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The Burden of Proof: Mathematics, Gender Performativity, and Delusion

Good Lord! They are appraising me!

—Lady Elizabeth Murray, Belle

When The Mates walk in, I avert my gaze and tuck my hair behind my ears. To my left, a friend prints a title, pauses, erases, rewrites. To my right, another checks the volume on their tablet, mutes, un-mutes, then mutes again. The group behind us, mere seconds ago debating the effect of water on excretion, watch their inhibition walk through the door and take its rightful place in the front row. Seven minutes have lapsed since most students convened for today’s class, but a workshop in the absence of bright young mathematicians is one of absolute futility. To this, I unequivocally agree.

The workshop commences. My attention cycles between the digital clock on the wall, the question a peer is asking that I too pondered but could not ask, and the indignant, spirited brunet remarking to a less enthusiastic, taller blond that he had indeed “already learned this”; had “solved the problem already”; had “said that before”. Periodically, the professor poses a challenge to his budding first year disciples, or so I am told, by the lewd shuffling of paper, the neurotic clicking of pens, and the rightful union of pencil meeting paper, as students scrambling to feel the hit of braggadocio, of a real win—an analgesic to soothe the wounds of past competition, and an amphetamine to set the mind alight with pride.

I scribble down an answer and my friend and I compare our proofs; we conclude that mine is correct, but not right. The professor wanders around the room to peer awkwardly across shoulders and appraise the work of his students, and to be efficient he does not bother with ours. When he asks if anyone would like to share, his chagrined expression betrays the openness of this call to action. From my seat in the dark, I try every language that he might recognise, but nothing can draw his attention; the words hang in the air, wailing from the shadows, dancing on my lips like an incantation. To his, I return a meek, unknowing stare.

It is a truth universally acknowledged that women students are not included in this democratic call to the likes of any one, that psychosocial smallness as a spiritual practice is but a minor formality to be observed by those granted the enormous privilege of access. If our fidelity to silence is so permeant, so omnipresent, why does it feel so unnatural, like a nameless, faceless malaise? Beyond breaching this academic space, the right to spiritual growth, to personal development, and to self-determination, is nevertheless differentially allocated to oscillate outwards from the epicentre of power and fatigue at the margins. I am writing to remind that, in a social and political context that promulgates for theoretical inclusion but is broadly ignorant of praxis, the apparent mainstreaming of deviance and relaxation of social mores rebrands hierarchy as more benevolent, perhaps, but changeless, eternal, appropriate, and arising out of ourselves. This process of shifting marginality ever so slightly, diluting subgroups systemically deprived of rights and privileges into individuals, is arguably more dangerous than its predecessor precisely because of its deniability.

