This essay contains a portmanteau of two strands of narratives from which the reader can choose his or her own critical engagement; either biographical or literary. The science fiction aspect of the narrative attempts a critique of queer feminist science taking place at an ontologically abstract level to force a re-reading of the mathematical sciences via a politically astute lens of feminist epistemology. At the same time, the essay participates in a close reading of the intellectual biographies of Emmy Noether and Maria Goeppert Mayer to demonstrate the importance and revolutionary nature of their respective contributions to fields that would later converge into the most cutting-edge physics of today, as well as that of computation. A part of the essay critiques what was at stake for these two women who contributed enormously to shaping the imaginary of the world of theoretical physics and, therefore, the imaginary that informs the foundations of hard science fiction focusing on speculative and novel ideas of physics. The imaginary of theoretical physics is rife with a multiplicity of interpretations that shape how we like to perceive our microworld, and how that, in itself, influences our connection to the macro-world. Another part discusses the critical, creative, and intellectual drive behind my production of a queer feminist hard science fiction, the Schrödinger’s Notebook.
In the chapter “Why ‘Physics’ is a Bad Model for Physics,” from the book Whose Science? Whose Knowledge: Thinking from Women’s Lives, published in 1991 by Cornell University Press, Harding argues that most feminist critiques have failed to identify the fortresses that seemingly protect science from “critical, causal scientific explanation that the natural sciences insist on for all other social phenomena (77).” Most physicists and philosophers of physics would dispute Harding’s claim, because the problem of causality, at least of the foundational issues surrounding questions of determinacy, certainty, physical realism, and observations, are germane problems in physics and its philosophical disquisition. Read differently, Harding’s criticism is a call to arms for feminist criticism to get involved with the epistemological interrogation of the theoretical fundamentals of abstract sciences such as physics, stemming from the misperception that the field is not open to discursivity or social maneuvers. The modest goal of this paper is to produce an interjection that has been lacking, while moving the goal post further forward, thus enlarging the intellectual interventions of feminist theory.
Many of the earliest feminist interventions into science, or technology, derived from the turns that took place in cultural anthropology, literary studies, and cultural theory in the 1970s and 1980s that reversed their lenses so as to look inward into the critical examination of western cultures and the intellectual products that are the outcome of these cultures (McNeil). Hence, given the background and direction from where much (though not all) of science and technology studies have originated, there tends to be more interest in social than epistemological questions, while the internalist-directed philosophical analyses of scientific epistemology and ontology (particularly in analytic philosophy) would evaluate these fields in isolation of the social. Nevertheless, the traditions of literary and cultural studies are crucial for informing my transhuman reading of the subjects examined here. 
There have been rare, if any, instances of interventions by queer and feminist theories into mathematical and theoretical physics. Such lack is exacerbated by the small number of women who are participants in these two fields due to a combination of social and educational disadvantages over the course of centuries. In the cases of female scientists and mathematicians, their lack of public visibility means that even the most stellar contributions do not lend themselves as readily to public acclaim as comparable contributions by male scientists and mathematicians; moreover, female scientists and mathematicians are less likely to receive credit for their scholarship. Therefore, queer and feminist interventions are ever more needed in light of how scientific epistemology has been shaped by the social conditions of privilege (some more than others) of a majority of the practitioners in the field. Karen Barad, who has played an important role in comparing the indeterminate matter of quantum theory with queer entanglements, is a notable exception. Her work has made it possible to think about queerness beyond the materiality of the gendered: to incorporate queerness into the corporeal matter of science. Barad’s work illustrates how the inviolability of the ontological constitution of science does not render its epistemological position closed to political recuperation. One such example is her Derridean reading of Frayn’s play Copenhagen, about the imaginary conversations between Werner Heisenberg, Niels Bohr, and Margrethe Bohr. The conversations are framed in a manner analogous to interpretations in quantum theory that advocate the thinking of justice through the ethics of science and agency in decision-making concerning life-and-death situations (Barad, “Quantum Entanglements”).
