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Abstract

Numerical power, typically understood as strength of certainty in statistics or as a functional property in mathematical contexts, takes on alternative semiotic meanings when applied discursively in contested, lived spaces. This paper discusses the political instrumentality of numerical descriptors for particular types of cultural studies projects, a discipline with a decidedly political foundation which is dedicated to uncovering and revealing naturalized power structures. Beginning with a discussion of why quantitative methods are historically ostracized from cultural studies, a traditionally qualitative discipline, this paper then addresses three ways data analysis can benefit cultural studies. These three roles include the contribution of magnitude, the construction of models as metaphor, and the selection of dialogic sites for critical qualitative intervention. To demonstrate this tri-parte schema which complements various methodologies, this paper reimagines several canonical pieces from political economy (Gibson), psychoanalysis (Lacan), ethnography (Ma and Cheng; Geertz), and digital technologies (Deuze). Ultimately, these are potential areas to expand the rhetorical force and dialectic appeal of some projects, but it is not for every project; these three roles are always situationally contingent.

Cultural Studies is a discipline invested in high-stakes situations. Whether it be issues of race, class, or gender, in settings online or off, local or global, this field handles the cultural gloss which covers how political, material, and affective resources are controlled. By taking a broad approach, Cultural Studies (CS) analyzes the norms and institutions of power to discover systemic issues underlying all daily activity. This task, however, is not always welcomed by either the academy or society. By offering mechanisms of critique, CS is frequently vilified as overly critical or, in the worst cases, simply ignored as an overly subjective activity. This is a major disservice to the positive contributions which critical perspectives have brought and will continue to bring to discussions of society and change.

This paper seeks to describe one way to modify this overcast and despondent view of Cultural Studies while also preserving its political edge. CS is in direct competition for a space to exist along the entire spectrum of its systemic needs for affective, attentive, political, and material resources. This competition is frequently discussed as a crisis, as CS departments in America continue to shrink in size. Similar to any perspective placed in competition with other viewpoints, individuals responding to criticism attempt to delegitimize external critiques by denouncing the outsider’s methods and discursive appeals. In the case of most humanities’ scholarship, other fields have defined an “objectivity” barrier which humanities’ scholars cannot or chose not, for philosophically valid reasons, to overcome. Rhetorician and feminist scholar Celeste Condit describes this process in her text How Bad Science Stays That Way. From her personal experience, “the definition of worthy critique as requiring accompaniment by scientific data insures that only [others] working in the area can publish criticism… All other analytic critique of research, and therefore all critique by humanists, social scientists, and critical theorists, is thereby ruled out of consideration… as merely ideological” (1996, 93). In response to this discursive barrier to “objective” forums, many scholars have opted to continue their own discussions in separate delimited spaces. However, CS is a political enterprise, frequently engaged in progressive political activism. For this reason, I believe CS is poised to become directly engaged in this dialectic by surmounting the “objectivity” barrier.

This move is a strategic and rhetorical one. I propose the utilization of quantifiable data or numerical descriptors in particular types of Cultural Studies’ projects to give them a political edge. The remainder of this paper will describe the descriptive and qualitative appeals of numbers as a discursive product, not a purely mathematical object, for several common CS methodologies. A brief discussion of the philosophy underlying quantitative and qualitative data and associated theoretical orientations will explain why numbers as discourse is necessary to avoid contradiction. Next, a three part schema for the proposed numerical approach will be outlined, including issues of magnitude, metaphor, and critical intervention. Finally, a series of canonical and contemporary CS texts will be re-imagined under this paradigm, revealing both promises for growth and pitfalls to be avoided.

The eminent sociologists Glassner and Moreno provide a grounding discussion of the origin of the “quantitative” vs. “qualitative” divide for human sciences. These various approaches to social data are actually linked to the ontological and epistemological assumptions of various theoretical orientations, and those assumptions mean that certain approaches are sometimes diametrically opposed and irreducible to a common ground. In an attempt at brevity, I will summarize their discussion here. The use of quantitative data actually takes two different forms: the first is when math is actually a quality, that is, as Sociologist May Brodbeck explains, “a quantity is a quantity of something. In particular, it is a quantity of a ‘quality,’ that is, of a descriptive property” (573); (in Glassner and Moreno, 1989, 10). The other use of quantity is when quantity is an object in its own right; the study of quantity as object is what we know as “pure” mathematics. The philosophical thread which connects math –the fields which study “pure” systems, or those disconnected from any empirical orientation– to other quantitative methods places them off limits for qualitative research. If the quantity as object is used with qualitative data, it becomes inappropriate methodological liberalism. Glassner and Moreno describe this as, “the Fallacy of Ameliorative Dualism (FAD), committed by one wishing to admit to the canon of some field of study theses without obvious systematic association to one another in an attempt to satisfy advocates on both sides” (1989, 8) [emphasis added]. FAD projects abuse the various types of data, drawing false conclusions through inappropriate treatments because, on the most rudimentary level, quantities as objects do not exist in our universe. Treating data from our empirical world with tools designed for the mathematical universe creates unintelligible results. Likewise, mathematical data created to be an object does not behave in expected ways when subjected to our empirically grounded methods.