To maintain illusive power in the delicate dance of our one-up/one-down system, the ‘good’ deviant must master the fine art of dissimulation, of assuming whatever appearance is required to best manipulate a situation; to mask true feeling. For any woman mathematician to claim citizenship—the right to be permitted into masculinised academic spaces—they must assume (tacitly, or not so) the mantle of policing the borders against those who do not conform to the standards of the ruling class to the same extent as they might. Since the actions of the ‘good’ deviant are adulated not as mimicry but as innate goodness, what emerges is a new policing system to designate respectability by discerning between appropriate and inappropriate behaviour that is ultimately rooted in structural inequality. Gatekeepers of respectability are then tasked with championing dominant narratives and ignoring that the genesis of the respectable deviant first arose in an environment that antagonised all deviants. Respectability is appropriated again and again by those that rule the margins, who can remain in blissful ignorance of their complicity with structural oppression so long as they can remain upstanding—respectable. When we force women and femmes to internalise these oppressive standards of assimilation and accommodation, we render even the expression of feminist issues an exercise in navigating privilege, in policing the right to critique, express anger or fear, ask for help, and have our pleas heard. The emotional labour required to mask the raging maelstrom of emotions invoked when our personhood is violated, to resist the urge to challenge much less confront those who have harmed you, is incredibly onerous precisely because it is an act of dehumanisation. Respectability provides an illusion of control over our own narratives, when in fact the ultimate culprit is, in the words of bell hooks, the ‘imperialist white-supremacist capitalist patriarchy’. Indeed, the mere fact of losing composure, of feeling wounded, is a sign of weakness in this regime of individual capacity, for ‘good’ and ‘bad’ deviants alike. Airy gesturing towards the inevitability of discrimination places an unequal burden on women to manage risks, repercussions, and reparations, positing male contempt of women’s autonomy as a brute fact and women’s manoeuvring around it as imperative. Locating the genesis for transformation in women, not wider relations of domination, here lies confidence culture: coined by Rosalind Gill and Shani Orgad, the movement holds that neither patriarchy, capitalism nor entrenched institutional sexism that hold women back, but primarily their own lack of confidence, which is an entirely personal matter. Valorisation of confidence as a psychological stance that grants individual power is at work in sentimental pleas for women to ‘be assertive’ and ‘be tenacious’, rhetoric that is especially ironic by way of skirting evasively around a glaring pitfall in this path to women’s liberation: that women are punished for emulating the very attributes that confidence culture claims will be their ticket to parity. The fabrication that women, by way of speech and temperament, can achieve greatness, disenthral themselves from the clutches of patriarchy, and advance equality and diversity for all women, tricks us into viewing adversity as character-building, and confidence as a form of self-work that each woman must undertake to respect themselves for not succumbing to unfavourable circumstances, and fly the flag for all women. Motivational self-talk may provide the necessary surge of positivity and self-realisation required for a job interview, or public speaking, but falls gravely short as a substitute for radical political movement. Shunning vulnerability as ugly, abject, or shameful, we force yet another act of dehumanisation upon women: that being self-respecting means to be devoid of, or at least vehemently deny, feelings of insecurity and lack of confidence. In the words of Gill and Orgad, if ‘confidence is the new sexy’, then ‘insecurity is the new ugly’. Therefore, to be insecure—to be human, to reject a manic insistence upon the invincibility of oneself and the capacity of oneself to unilaterally enact revolutionary change—is to be ugly, and more importantly, to be unfeminist. Women’s speech, both demanded and idealised, both touted as a marker of progressive politics and wholly ignored when spoken by the wrong kind of victim, bears an insurmountable burden: that of bringing attention to injustice; of improving gender relations; and of resolving violence. Our community, which has studied the language of encouragement and empowerment, continues to hold tentativeness in great contempt, asks of women and femmes like myself a robust self-knowledge and chimeric capacity for vocal expression. The injunction to speak retrospectively, prospectively, and protectively—that only clear speech can prevent future wrongs and address past ones, that to clearly know and speak on one’s subjugation is critical to galvanise others towards parity—frames outspokenness as a requirement of any self-respecting feminist subjectivity. It is under this injunction that I write, to achieve my self-respect, to invite an invasive tourism of my reality (though curated), and to provide the only material that can elicit the attention of those otherwise unenthused—obscene imagery of violence and derivatisation.

Coined by Ann Cahill, derivatisation as an alternative to the model of objectification is helpful in understanding the full extent to which prejudice deforms testimony, proclaiming ulterior motives and underlying causes for what would be considered neutral deposition from an unmarked individual. Regarding cultural prejudice, Julia Serano uses the term markedness to describe the perception of particular traits as ‘conspicuous, fascinating, unnatural, abnormal, questionable, suspect’ within marginalised groups, which drive us to ‘pay them extra attention and scrutinize them disproportionately’. Cahill explains that to derivatise a person is ‘to portray, render, understand, or approach a being solely or primarily as the reflection, projection, or expression of another being’s identity, desires, fears, etc’. In short, elements of the derivatised person’s being are muted at the behest of the derivatiser, attenuating the subjectivity of the former to suit the latter’s fantasy. Carolyn M. Cusick employs this framework to model testimonial injustice:

When one is unduly denied credibility, there is not a misrecognition of persons as being things and therefore not fully persons; there is an active, willful misinterpretation of the evidence from victims’ own bodies and lives and a derivatizing of them as persons for others rather than for themselves. The listeners to testimony are treating themselves as the only active participants in a testimonial exchange despite identifying a testifier as having some knowledge; that knowledge is constructed as both limited and gleanable by only the listener’s efforts rather than by shared efforts of the testifier and listener.