Since their beginnings, feminist technocultures have taken a more innovative turn by including the study of performativity and multi-modal transgressions. Such transgressions include the presentation of non-linearity as models for arguments that are not continuous but contiguous. Additionally, theories within feminist science studies become the go-to for making sense of the materiality of a fictionalized/constructed body laden with multiple cultural inscriptions and social immersions. The body (that could be corporeal or metaphysical), whether situated within the space of the actual or the virtual, is the container for the superposition and interplay of dominant and suppressed (recessive) cultural and biological values. Even when the body is able to exert and stake the claims of the marginal, there will always be different intersections of resistances: one might ask whether such resistances could themselves downplay the autonomy of a body pushing through the tension, including the gendered body that could or could not insist on its difference, thus impacting the latter’s interactions with epistemology.
In her essay, “The Implications of the New Materialisms for Feminist Epistemology,” Samantha Frost wonders whether an engagement with historical materialism can destabilize feminist epistemic readings of the essence of biological materiality in binary relation to cultural power relations. Could epistemic standpoints stemming from particular engagement with the inertness of matter that is shaped by norms and social constructs be better dissected? Her arguments foreground certain troubling aspects of essentialist and social constructivist practices grounded in the dichotomy of culture and nature, with the expectation that one be led to a more straightforward understanding of the state of causation pertaining to the aforementioned dichotomy. Frost argues that new materialist readings aim to “counter the figuration of matter as an agent only in virtue of its receptivity to human agency. They try to specify and trace the distinctive agency of matter and biology, elucidate the reciprocal imbrication of flesh, culture, and cognition, investigate the porosity of the body in relation to the environment in which it exists, and map the conditions and technologies that shape, constrain, and enhance the possibilities for knowledge and action.” Hence, perspective, as a constructed narrative of experience, is a rhizomatic matter that precludes the uniqueness of any social or gendered perspective, as the focus on any particular perspective merely collapses the other factors from consideration, but does not exclude their already-there impact.
Hence, the essay aspires to make the connection between mathematics, theoretical physics, and feminist technoscience more evident even as the non-linearity of such connections must be emphasized. This means reading against the grain of the current philosophical and historical discourse. It also means making jumps between arguments that are not dissimilar to the ‘quantum jumps’ articulated by Whitehead in his Science and the Modern World as representations of categorical leaps. In his thinking, the move from classical to quantum modes of thinking represented an ontological jump, which we know to be untrue today given that the leap is purely epistemological; the ontology as embodied by the mathematics and mechanical worldview enables points of continuity between classical and quantum mechanics, even if some rules appear to have changed. However, I am aware that many of the substantive arguments I want to make regarding the politics of the scientific epistemology get occluded by the high level of technicality in these objects. I hope to somewhat alleviate this by limiting my technical account to an impressionistic level and focusing on the impact that politics internal to epistemology has on practices thought to be external to the scientific facts. This connects back to the argument made by Frost on the problem of untangling the different factors of causality.
Before continuing, I should explain what I mean here by speculative theories, especially the enactment of speculation that overlaps the theories of the physical sciences with science fiction. Speculative theories are theories that could not directly explain the relation between cause and effect, or provide a determinate explanation to an outcome. However, this does not mean that the theory has no basis in hard facts or empirical data: it merely means that the theory is open to further re-interpretation and reconstitution as new possibilities emerge. Speculative scientific theories, as epistemological imperfectness overlying an ontology that is always at that point of becoming complete, do not object to considering subjectivities and affectivity that are part of the knowledge production. Debates internal and external to science can then be illustrated through carefully constructed thought experiments that consider these debates separately and together. Subjective affectivity constitutes the social construction surrounding theory predictions and thought-experimental narratives that have significant roles in the interpretive act. We must also consider the importance of experimental design for bringing theoretical predictions out of their under-determined stage (where cause and effect have no direct correlative).The consideration of the experimental in partnership with theory is vital to an expanding feminist epistemology and intrinsic to thinking about how one can then go about ‘queering’ one’s interpretation of scientific theories and practices.