Therefore, Glassner and Moreno suggest only using qualitative mathematics (quantities which describe qualities) when using qualitative methods. This means that the quantitative data must first and foremost be a discursive object, existing in the same realm as other qualities expressed in language; “At the data analysis stage as well, words are not eliminated or converted into other symbols, but organized by the addition of analytic marginalia (more words)” (Ibid, 7). The three part schema suggested by this work follows this philosophical condition. My three suggested roles of mathematics within Cultural Studies comply with the demands of methodological rigor while also using the language and tools that other fields find compelling. Understood this way, quantification is a process of framing. As sociologist Charles Smith explains, “quantification is part of a particular way of defining the situation. It cannot consequently be understood in and of itself, but must rather by put in the context of multiple interpretive frames of reference” (In Glassner and Moreno, 1989, 32). As part of a holistic approach, the inclusion of quantification is a strategic, discursive move with the potential to enhance the political efficacy of the field.

Data analysis is not unheard of in CS today as an elegant way to demonstrate the magnitude of a project. Particularly in technology research, meta-data is easily gathered and utilized to bracket a project and legitimize the analytic conclusions. However, that is not the only place where such information is appealing. Most cultural studies projects can use some measures of magnitude to enforce the importance of their research. Circulation numbers reveal access and consumption of media objects. Attendance can reveal the place of institutions across a social group. Demographic information can punctuation our understandings of the ways class, gender, and race are used as exclusionary barriers. The magnitude descriptor, in particular, is not prone to problems of data contradiction because its role is to contextualize. So even in the contingent situations where scholars perform dense and deep qualitative analyses, a place where numerical information could be essentialist or distracting, a contextualizing remark does not detract from the project’s goals.

Magnitude or context is usually where data’s relevance ends for most Cultural Studies scholars, however, there are other discursive possibilities for quantitative data and analytics. The next involves metaphor. Critical understanding is a learned literacy, requiring its own knowledge of theory, practice, and language. Cultural studies has a rich history of complicated theory underlying and infusing its language, and, without the proper educational background, it is utterly perplexing. The use of mathematical principles and concepts as structural metaphors expands the rhetorical appeal and explanatory capacity of CS explanations. This technique also fosters benefits for those scholars who engage with mathematical concepts; these activities assist in creating a forum for shared cross-disciplinary discussion and provide new ways to conceptualize and describe cultural phenomena. This process of technical language qua metaphor and adoption by other fields is most famously exemplified by Albert Einstein’s theory of relativity. Relativity is a complicated technical concept which explains how the measure of various quantities are dependent on the velocity of the observer, and yet this concept was embraced widely outside of physics to great effect. Similar mathematical language could be the key to broader circulation of Cultural Studies work and interpretations of society.

The final mode of engagement with numbers accesses models and statistical testing as both an analytic method and as a crucial political part of the project. This is to engage critically with particular methods which are responsible for institutionalized silences and what Condit describes as “bad science.” Silences occur when, “a set of research practices produce, in a sustained fashion, conclusions that are insufficiently rich to account for the material phenomenon under investigation in terms of the resources available in the linguistic code and with the available scientific resources” (Condit, 1996, 87). As she explains, truth occurs in degrees, and certain projects are unethical because they fail to provide enough truth in their essentialized models; bad science disenfranchises and disempowers individuals in their daily lives.