Serano argues that markedness invites suspicion—to ‘ask questions’ and to ‘view [the individual] as suspect’—under the presumption that the marked individual’s behaviour by nature ‘attract[s] attention’. In the context of a mathematics classroom, the presence of women mathematicians becomes public spectacle, such that entry requirements are not sufficient in confirming mathematical competence, rather, the right to entry is to be systematically questioned and reciprocally proved, and any blunder can see this competence card revoked. The lofty chimera of ‘mathematical competence’ is more or less a misnomer that disguises the institutional, discursive extrapolation of classroom authority, masquerading as a system of correlation between the normative quality of a contribution, and the production of authority, privilege and access. Influence, according to the framework developed by Randi A. Engle, Jennifer M. Langer-Osuna and Maxine McKinney de Royston, “emerges out of the social negotiation of influence itself and the following four components that interact with it: (a) the negotiated merit of each participant’s contributions; and each participant’s (b) degree of intellectual authority, (c) access to the conversational floor, and (d) degree of spatial privilege.” A following paper by Langer-Osuna examined interplay of authority within small group mathematical problem solving and emphasised how social authority (derived from popularity) and academic authority (derived from perceived intellectual ability) heavily informed evaluation of students’ ideas and behaviours by teachers.

From the onset, The Mates were fuelled by a consecrated reservoir of social and academic capital with which to justify their authority, granting them unbridled access to the conversational floor. This authority then served to explain away antisocial behaviours (interrupting peers, conducting loud conversation during lectures) employed by The Associates to demonstrate membership. Frequently, this group would engage in outwards- facing, ostensibly private work-related conversation, carefully oriented for an audience. In fact, workshops would frequently halt such that these performances could reach their natural conclusion. It became the business of The Technophiles, the symbolic others, and the professor alike whenever The Mates had correctly mastered the challenge at hand or were unenthused about the workshop’s direction. Family therapist Terrence Real tells us these performances are rarely for self-benefit alone: “most [men and boys] feel at least as much burdened as enhanced by the need to perform”. I use the term ‘performance’ here in keeping with a poststructuralist understanding of gender as discursively produced through stylised acts, whereby anticipation of a gendered essence produces that which it posits as outside itself—in short, anticipation conjures the object. Philosopher Judith Butler describes how these ritualistic performances achieve “hallucinatory effects through naturalisation in the context of a particular body, understood (at least in part) as a culturally sustained temporal duration”. The professor’s acceptance of antisocial behaviour, predicated on the anticipation of this behaviour by other students, colluded in the disproportionate spatial privileging provided to The Mates, in terms of both physical space (their location in the classroom, degree of visual attention), and access to the conversational floor (proportion of contributions, permeability of personal discussions). Students from all factions fawned over praise from the professor, though the The Mates were disproportionately bestowed positive affirmation, maximising perceived intellectual merit at the expense of others.

For The Mates, the sum of their socially negotiated authority, merit, access to interactional space, and access to the conversational floor produced an echelon of influence greater than that of any other group. Tacitly or not so, The Mates carefully monitored the progress of the entire class, though performed to appear entirely disenthralled by the relationships of power that discursively organised the classroom, and the mechanisms that shaped the construction and distribution of intellectual authority among students. The Mates were just as preoccupied with the forces that be as their less socially revered male classmates—The Technophiles—and their women peers, but they understood that any versions of ephemeral, counterfeit power afforded to other members of the class would ultimately leave their real power uncontested. In truth, The Mates would, implicitly or explicitly, check those attempting to exceed the intellectual or social boundaries of their status, ensuring that they always won what one member described as “the war”—this crusade, I take it, was one of gender.