Were one to examine the official history of quantum mechanics, one gets the sense that it is a narrative of white-male dominance and female tokenism. Even as an increasing number of women and minorities are majoring in physics, the physics they study appears pedagogically immune to other forms of interventions as its traditions of thought and knowledge transmissions are kept on a mostly ‘straight’ narrative promulgated by introductory and even advanced textbooks. But, were one to enter into a thorough examination of the development of quantum theories, one would soon find many segues and theories that never quite entered into the mainstream of discourse, since most of these were never included in the popular textbooks used by students.
Historians of science like Frederick Gregory argue that the scientific revolution of western civilization, which reified the mechanistic conception of nature, ensured the continuation of patriarchal attitudes towards knowledge as had happened throughout the development of the theory of mechanics in physics. One such example is the inclination towards the anthropomorphization of the universe and a refusal to consider a universe that can exist outside the empirically determined. This is made possible because the same clerical institutions that had hitherto resisted the epistemic changes during the scientific revolution had appropriated the same mechanical (abstract) view of nature as a tool for resisting a more organic, or other possible, views of nature that the church would not be able to regulate as easily. As Gregory argues, “the view of nature as a self-developing autonomous organism was discredited and replaced with a nature controlled and ruled by God the giver of fixed mechanical law.” The mechanical view of the universe, Gregory claims, is exemplified in how the male-dominated clerisy had decided what scientific questions were important and what approaches should therefore work, embodying again the classic privileging of the intellectual choices of male authority (Gregory 51-53).
While there might have been women who were contributing to the world of abstract ideations before the twentieth century, the perpetuation of masculine versus feminine ways of knowing (which, while a gendered discourse, has the insidious propensity of over-reaching into literal differences of the biological sexes and ignoring sexual différance) ensures the continuous ignominy of that pronounced as feminized ways of thinking. Knowledge driven by the ontology of mechanics is thus seen as constituted within the privilege of the masculine, with interventions from women discouraged.
Much of the work in feminist science studies and also feminist science fiction is usually centered on issues of biology and the medical sciences, which is to be expected given the profusely important stakes in these areas. But there has not been as much attention paid to how feminism can be active in the physical sciences; not merely in terms of pushing for greater accessibility and receptivity of these fields to women and girls, but how feminist epistemologies can shape the knowledge practices in the field. In fact, two trained women physical scientists, in their 2006 NWSA paper, “Interpretations of Feminist Philosophy by Feminist Physical Scientists,” sounded the clarion call for greater attention with regard to knowledge practices in the physical sciences (Belcastro and Moran). It is easy to understand the reservations that most would have in dealing directly with modern physics theories, given the seemingly high level of esotericism of the subject (let alone the obtuse mathematics), where a single mis-step (or even an out-of-context misinterpretation by a reader) can subject one to a level of ridicule reminiscent of the Sokal hoax.
But should one be interested in taking up the challenge of examining mathematical-physical theories in relation to politics, one might begin by taking a closer look at how the foundational concepts and philosophies embedded within quantum theory can be made amenable to a feminist re-reading, with the latter foregrounding powerful ontological revisions. Karen Barad illustrates such possibilities in her re-appropriation and re-presentation of Bohr’s theories, such as his theory of complementarity, which is the reconciliation between classical and quantum mechanics (macro versus microphysics) in terms of how they could be measured, through the enaction of agential realism. She then applies agential realism to issues of interest in feminist theory and feminist activism, such as reproductive technologies and discourse on the body. However, it is not evident that she has applied agential realism, as a valuable material tool, for politicizing the interpretations she made in connection to the standard readings for producing more challenging interpretations of the Bohrian epistemology, thus opening the official reading to further interjection.
