustive list of my own utilization of the asymptotes metaphor. I have, also, used it to te ach and engage concepts as varied as race/ ethnicity, class, elite/ subaltern, self/ other, and so on. Here, I focus on Gender, semiotics and abject for their illustrative and explanatory value. When I first began teaching and attempte d to explain that gender is a social construct or set of socially normative understandings, I would look out at a classroom of blank faces. I tried lists on paper, on the boa rd. I tried discussion. I even tried free-flow brainstorming. These did not seem to be working, because as the semester(s) progressed gender would need to be explained again a nd again. However, the first time I tried the asymptotes metaphor it worked, meaning no more semester-long reiterations of what gender is and what it is not What follows is a discussion on how the asymptotes metaphor works as a pedagogical tool for explaining gender.


I generally begin with a series of seemingly simple questions. What is your sex? What is your gender? How do you know? This last question is where the greatest amount of discussion and the crux of the pedagogical action occurs. After several minutes of scrambling around the board, while either students or myself try to get all the responses up, I ask if everything on the board relates to one or more than one topic and what is the topic(s). In most cases, I end up with two lists: sex and gender. At this point, I draw a figure on the board (see Figure 1: Y=1/X, pg 3). This figure becomes the background for the discussion to follow, as it does in the classroom. In its first incarnation, the figure is blank and the general mathematic rules of asymptotes are defined (see asymptote discussion pg 3-4 and footnotes 1,5,6, and 7). Now, that these have been set, I can move on to labels in the figure: specifically, sex and gender (see Figure 9: Sex, left, and Figure 10: Gender, below). I have the class subdivide the lists into categories. For example, sex may contain biology, genetics, physical or bodily differences and so on. Once the subtopics have been formulated, these are also placed in the figure under the related major topic. The question now becomes: how distinct or definitive are these topics? And, how do these topics interrelate? What happens is a shifting into either mathematic or logic based relations: A + B = C or If A, then B, etc. These figures (Figure 9: Sex and Figure 10: Gender) are the foundational conceptions and assumptions about gender and sex that are 37


problematized and interrogated to encourage the students to re-interpret and engage these topics. I focus on sex (Figure 9: Sex) first because this is where many students assume facts and/or hard and fast answers about sex are or come into existence. In Figure 9: Sex (above), I highlight how there is a general conception of only two options for sexing the body. Female and male are conceptualized as separate and distinct categories. I, then, have the students return to the original lists made (prior to the figures) and find and input the information they see or comprehend as belonging to the male sex and female sex. Following this, I begin to question and problematize the distinctions that have been made. For example, what about xx-males or xy-females? Or what about the children born inter-sexed 27 ? After problematizing these distinctions, the students begin to see that information they believed to be concretely contained within the curves, actually bleeds over into a middle space between them. What this does is destabilize the grounding concreteness that sex is assumed to be, because if a range of hormones, chromosomes, and bodies are available, then how can sex by divided into only two groups. In the beginning of the discussion of sex, the asymptotes (xand yaxes) are conceptualized by students as the frames and boundaries 38 27 I generally give a brief overview of the distinctions between intersexed and hermaphrodite. This discussion however is outside the scope of this work. For the full discussion of this topic see Anne Fausto-Sterlings Sexing the Body: Gender Politics and the Construction of Sexuality. New York: Basic Books, 2000.


over which sex cannot cross. However, by the end, these same asymptotes, actually illuminate the range of sex combinations (genitals, chromosomes, hormones, etc) possible. From this figure (Figure 9: Sex), I move to the gender figure, which is a reiteration of Figure 9: Sex but with gender as the focus. And, I begin the process again. However, because the stage has been set for a new conceptualization, I have the students either come up to the board or get in groups and have them fill in the figure. In this new figure, Male and Female or Masculinity and Femininity are in the same locations as those present in the sex figure (Figure 9, above). The general types of information that the students come up with in regards to gender are located in the upper right and lower left respectively. The distinction here however is that the students are thinking of the asymptotes and categories in more than one way simultaneously. They look to find these things that make female and male distinct, but they also look for any that can cross over and bridge the space between. The twist for the student comes in when they begin to realize and conceptualize gender, and then sex, as being built of societal and/or social frames of reference and rules. So that when I combine to the figures (revised as Figure 11: Sex and Gender, left), the distinctions and connections between the categories of sex and gender actually work to re-conceptualize them as mutually exclusive and interconnected at the same time, through the interaction of the curves and asymptotes of the figure. When first asked about their 39