If Cultural Studies engages with these methods fully and acquires different results, it reveals the ideologically infused research process for those claiming “objective” study of social phenomena. The best example of this is the critique of the normal curve (a probability density function) as a defining standard for what is “normal” (a moral valuation) in society. The normal curve informs parametric statistical tests as a mathematical concept, yet was adopted without reflection to describe large groups of people. By taking a model which works for certain substantive systems which are known (e.g. the growth rate of organisms follows a normal curve), and then assuming it applies to all human behavior, researchers make grave mistakes with astounding real world consequences (Ziliak & McCloskey, 2008).[1] In fact, the No Child Left Behind policy was initiated in the United States on the basis of research which assumed learning follows a normal pattern, and therefore students could be compared against this curve to determine success or failure. This policy caused significant and long term harm to the education of millions of American youth. Stephanie Grey, in her article, The Statistical War on Equality: Visions of American Virtuosity in The Bell Curve, performs a statistical analysis from a critical perspective, revealing that the un-reflexive use of parametric statistics creates racist, classist, and sexist policies. By utilizing the technology and instruments of the original project in her critical research, Grey engaged a larger audience. This type of vital appraisal is rare, yet, since it intersects with the representational issues theorized by CS and is tied to how discourse shapes materiality, there is room for CS to grow into this arena of analysis. The use of data or statistical analytics in new cultural research projects also opens other projects for interrogation, revealing the contingent nature of “objective” social facts. In the current climate of increased STEM funding while the humanities are downsized, it is especially pertinent and crucial to address these problems and convince a large section of the Academy of the dangers of poorly performed analytics.

The three roles for mathematical inclusion –magnitude, metaphor, and critical intervention– must be considered alongside dominant methodologies in CS. The final section considers approaches to political economy, psychoanalysis, ethnography, and digital technologies and cultures to explore issues which may arise from the bridging of the quantitative-qualitative divide.

The first research type, political economy, is a lens which places several expectations on the cultural studies scholar. Towards the end of the last century, Media and Communication’s expert Nicholas Garnham wrote an indictment against what he saw as a diminishing interest in economic determinations of cultural production. In his piece, he claims that the true key to unlocking dominant structures is class (as opposed to race and/or gender), and that class inequality is formed through capitalist modes of production (Garnham, 1995, 70). As an exemplar of this approach, Timothy Gibson researched the City Living, DC Style campaign to attract suburban dwellers to the newly developed urban center. Through his project, Gibson discovered that DC’s campaign was actually a classist project because the discourse was directed at upper/ upper-middle class suburbanites through encoded messages. His method involved collecting an ecology of text fragments, “a loosely bound collection… a complex intertextuality [of] ‘the brand,’” which he interpreted for the reader (Gibson, 2005, 265). After he collected a coherent and wide swathe of these fragments, he analyzed them using semiotics, uncovering themes and messages. He also supplemented his article with several interviews with local experts and by observing a living DC expo.

The first way to improve Gibson’s piece through implementing mathematical properties is the inclusion of summary mathematical information. Numerical qualities are succinct. Even though Gibson’s methodology was a semiotic approach, used to search for the fingerprint of economic production in cultural affairs, he only demonstrated semiotic analysis on one advertisement. By any standards, a single demonstration is not compelling. However, the addition of quick, concise, orienting contextual remarks would leave room for three or four demonstrations which really delve into the ways that DC’s government and their expectations for the tax base fueled and controlled the campaign’s target audience and message. This use of quantities, in particular, would provide Gibson magnitude by creating space for other sorts of evidence, but he could have also included more information in numerical descriptors. While he did provide the city’s population (262) and a percentage of the District’s property which is exempt from taxes (263), he did not clarify several ideas which provide orienting context and an idea of the magnitude of the problem, such as the class striations and income divides and types of production involved in the region’s fluctuating population. One final issues is Gibson’s time spent researching the campaign. The inclusion of population fluctuation data assists in pattern recognition. As a 2003 project, it is surprising and puzzling that Gibson’s discussion of DC living never included the post 9/11 military and surveillance build up within the beltway and in Northern Virginia. Perhaps this was due to his stay which only allowed for a short term synchronic study, but longitudinal data facilitates a diachronic perspective and potentially richer results because it extends the reach of the scholar.

The next approach is psychoanalysis, a method born of clinical practice, yet useful in uncovering unconscious meanings, desires, and anxieties within cultural artifacts and social trends. This method in particular is already heavily oriented towards a universalizing “objectivist” position, with medical and therapeutic practices in its history from Freud. The most recent bearer of this master school was Lacan, with numerous disciples emerging in feminist movements and vulgar cultural criticism.[2] Lacan, however, is at the fore of the pack in regards to quantification for his use of mathematics in demonstrations of the unconscious. In fact, Lacan applied pure mathematics, specifically topology, linear algebra and algebra, to explain the formation of the psyche and its relation to the self later in life. As explained by a trio of mathematicians funded by Louisiana State University, Lacan’s use of topology was an insightful choice for bridging humanists and mathematicians because, compared to other pure branches of math, topology can be graphically and visually represented very easily. So, while the mathematical and logical forms are very complicated, the visualizations of the concepts are not difficult to grasp. However, as Guissé, Leupin, and Wallace explore a very technical expansion of Lacan’s topology, major methodological issues emerge.