Feminist scientific epistemologies have much to say about the specific assumptions of knowing that take place during the process of de-naturing and reconstruction (a cyclic process of breaking down current epistemic structures for new configurations to be produced). These epistemologies work well in complement with feminist technocultures to produce a set of critical methods that could provide deeper interventions into science by challenging the status quo in sociological and philosophical foundations. It is valuable to know what feminist scientific epistemologies can say with regard to forms of knowledge that rest uneasily on any discourse of gender politics, such as the mathematical sciences, even though such knowledge’s survivability and re-formations are partly the result of knowledge ideals that arose from social specificities, such as institutional recognition and access to resources, networks, and collaborations. At the same time, feminist epistemology shares parallel critical baggage and motivation with that of postcolonial theory, through a common subaltern genealogy, and the inclusion of postcolonial studies into the discussion can further enrich queer feminist intervention.
However, before we proceed further, I would like to explain further the structure of this article. The writing in this article will always be in the form of a triptych, with particular paths that the reader can choose to follow. I begin with a core introductory overview of brief critical discussions on the epistemic fields inhabited by the two women physicist/mathematicians of interest here: Amalie Kauffman Noether/ Emmy Noether (whose contribution was in the mathematics of symmetries and invariance, both cornerstones to the development of quantum theory) and Maria Goeppert Mayer (whose work was on the theory of nuclear shells). These explications are meant to provide a foundation for evaluating feminist epistemology against women’s positions as socially immersed subjects of the scientific community who then perform cognitive labors as an outcome of their immersions. While these women occupied marginal positions at the time of their labor, their contributions grew to become part of the dominant discourse. One might ask what maneuverings went into legitimizing and validating the importance of their contributions. The answer possibly, though not straightforwardly, exists in relation to the privilege these women experienced as tokenized subjects in their relation to their epistemic engagements. At the same time, the margins of their differences were submerged under the dominant practices that they did not resist.
Thereafter, the reader can choose to explore further the individual works of the two women. In the more detailed discursive biographical-theoretical discourse, one gets to read the socio-political bodies of the women against the intellectual work in which they were participants, with more technical details on their contributions delineated, and about the importance of their contributions in shaping the disciplinary features of current technoscience. This section is also where I attempt a preliminary engagement of theories in the abstract sciences (mathematics included) using more humanistic feminist epistemology as another mode of reading the biographies of these two women. Therefore, the discussions in this section are less descriptive than analytical, which include the propagation of arguments that are not always historical in nature.
On the other hand, the reader can jump directly to reading about the speculative science fiction project that I am working on. I will then explain the theorization and background that informs the postcolonial-feminist-queer hard science fiction I am writing. I argue that there are parallel epistemic strains in queer and postcolonial discourses, as both arose from the desire to theorize one’s situatedness at the margins while also attempting to theorize oneself out of those same margins. The goal is to contribute to meta-narratives that can free one from dominant master narratives. Of course, how possible that contribution is depends on the number of risks we are willing to take. It is my intention to test the limits and durability of the theories I propose here before subjecting them to a fictionalization process. The method of fictionalization also enables the theoretical exploration of certain social experimentation in superimposing the material perspectives of the micro-worlds with that of the macro-worlds where hard and speculative scientific problems and histories are involved in continuous interactions. In light of that, I argue that the explication of the ‘real’ through a critical reading of the production of these two women can foreground the limits contained in the fictional while problematizing the existing conceptions of the scientific method. The point is to invoke the potential for physics, and particularly mathematical physics, to incorporate qualitative queer interpretations.
Or, one can choose to read everything available, to see the interplay between the actual and fictive without there being a linear correlation of the two. The article is laid out such that, regardless of the initial choice made, one always has the chance to go back to the path not taken.