40 sex and gender, many students gave the same answer without cons ciously understanding whymeaning that for them sex and gender we re the same concept, just a different word. However, after the separate but relate d discussions of sex and gender, the students tend to see these as separate. The final ques tion I ask is what allows this seemingly incongruent conception of sex and gender as both connected or same and separate or distinct? The response generally is society or social norms. Thus, in the end, the students realize that the curves function to show different frames of reference for sex and/or gender, while the asymptotes are the overall societal framework that designate the conceptualization of eachi.e. gender and sex are constructed through society. This conceptualization of asymptotes is rather straightforward due to the tangible or physical nature of sex and gender, however the asymptotes metaphor also works for less tangible, more conceptual topics like semiotics. Semiotics, the general philosophical theory and study of signs and symbols within artificial and natural languages, is approached differently depending on whether it is part of discussion in an introductory cour se in Womens Studies or engagement and argumentation in a more specialized feminist theory course. However, in both situations, a general overview occurs and this is wh at I will focus on. While teaching, semiotics generally comes to the fore once the first sets of (academically focused) writing assignments have been turned in. In many cases, the subsequent class is, at least partially, devoted to the importance of language and linguistic choice. I draw a rectangle on the board (longer sides vertical, shorter side horizontal). What have I just drawn? A rectangle. Then, I draw a stick figure at the upper central por tion. What is this? I receive several answers: It s a door, its a bathroom, a door to the mens restroom, and


41 so on. Following, I ask, How do you know? Af ter, being bombarded with answers, I have them contemplate how the connection between this symbol/sign and the physical location or space is made. To clarify my poi nt, I draw and shade in a triangle over the stick figure with the apex at the conjunction of the torso and arms and base just past the conjunction of the legs. Is this the same figure?, No, its the ladies, womens bathroom. Generally, the students are scra tching their heads and I write a simple equation on the board: symbol one (stick figu re) = mens bathroom. Is this a valid representation of how we think of this symbol? Returning to the drawing, I erase the figure and write in Bathroom and ask if the meaning has changed and how. Now that the frame is set, I can finall y begin the discussion of semiotics. What occurs is a positioning of the problem as assumed meaning(s) from words or symbols. To explain this, I change the e quation or relationship of the symbol and meaning and the word and concept, with the symbol/word over a line and the meaning/concept underneath. It is assumed or accepted that th ere is a concrete connection between the words/symbols we use or see, without thin king about the impact this might have on comprehension and meaning. These assumptions become very important in speaking and writing because we can end up with unintende d meanings and concepts being included. Moreover, the arbitrariness of these assume d concrete connections is eclipsed. For example, the term gay has had multiple meaning and many different levels of value. Instead of compiling a list per se, I draw a figure on the board (see Figure 12: Gay, below). In this figure, I add the term gay inside one curve and a few meanings in the other. Oft times, it is assumed that a term can just be used and others will know what is meant. However, think about the different ways that metaphors, double entendres,