For one, Lacan describes his mathematical program as using topology “stupidly” that is, his approach demands users “follow topological logic to the letter, and not transform it into a metaphor, which makes [it] nonsense” (2009, 1). As Guissé, Leupin, and Wallace point out, “this work can be done, obviously, only by professional mathematicians (especially topologists), who have an understanding of Lacan’s use of mathematics in the framework of psychoanalysis. This is a rare breed indeed” (2009, 1-2). Indeed, that is a rare breed because, as I mentioned earlier in the methodological section, this use of topology is a divergence from the ontological and epistemological systems covered in humanistic inquiry. As such, analysts and cultural theorists are not prepared to utilize this quantity as object method.

Beyond that, however, such a literal mathematical formalism calls into question Lacan’s entire enterprise. If the use of Lacan’s pure mathematics is not one of metaphor, then his association of the two bodies of material is dubious at best. There are no compelling links for literalism between the human mind and topology and, in fact, even if such an arbitrary connection were statically established through Lacanian methods, there is no convincing or conceivable way for those two disparate systems to function dynamically in identical fashions. What this means is Lacan, instead of arguing that the human unconscious is like a terrain, with folds, bends, cuts, and particular orientations, where the processes of topology only need to be “similar” to the minds inner workings, he argues for this: instead of dynamism and interpretive flexibility, a literal mathematics forces the psychoanalyst to describe the mind via a different technology, with no warrant or ontological synthesis for why that can be the case. Alternatively, as is arguably the case for contemporary users of Lacan’s psychoanalytic treasure trove (Judith Butler among several), topology as metaphor is a fruitful and insightful project for changing the analyst’s orientation to cultural production, revealing intriguing discoveries in the methodologically coherent world of quantities as qualities.

The next approach, which is almost as common as the many forms of textual analysis, is ethnography or pseudo-ethnographic collection methods. The major figure for the deep play and rich description available from ethnography is Clifford Geertz. One of his many famous works, Deep Play: Notes on the Balinese Cockfight, weaves anthropological knowledge with his first-hand experiences from years of participant observation. His segment addresses the symbolic meaning behind the male figure and cock fighting, demonstrating the other dimensions behind economic behavior.

Geertz’ piece is an example of a text which would only be diminished by the inclusion of quantification. First, his article was intended to be literary and was published for a literary audience in Daedalus; the inclusion of numerals would have disguised the richness and symbolic depth to Geertz’s prose and narrative flow. Further, Geertz was also working within a different time period where nominal labels could still successfully conjure accurate pictures of large groups of people. Globalization was on the horizon in 1972, but in 2013 it is now in full force, especially with population movements and extended communication networks. Historically, stating the country where research was performed was sufficiently descriptive- the attributes of a group, at least demographically, tended to be consistent and slow to change. Now with permeable borders and rapid change, greater clarification is necessary for ethnographers to enclose a population, community, social space, or affinity group.

That change in times is why mathematical descriptors are increasingly useful for contemporary anthropologists. For Eric Ma and ‘Helen’ Cheng, a bracketing, especially given changed conditions of globalization, is fundamental to conveying their project. During a two year study of migrant workers in South China, Ma and Cheng found that young women and men from rural farming villages had to negotiate their understanding of love and relationships within the more liberal urban context. One problem with their piece, however, is that it never clearly states the scale of the behaviors they are observing. While the study of small groups is interesting and useful in its own right, it is difficult to believe the importance of this pattern for the entire country of China without further elaboration. For example, vague language such as this leaves the reader with no reference point: “medium-sized factory,” but what is the range in factory sizes?; the workers “shared socioeconomic status,” but what does that mean for rural Chinese workers in 2003? How wide is the gap between rich and poor?; “many Chinese have been [moving] to the city,” with “massive migration” (Ma & Cheng, 2005, 308). These ethnographers never tell the reader how big is big? Are these three girls you interviewed while serving as their English tutor, or are your observations something that appears systemic and culturally bounded?