Subjugation of women peers by The Mates was affirmed through inconspicuous displays of authority, and whilst neither group formally interacted throughout the entire twelve-week semester, members of The Mates would regularly remark from across the room that “[he] think[s] they made a mistake…yeah, we’re right”, especially when these mistakes were alluded to, or identified directly, by the professor. Contrastingly, performances of domination over other male peers were overt and unambiguous. For example, when a member of The Technophiles suggested that the class play a game at the end of the semester (this offer was not extended to women students), some members of The Mates laughed whilst others ignored the offer entirely. This one-up/one-down dualistic power dynamic underscored the relational production of two masculine subgroups; one that mirrored fervently hegemonic, sexually dominant archetypes; the other a more ‘rational’ subtype with less social and intellectual merit. For The Mates, dominance was an implied fact of being that necessitated only occasional dyadic displays of power over others, but for The Technophiles, dominance was to be repeatedly proved.

Interestingly, The Technophiles felt entitled to repeatedly co-opt the proofs and solutions developed by women students as their own. Members of The Technophiles would attempt to discern and replicate work from afar or would approach their peers and instigate a short exchange. These interactions were both uncomfortable and alienating, as another woman peer and I would reciprocate, hoping to open new lines of communication and expand our collaborative networks, only for our responses to be ignored as The Technophiles perused our work, before silently withdrawing and returning to their workspace. The Technophiles did not attempt to cajole The Mates with this kind of fair-weather friendship at any point throughout the semester. Women mathematicians, punished and praised for their work and their temperaments, learn to valourise injustice as a simple fact of their being. Pressure from all directions encourages the endless pursuit of an unobtainable goal, in which we induct ourselves into a Sisyphean cycle of fruitless work all to sustain a pool of low-cost, disposable female labour. To steal from The Mates is to violate the very institution of mathematics; to steal from women, however, is not merely to put work that would otherwise be wasted to good use, but to participate in a political and pedagogical system that naturalises women’s labour to exist solely for the purpose of appropriation.

Though exploitative for obvious reasons, this conclusion is highly rational when evaluating the power differential between women students and our professor, which foregrounded the overall discursive production of authority. Though the majority of small group collaborative work occurred in the absence of a professor, Langer-Osuna promulgates the unique positioning of the mathematics teacher to revolutionise these group dynamics: by “directly attend[ing] to issues of status, engagement becomes more equitable. For example, in complex instruction, teachers explicitly seek authentic, public, or semi-public moments to elevate the mathematical contribution of low status students, raising their relative status levels. This can balance participation levels as well as shift peers’ perceptions as to who can do mathematics”. In a similar way, teachers have a unique capacity to intensify inequality in all aspects of learning, which characterised many of the interactions between myself, another woman peer, and our professor. These included candid assumptions of incompetence, overt prioritisation of other students’ pedagogical needs over ours, or flippant comments about the immiscibility of women students with the rest of the class whilst championing the very power differentials that maintained this.

I recall one notorious collaborative session with a Technophile in which a fellow woman student and I were subjected to repeated physical and psychological attacks, involving an object thrown at my head from behind. In response, the supervising professor stated calmly that “we don’t throw things at people”, whilst the other members of our small group did not comment. Dehumanised himself, the Technophile felt not merely enabled but compelled to dehumanise a peer—to theatrically consummate a set of political beliefs. This display of male chauvinism, likely stemming from The Technophile’s sense of himself as powerless and ineffectual in relation to the ruling male class, attempts to signal common ground (that being a propensity for domination) between himself and his classroom superiors, and be reassured that his dominion is legitimate, corrosive, and venerated by men of greater social standing. This is, of course, a delusion.