oxymorons, etc. are used. In these cases, multiple meanings are intended. But, this same doubling or multiplying of meaning can and does occur with other words. Returning to the figure, gay can be utilized in speech and writing in a number of different ways and this choice, no matter how much we disagree, is always arbitrary. For example, looking at the lines in the center of Figure 12: Gay (right), which individual or group of meaning(s) can or could be used? To clarify, imagine a group of friends is sitting together and one of them says, Im gay. Emotive and psychological reactions aside, what is this individual saying? Looking at the figure, there are several different meanings to choose from and we must assume and infer which one the individual has chosen. For example, the line in the upper left (see Figure 12: Gay, above), could be seen as representative of the former statement. To look at it in a different light, what if the statement was thats gay? Here, again, an inference and connection occurs. But, when speaking, there are many other bits and types of information to aid us in making the appropriate connections. In writing, all we have are the words on the page and their relationship(s) to each other. What becomes important is the realization that a term cannot ever completely capture the object or concept it attempts to name. 28 Another figure is used to illustrate this point (see Figure 13: Signs, below). 42 28 Within Philosophy, this dynamic has an extremely long history. However, an overview or review of this is not available due to space constraints. Some excellent starting sources are Elizabeth Grosz Jacques Lacan: A Feminist Introduction (London: Routledge, 1990) and Ferdinand de Saussure Course in General


This figure gives a representation to the interactions between names/terms and objects/concepts. The names/terms or signifiers are contained in one curve and the objects/concepts or signifieds are contained in another. 29 For comprehension, the signifier curve contains the word restroom and the signified curve a couple of different definitions. The asymptotes (xand yaxes) and the space between the curves represents the gulf of legibility and intelligibility, the space of arbitrary choice. What this figure exemplifies is the inability of signifiers (the bathroom) to ever, in any exactness, concretely/permanently connect to signifieds (conception of bathroom) because the name/term is never the same thing as the object/concept to which it refers. And, because there is not an exacting relationship between these, language and linguistic choices are always open for disruption and misinterpretation. Semiotics, or the study of signs, reminds us that language is relational, metaphorical, and conceptually conscientious. Specifically, this metaphorical relation is precisely the dynamic that Figures 12 and 13 highlight via the asymptotes. 43 Linguistics in Critical Theory Since 1965, edited by Hazard Adams and Leroy Searle (Tallahassee: Florida State University Press, 1986). 29 My understanding and conceptualization of signs and semiotics comes from Elizabeth Grosz Jacques Lacan: A Feminist Introduction (Condon: Routledge, 1990) and class discussion in Dr. Carolyn DiPalmas Advanced Feminist Theory course at the University of South Florida


44 Additionally, the asymptotes metaphor al so works to map the space of arbitrary choice or gulf in legibility and intelligibility by working as explanation and conceptualization of abjects or process of abjection. Teaching and discussing the concept of abject(s) and the process of abjection is a study in the act of refe rence. As abject and abjection are quite conceptually difficult to understand, it is often necessary to reference previous class and (as is the cas e here) written discussions. Furthe r, it is easier to look at abject and abjection as separate topics/concep ts and then pull them together than to try and explain them in tandem. As often happens the concept of abjects comes to the fore when students either hear or read the term and the hunt for frames of reference begins. To discuss abjection, I always try to retu rn to a moment in class or a passage in the readings that the students have either read or at least remember. Oft times, this is the sex/gender discussions, where questions of the knowing of sex/gender are still problematic. I redraw the figures for sex a nd gender (see Figure 9: Sex and Figure 10: Gender). After doing this, it becomes important to have the students reiterate the previous framing of these figures, give or have them define some specific terms, and have the dynamics and terms re-conceptualized to ve rify understanding. Two terms of importance here are legible and intelligible And, to aid in un derstanding, I ask th e students to label and/or note each term and dynamic in the figure, and to identify what is the overall frame of reference or lens of con ceptualization. For Figure 9: Sex (pg.37), the overall frame is science or medical discourse with each term (inside or outside the curves) being legible and intelligible; while for Figure 10: Gender ( pg.38), the frame is social normativity with all the terms again being legible and intelligib le. To begin the process of understanding abjection, I have the students relabel the fr ame for sex as social space, and ask If the