Whose Knowledge and Whose Science, To Echo Sandra Harding
Echoing the sentiments of Harding, I read the works of Noether and Goeppert Mayer as liberatory attempts at epistemic subversions that involve the dismantling of the current scientific order from a position of precarity. For them to arrive at the conclusions they did about their work, they had to move outside the dominant thought-styles of their respective fields (Noether more so than Goeppert-Mayer) so as to analyze the scientific problems they were faced with. Then they had to re-articulate their analyses in a language that would make sense even to the most stubborn members of the scientific community. They flipped the order of linearity in mainstream mathematical and physical thought of that time, through the advancement of an alternate logic (though one still within the constraints of scientific logic), by reconstituting the explanatory theories current at that time. Therefore, they challenged the ‘normal’ progression of the mathematics and physics they worked in by advocating other ways for thinking about the hard problems they faced. This is a form of inscrutable transgression that uses subtlety in its undermining of an environment that devalued the contributions of women scientists and mathematicians through the continuous denial of academic positions and honors.
At the same time, one cannot forget that these women occupied positions of privilege even if they had to work at the margins of the scientific institutions of their time. They had had influential male mentors: beginning with their fathers, then colleagues, and a husband in the case of Goeppert Mayer, each of whom supported their work and provided them with unfettered access that most women could only dream of having. While their work should not be read against the background of their token privilege, their privileged position, in social as well as political proximity to the male elites in their fields, must not be underestimated. When they managed to achieve recognition later in life, the achievement was premised on how well they had managed the external political operations while working through subtle internal subversions, with the latter being mainly hidden.
One might assume that the two women have a ‘feeling’ (invoking Evelyn Fox Keller’s claim of Barbara McClintock in A Feeling for the Organism) for the scientific objects they work with in ways that have nothing to do with their gendered position, but everything to do with their creative contribution to the epistemic and institutional spaces they occupied. They indirectly contributed to an emergent scientific imaginary that shapes some of the popular themes in hard science fiction works focusing on the physical sciences, even if men rather than women produce most of these works. They overcame institutional and social hurdles through a combination of strategic alliances and dedication.
The practices of these two women scientists reconstitute notions of ‘competition’ and collaboration in their social milieu; they were responsible for contributing to the foundational ideas in physics and mathematics that facilitated the predictions and speculations of physics theories and objects that would later emerge in creative non-fiction and speculative science fiction. They also worked in collaboration with mostly male physicists and mathematicians through the exchange of ideas. However, that required political savvy and delicacy, since the women would have to find the best way to insist on the legitimacy of their ideas even when those ideas, however promising, could not yet be unequivocally demonstrated.
Mothers and female mentors were invisible in the life stories of these two women, at least in the accounts I have been able to access. Yet one could speculate that their mothers, married to fathers who were eminent in the scientific world, would have been aware of some of the more profound advances going on even if their knowledge were only peripheral. Little is known of the hidden services these mothers performed for their scientifically inclined husbands and daughters. More work would have to be done to unearth the influence of (non-scientific or scientific, in the case of Marie Curie) mothers on female scientists and mathematicians, since this could provide a clearer explication on the limits of agency that women are able to negotiate. In the case of Noether, she did eventually go on to mentor women mathematicians during her truncated time at Bryn Mawr.
Their respective contributions challenged the technoscientific thinking of their time, and continue to do so thereafter. In the case of Noether, symposiums were held in her honor decades after her death. Papers, in both mathematics and applied mathematics, have been produced that demonstrate the refinement and extension of her original ideas and methods. In the case of Maria Goeppert Mayer, the recognition came latterly in the form of a Nobel Prize in physics. She became the second woman to win it after Marie Curie, with the prize shared with two other male physicists, one of who later became her co-author. The implications of their work in mathematics and quantum physics can be read as knowledge not demanding of a ‘final control’ or finiteness, allowing for subjectivity even in objective analyses.