It may be that he did not wholly identify with aggression, but upon uncomfortable feelings of inadequacy and helplessness that arose upon repeated wounding from other forms of dominance by The Mates, he responded with rage to the threat of proximity to these vulnerable parts of himself. Moments of shame broke through to his consciousness and were repressed with the narcotic of dominance, attempting to ameliorate the pain of alienation by engaging in behaviours that exacerbate alienation. Shame states, or failures in self-esteem, are experienced as a sense of not being enough and not mattering; as emptiness, fear, or impotence, in anyone who is sufficiently disempowered. Discomfort of the shame state is then defended against by intoxication and grandiosity—an external prop for self-esteem regulation.

The implications of gender parity in this context are thus rife with contradiction. As power is withheld from women peers and granted differentially to The Mates and The Technophiles, their assumption of these elite mantles is heavily policed, by themselves, their fellow members, their professor, their women peers, and the academic system in which they are situated. To maintain power over their women peers is to engage in an act of self-mutilation that puts an end to the capacity for relatedness, collaboration, connection, and the capacity to extend oneself for the purpose of supporting one’s or another’s growth. That to reach absolute self-actualisation men need to separate from women is a core teaching of psychological patriarchy: a “dance of contempt”, which Real defines as “a perverse form of connection that replaces true intimacy with a covert dance of dominance and submission, collusion and manipulation”, treating “one half [of oneself] as exalted and the other as devalued”. In stark contrast with this idea is the presupposition that all people are created equal, that one’s inherent worth can be neither greater nor lesser than another’s—a principle that underscores healthy self-esteem. This internal essence, expounded by Real as “the capacity to cherish oneself in the face of one’s own imperfections, not because of what one has or what one can do”, is incompatible with the socialisation of men and boys to derive their value only by ‘doing’ or ‘performing’, not by simply ‘being’. Whilst membership to masculine subgroups in our classroom is precarious, insecure, and always in danger of being revoked, a sense of self-worth and relational connection—of mattering to someone, of being worthy of intimacy and connection—by contrast always imparts a secure sense of membership. Healthy self- esteem still recognises nuanced discrimination of strengths and limitations, but nevertheless cultivates the pretext for achievement as a labour of love that exists within the context of secure selfhood and mutuality, not an act of grandiosity that compensates for a lack of connection. Patriarchy, then, teaches men and boys to appraise themselves against unrealistically narrow and perfectionistic standards of productivity, ability, and dominion, forcing upon them the crux of performance-based esteem. Compulsive to a point that it undercuts both relationships and performance, performance-based esteem undermines one’s capacity to respond to their environment, and whilst the origins of one’s distress are internal, the consequences of this emotional desecration are most prominent in one’s external relationships.

It follows that we need not promulgate a feminist insurgence interested in reform of these classroom dynamics as an end in itself, not as a stage in the progression towards transformation. Integral to the radical politic that we envisage is a collective, affirming call for boys and men to join the feminist movement and be liberated from patriarchy. A vision of feminist imagination that dreams of women as the social equals of men is problematic precisely because of its depoliticised, ambivalent relationship to oppression, mired in the ignorant reverie of all men revelling in a common hegemonic privilege and all women suffering from a common oppression. Failure of our class to practice interbeing and partnership—to which gender equality is essential—teaches us that men and women alike must look beyond patriarchy and explore new models for self-assertion that do not hinge on the construction of a symbolic enemy ‘other’ against which they can define themselves. To centre mutuality and the personal growth of all people, is to promulgate a reconstruction of power from an exercise in domination to a creative and life-affirming force. When power is an act of strength and ability, that brings a sense of accomplishment and contribution to the community, we are empowered to reject the definition of oneself put forward by the ruling class and develop positive self-concepts. To eradicate an academic system that disenfranchises the silent majority of students in favour of select benefactors is to abolish domination and elitism in all relationships, to challenge the cultural basis of group oppression across all spheres of personal and public life, to enshrine self-determination as the ultimate good, and to embrace the downfall of academia as we know it.

Anonymous

The author Anonymous

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