frame has changed from science or medical discourse to social space, are all the same terms or topics still readable and knowable? And, if not, which one(s) have changed and why? Several reactions and events generally occur. One, chromosomes and hormones become illegible because in social space they cannot be seen. Two, a debate ensues as to whether or not genitals should be listed as illegible and/or unintelligible or if they should be included in secondary sex characteristics as they are referential points for complementary genitals. Three, the division or distinction between sex and gender starts to collapse or is, at least, up for serious debate again. And, finally the concept of sex in and of itself comes under fire because it seems to be disappearing. After a few minutes of discussion, debate, and anxiety, I redraw the sex and gender figure (See Figure 11: Sex & Gender, pg.39) and ask the students to remember the discussion where we talked about gender and sex as both being socially constructed. I do this to reiterate the problem with seeing sex or gender as fixed. Further, that the frame of reference or lens of conceptualization that we choose affects what is available to be seen and known. To further explain, I draw a new figure on the board. I start with the standard curves and lines that have been used previously, inside each curve I put the terms parents and parenthood, with the edges of the curves and the asymptotes designating the limit(s) of who are parent, what parenthood entails, and so on, with non-/unfit parents outside the curves. I ask, How these are learned or understood comes from 45


46 where?, with general responses being par ents/experience, community, culture, society, religion, etc. With these in mind, I ask, Where would homosexual pa rents fit into this figure?, knowing, of course, that this w ill cause discussion and debate. After a few seconds, I ask them to calm down and see if they can understand what I am adding to the figure. The new/revised figure (Figure 14: Abject ion, right) has 2 new curves added and on the horizontal line (x-axis or asymptote) I have written homosexual parents 30 In the brief discussion and debate that ensues th ere are many sides, however there are two general camps and each of these will have an impact on how the figure is conceptualized and understood. As a general view, in the left side of the figure the curve moves up to include homosexual parents, while the righ t side curve moves away from homosexual parents. This distinction is where the idea of homosexual pa rents can be seen as being included and excluded. Now, I turn attention to the terms put forth earlier. I ask, has the term or concept of homosexual parents always been around or in use? with the answer generally being no. Then in that case, here was a time when the idea and concept of homosexual parents along with the term did not exist? Y es. So, returning to the figure, the right side could represent a time when homosexual parents was outside of knowing and the left side could represent pr esent time when homosexual parents as term and concept are known. Specifically, then, the discussion and debate was centered around whether or not homosexual parents s hould be included or excluded in/from parents and parenthood, meaning one side encourages homosexual parents continuing 30 I have placed homosexual parents on the horizontal line because of the argumentation of previously abject, currently legible and intelligible gay and/or lesbian parent. This will be more fully explained as I move through the rest of the discussion.


to be legible and intelligible while the other encourages or pushes for illegibility and unintelligibility. Abjection, then, is the conscious or unconscious desire/intent to remove or push a concept, term, idea, etc. from being known and understood. This does not mean that the concept, idea, or in this case persons do not exist, rather that there would be no way to conceptualize and comprehend it/them. To hone this down to what abject, as a term, means then I return to the blank curves and lines and inside each curve write the terms rapist and rape (see Figure 15: Abject, below). I ask, What comes to mind when you see the words? The most common response is men. Does this mean that only men are rapists? The general responses range from adamant yes to qualified yes and nos to adamant nos. Does anyone know the current legal definition of rape in Florida? In a few cases, I may have one or two students know; however, more often, the students dont know the current legal definition. The current legal definition is Sexual battery is the oral, anal, or vaginal penetration by, or union with, the sexual organ or another or the anal or vaginal penetration of another by any other object. 31 What this means then, in relation to this figure, is that anyone over the age of consent (which in Florida is sixteen) can be charged with rape. However, 47 31 Florida Statutes: Title XLVI (Crimes) Ch. 775-896. Chapter 794 (Sexual Battery).