Also on this front, Ma and Cheng seek to “go beyond narrative analysis by exploring the materiality and corporality of migrant’s experiences,” especially using the body and its symbolic “nakedness” in this transitory time (2005, 310). This “nakedness” concept is evocative but underdeveloped. The scenario of postmodern anxiety these women feel is suitable for the use of mathematics as metaphor. While the authors use a wide and comprehensive group of theorists to describe their observations of the young Chinese migrant workers, they never clearly show their own contribution to that body of knowledge other than applying it carte blanche; their argument goes [environment] affects the body due to [body of theory]. Topology provides insight in discussions of manifolds. For example, the knot is an excellent metaphor because it demonstrates the multiple dimensions that the same number of bends are configured in to respond to space around the manifold. These pretzel knots break, merge, bend, and bind. They are materially relevant and visually compelling, almost sensuous.

Manifold

Finally, the treatment of digital culture and digital networks by cultural studies scholars is fundamental. A prominent discourse in society today holds that the internet is a flattening technology which erases the systemic injustices of race, gender, and class. This idealized version of reality argues that the virtual is a democratic escape from the impoverished communication of our corporeal spheres. Mark Deuze is an example of a scholar using techniques from other fields in innovate ways in order to demonstrate their potential for critical intervention. In his 2006 piece, he used a form of primary component analysis, traditionally used to distinguish features of photographs which are most “important,” but he built a thematic list of components from digital networks, then processed then reflexively, changing the standard for judging what is “important.” Old network analyses tend to focus on the things which are the same across a network, using these standards to define the culture. Deuze instead used the divergences and conflict to discuss the issues. Such a stand point epistemology altered completely the outcome, and it is all due to a new approach to network analysis. His ideas are commendable, and something desirable for future CS projects, especially when society believes we are “post-sexism, post-racism, and post-classism.”

The politics of the academy sometimes call for new and uncomfortable measures. The adoption of mathematical descriptors in the humanities is one case where more theorization is needed and practice acquired to bridge the gaps. Hopefully, by speaking a diverse language, expanding conceptual tools, and demonstrating the ideology endemic to certain methods, CS and other critical enterprises can convince “objectivist” scholars of multiple and dynamic views. More funding would be nice too.

References

Condit, C. (1996). How bad science stays that way: Brain sex, demarcation, and the status of truth in the rhetoric of science. Rhetoric Society Quarterly, 26(4), 83-109.

Deuze, M. (2006). Participation, remediation, bricolage: Considering principal components of a digital culture. The Information Society, 22(2), 63-75.

Garnham, N. (1995). Political economy and cultural studies: Reconciliation or divorce? Critical Studies in Mass Communication, 12(5), 60-71.

Geertz, C. (1972). Deep play: Notes on the Balinese cockfight. Daedalus, 101(1), 1-37.

Gibson, T. A. (2005). Selling city living: Urban branding campaigns, class power and the civic good. International Journal of Cultural Studies, 8, 259-280.

Glassner, B., & Moreno, J. D. (Eds.). (1989). The qualitative-quantitative distinction in the social sciences. Dordrecht, The Netherlands: Kluwer Academic Publishers.

Grey, S. (1999). The statistical war on equality: Visions of American virtuosity in the bell curve. Quarterly Journal of Speech, 85, 303- 329.

Guissé, A., Leupin, A., & Wallace, S. D. (2009). Lacan’s Mathematics: Vector analysis of speech in a Moebian context; Epistemological cuts or births? Louisiana State University, College of Arts and Sciences, Research. math.maconstate.edu/swallace/Papers/TheMathematicsOfLacan_3.pdf

Lacan, J. (1977). The mirror stage as formative of the function of the/ as revealed in psychoanalytic experience. In N. Badmington, & J. Thomas (Eds.). The routledge critical and cultural theory reader. New York, NY: Routledge.

Ma, E., & Cheng, L. H. (2005). ‘Naked’ bodies: Experimenting with intimate relations among migrant workers in south China. International Journal of Cultural Studies, 8(3), 307-328.

Ziliak, S. T., & McCloskey, D. N. (2008). The cult of statistical significance: How the standard error costs us jobs, justice, and lives. Ann Arbor, MI: The University of Michigan Press.

[1] Statistical significance and substantive (or empirically validated) significance are a major problem in applied statistics work. The mathematical models which provide “powerful” results from the p-value are only talking about the likelihood of that particular sample re-occurring and the same test statistic being calculated. The p-value does not signify that the results are accurate for society or the qualities the numbers describe, but that is how they are frequently interpreted.
[2] “Vulgar” is a light-hearted jab at Zizek and his provocative performances.

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