Final control, as invoked here, refers to the containment of an arbitrary value based on the assumption that there is an absolute standard of epistemology for objectivity to be situated. Instead, what is called for is the willingness to swim in the ocean of “dis-engagement” in a manner that is both mutual and unequal in the structuring of nature/culture, acknowledging that an attempt to draw boundaries can fail. Therefore, it appears that the only way to proceed is to see nature as a coyote with ever evolving meanings in its embodiment (Haraway 201). However, I doubt that either Noether or Goeppert Mayer would think in such Harawayan terms in relation to what they do, being, as they were, women who were trying to work within the constraints of fields that they were also pushing forward. Their works, on the other hand, took their own course outside the control of any one individual or institution, and therefore the representations of nature, as embodied by the ever refined epistemics, are never stable. The process, sociality, and product of scientific labor can be thought of as occupying a trinity of ontological-epistemological relations: image (the conceptual shape the science is imagined to contain); object (the image-subject interrogated); and mediation (existing/new medium whereby arguments undergo apophantic evaluation prior to transmission). This other layer of a triptych is also representative of how my arguments are played out in the next three sections of the essay.
Both women are the embodiment of cyborgian, scientific, and cultural multiplicities: their ideas challenge the privilege of the masculine insistence of its epistemic superiority through nuanced and subtle transgression; the transgression comes in the form of inserting the self into the stages of becoming that are integral to enabling the paradigmatic shifts necessary for the production of a “new” paradigm in physics. In other words, they rocked the boat quietly through subtle forms of intervention, one of which was to use their solid scientific productions to stake their intellectual claims. Depending on how one sees it, such subtlety may be considered insufficient for encouraging more female participations in similar knowledge production, and does nothing for the elimination of tokenism taken for representation of female successes.
However, the exceptionalism that is pervasive in the aforementioned tokenism masks other less overt forms of institutional devaluation and marginalization. Such exceptionalism required women to have greater confidence in their abilities so that they could earn respect through their work. The stress of working in such marginal environments cannot be underestimated, and parallels the adjunctification of the academy in the US institutions of today. While the world of physics does not need to be reminded that the most profound mathematical contributions that enabled the beginnings of a mathematical field theory, which led to the theory of quantum fields, came through the labors of some exceptional and better-known women scientists, the vital but less dramatic contributions from other women physicists and mathematicians get swept under the carpet and not paid the attention given to the same (or lesser) achievements of their male counterparts.
Therefore, the formal ontology underlying all physics theories across the classical and quantum spectrum is invariant to whatever social influences or conditions producing that ontology. In other words, the laws that determine the scientific theories proposed will not change regardless of the specific ideologies or institutional conditions of the scientists formulating them. One can read formal ontology as an androgynous figure that does not subscribe to any determinate categories of ideologies (gendered or otherwise) and is a composite of a series of different categories that could combine and split to re-emerge as an entirely new epistemic category. This formal ontology then attempts to communicate the physical reality, where the process of communication undergoes re-interpretations, which are open to multiple interjections from the most subjective to the more objective, but never in a form that is ‘detached.’ The interjections range from the sociology of its research programs, to the interactions between the scientists, to the philosophy of proofs. The androgynous, considered through the mathematical sciences, and therefore dissociated from direct social entanglement, is situated outside the phenomenon of the dichotomously gendered epistemology.
The androgynous figure of the abstract-exact science and its products are not undifferentiated, but instead, represent a form of non-normative differentiation, where the epistemics (factual interpretive areas of knowledge also making truth-claims) are differentiated from the ontological (formal equations, socially invariant, with dollops of objective truths). But even in their differentiation, epistemology and ontology exist as a Harawayan knowledge-hybrid cyborg. I ask the reader to consider scientific production as a product of androgynous epistemology. The dissemination of such an epistemology enables the breaking of the first layer of exclusivity by moving away from strident binary thinking to encourage an explosion of pluralistic standpoints.
While knowledge accumulation and production appear apolitical at the point of their making, the readings of the knowledge, and thus of the mathematics, can still be politically reconstituted, particularly for understanding why certain interpretations are able to generate greater acceptances over others. I argue that the creation of an androgynous mental model for thinking through current and developing mathematical epistemologies can potentially make political engagement feasible even for highly esoteric mathematics. I do this not by insisting on any lack of solutions and objective explication in mathematics, but by being cognizant of the fact that what underlies the objective is subjective social discursivity. As mathematics requires the mastery of specific knowledge genealogies, it and its ancillary epistemics can exist outside the context of institutional hierarchies once their bodies of knowledge are depoliticized. All participants in knowledge-making have equal access to making epistemological interventions, with the latter representing the decoupling of the condition of production from its final outcome.