48 this is only the case because the law changed thrity-plus years ago 32 prior to that only men could be charged with and only if it involved sexual penetration by the man on a woman against her will or a child because th ey could not consent. Therefore, under the old law, women could not be charged with rape per se, because of the way it was worded. Only men could be rapists because women were abject under the lawthere was no way to conceptualize women as perpetrators of rape. However, women have entered intelligibility and legibility under the current law. So, in the figure (Figure 15: Abject, above), under the old law, women would be outside the curves, outside the legal definition of rape. The edge of the curves and the xand yaxes (asymptotes) then are the transition point between what is abject and wh at is legible and intelligible under that law. Therefore, abjects are both those thin gs/ideas/concepts be yond legibility and intelligibility and those that disappear from the seen and known through the process of abjection. Through this section, I have attempted to highlight how the asymptotes metaphor works as a pedagogical tool. As a pedagogical tool, the asymptotes metaphor incorporates many of the points that Feldman and hooks posit as essential to pedagogynamely interaction, engagement, and cr itical thinking. I present the asymptotes metaphor, not as a replacement for other pedagogica l tools, rather as a new t ool that both highlights the variability and functionality of visual and perceptual meta phors as pedagogical tools and how this specific metaphor can be utilized to reconceptualize, engage, and teach. 32 The official date change to th e current statute was October 1, 19 72. Florida Law 72-724, sect. 7.


49 Metaphors and Asymptotes In this thesis, I put forth the mathematic al trope of asymptotes as both metaphor and pedagogical tool. In rec onceptualizing asymptotes out of their mathematical frame and into theoretical argumentation, I opened them to decidedly different implicit and explicit uses than thos e contained within mathematical di sciplines. The basic implicit use I wished to put forward was to encourage and illustrate the valu e and importance of interdisciplinary dialogue and utilization. My explicit use(s) of asymptotes was as metaphor and pedagogical tool. To do this, I im plemented asymptotes as a means to map and highlight how the body enters into and exist as both epistemological and ontological construct. I did this through the paralleling of asymptotes and feminist arguments about how bodies come into being and how they are known, with specific focus abject bodies, (en)framed bodies, and te los bodies/ teleological conceptions of the body. To recast this formulation of asympt otes as metaphor, I illuminated how metaphors, my own included, make theore tical positing and argumentation possible through their use as signposts and maps fo r comprehending and s ituating th eoretical discourse. I focused on how metaphor aids in theoretical argumentation as well as the ways that metaphor aids in the follo wing (conceptualizing) and comprehending (mapping) of this argumentation. I chose thre e well-known theorist-scholars from within the feminist canon: Judith Butler, Donna Haraway, and Kathy Ferguson. I utilized


50 metaphor and asymptotes to aid in outlini ng Butlers performance as a theoretical metaphor and as a means to map and understand her positing and argumentation. Haraways cyborg was illuminated as conceptu alization of metaphor as nexus or center point for the cross-conceptualization and interconnection of multiple dynamics and systems. In highlighting Fergusons mobile subjectivities, metaphor was positioned as a fluidic, situationally solid construct for the purposes of comprehension and utility within varying systems of di scourse and action. From this space of metaphor as tool, I shifted to pedagogical space to illustrate metaphors value in educational dynamics. Metaphor as pedagogical tool is not ne w; rather, I have put forward my asymptotes metaphor as a new tool for the co nceptualization of theo retical ideas as well as a means for the comprehension and utilizati on of conceptually diffi cult constructs and relations. Specifically, I high lighted how metaphor, particularly my own, worked to outline, explain, and resituate critical thought, engagement, and participation by encouraging and aiding students in the educational process. My hope was to show that the asymptotes metaphor could be utilized as a means to teach both concrete and amorphous theoretical concepts. To this end, I outlined how I have used the asymptotes metaphor to teach topics as varied as sex and gender to semiotics to the concept of abjects. My wish is that my asymptotes me taphor, along with other visual and perceptual metaphors, may be seen as viable pedagogi cal tool to revitalize and engage both educators and students.


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