Thinking about mathematics as an androgynous category enables the coupling of mathematical functions to real and imaginary numbers that could then be constituted as an entity to be read as containing social causality. It also allows the works of the two women to be read transgressively through the ejection of the subject from a fetishized gaze, and by refusing to subscribe to the exclusivity of relationships between modern mathematics and an alphabetized culture as the dominant causal argument for mathematical developments. The ancient mathematics of the Chinese and Indus Valley had demonstrated how highly sophisticated mathematics, particularly geometry, were generated alongside the development of pictographic forms of writings, and these mathematics were then applied as tools to mechanical arts and technology. What the ancient mathematics demonstrates rather simply is how the production of mathematics is not indifferent to cultural and social conditions.
To begin the process of transgressive reading, I will have to chip away at a Platonic idealization, an idealization that insists on mathematics being objectively detached and non-discursive. The Platonic idealization of mathematics represents mathematical solutions as inviolable and absolute. Instead, I want to advocate thinking about mathematics and the mathematical sciences as representative of the knowledge of constant becoming and re-invention. I intend for this process to return mathematics to a discourse that allows for more direct engagement with the why of physical materiality, instead of locating mathematics as distinct while still embodying the physical.
Therefore, I read mathematics outside the binary of determinism/indeterminism at the micro level, and determinacy/indeterminacy at the macro level. Such a re-interrogation of mathematics becomes increasingly pertinent in the age of new media and the digital medium that emphasizes a more multi-faceted representation of nature’s ontology. The Platonic ideal that infuses the method by which mathematics are thought about has located the latter in an abstractness that is no different from the written texts the humanists encounter regularly, a familiar yet unradical practice. According to Brian Rotman in his Mathematics as Sign, there is a privileging of the code as opposed to the more affective metacode, the privileging of alphabetic prejudice that erases the acceptance of the diagram as a useful and effective tool for doing mathematics. Hence, we end up with literal strings of very long derivations of symbols that are prone to errors. While there are diagramming methods in physics and also mathematics that try to illustrate particular concepts or intricate calculations, such as the Venn diagram for set theory, and the Feynman diagram for particle-field measurements, they are among the rarer instances of the invocation of the diagrammatic method for modern mathematical thinking. While I am not saying that the diagrammatic method is the only way to go, we must still consider why we privilege a specific form of mathematics over other possibilities. A more thorough excavation into the social-political history of mathematics could prove enlightening in this regard.
The method at work in the production of mathematics is not as non-discursive and objective as one thinks, particularly not in its illustration of physics. In fact, the work of Noether particularly, which would have extensive implications in the development of particle physics, had first utilized visualization (thinking about algebra in geometrical terms constitutes a form of visualization) in the process of integrating abstract algebra into geometry. This integration led to subsequent modern developments of abstract algebra. Such subsequent developments were then further developed by Noether and successive generations of mathematicians thereafter, into algebraic notations. These latter algebraic notations in turn have become so complex that the algebra produced is no longer intuitively imaginable without the deployment of visualizing software such as Maple and Mathematica. Is this embodiment of a trend towards abstraction a manner of demonstrating one is competent enough to be part of the old boys’ network of academic mathematics.
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Lee, C. (2013) Emmy Noether, Maria Goeppert Mayer, and their Cyborgian Counterparts: Triangulating Mathematical-Theoretical Physics, Feminist Science Studies, and Feminist Science Fiction. Ada: A Journal of Gender, New Media, and Technology, No.3. doi:10.7264/N3765C7S
This article has been openly peer reviewed at Ada Review.
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