Is Math Sexist??

You won’t look at math the same after reading this

Critiquing the theories and equations of math and science within a sociological context is one of the most interesting areas of feminist science studies. It’s hard to find research in this area, because it requires specialized knowledge of the subject matter as well as a sociology background. Often, we critique the historical and contemporary exclusion of women from these fields. For example, fields like Physics are dominated by white men who are still persistently blind to barriers to diversity . Furthermore, the concepts of rationality and logic in math seems infallible and rock solid. But remember, everything is man-made.

Resisting sociological contexts

A prevailing Western narrative is that “scientific discoveries” are “waiting” to be found—that they are independent of the observer and exist in isolation. That:

The assumed one-to-one correspondence between scientific theories and reality is used to bolster the further assumption that scientific entities are unmarked by discoverers: nature is taken to be revealed by, yet in independent of, theoretical and experiment practices (Barad 2006c) p. 41.

The development of Mathematics and Physics, from ancient times to modern day, though shaped by historical and social influences, have touted themselves as ‘neutral’ and separate from larger social applications.

While Newtonian mechanics has been conceptualized nature as a machine, 15^th-17^th century Europeans would have found the conceptualization to be offensive. There was strong resistance to the concept of the Copernican universe and the theory of relativity (Goldberg 1970 ; Sherwood 2011). The development and acceptance of widespread theories is often historically and context dependent—not a discovery waiting to be found.

Searching for the Perfect World

Historical neglect of social variables (e.g., sex, race, class) in mainstream science studies speak to the wish for science to reflect a so-called idealized, perfect world. In which the scientists and creator can lord over their work in a god-like fashion.

Predator-Prey model

In mathematical models of predatory-prey relationships (typically some deer on an island where wolves are trying to eat them), discount the myriads of reasons, forces, and actions behind the disappearance of certain species, these models focus primarily on changing rates of population sizes.

The most ubiquitous example is Newtonian mechanics whose principals were developed in a man-defined “perfect” world, including “ideal gases” or “frictionless” surfaces. In this world, energy is always conserved and relativistic effects are negligible. Much of this theoretical conception of physics was over-turned in the 20^th century. The notion of “observer-independent” calculations went out the window with quantum physics (Schiebinger 1999).

In quantum physics, everything is relative; measurements and observations change based on who is observing them and when. Most notoriously, light can be both a particle and a wave. Time is not linear, and space is not represented by Cartesian coordinates (Barad 2006e). Yet, quantum physics is often erroneously thought to apply solely to the “microscopic” world, and classical Newtonian physics to the other “macroscopic” world. However, quantum physics exceeds Newtonian physics in characterizing phenomenon in both large-scale and small-scale phenomena (Barad 2006d). Yet, Newtonian physics is more commonly taught to students.

Such simplifications might be justified for fundamental mathematical or physical calculations taught in undergraduate classes (though even differential calculus requires user-determined “boundary-setting” in calculations). Yet, laboratory experiments also require a definition of “boundaries” and “methods”.

One of the cornerstones of physics is discovering the origins of the universe. Biology, on the other hand, attempts to examine the influence of the physical world on actual phenomena (Schiebinger 1999). And these arguments for “objectivity” in physics were weakened when different values were used by different academic affiliations for the Hubble Constant (Bug 2003 ; Panek 2020).

Performing Science

Science is about establishing “worldly configurations” within a broader reality (Barad 2006b, pp. 87, 91). Fundamentally, science is about narrative building and connecting abstract rules to establish consistent principles for worldly phenomena.

For example, a laboratory experiment is often completed under highly controlled conditions. The results from this experiment are then derived from a certain version of the world as established by the creators of “science”. Their relevance to other experiences depends on how well the science was created. In a project that involves “field” observations—collecting samples from the natural environment or a population— may not seem “creative”. Yet, the scientist selects the sample population, frequency, conditions under which the data is interpreted, and builds a narrative based on the results. These narratives are then translated into principles, theories, and rules.

Even the actual performance of scientific experiments is subjective. There are numerous factors that influence the completion of a scientific experiment, from the person performing the work, to the apparatus, to the changing conditions in the laboratory environment.

As Barad argues, science is highly “performative”. Apparatus themselves can be re-worked, re-arranged, or rearticulated. “This is part of the creativity and difficulty of doing science: getting the instrumentation to work in a particular way for a particular purpose” (482). As many can contest, even for the most basic experiment, it is nearly impossible to replicate results exactly each time it is performed (hence the need to calculate averages and include standard deviations in results).

Furthermore, such assumptions are rooted in ableism. How science is “performed” is not thoroughly interrogated, because those that perform it are typically not conscious of the able-body that performs it. As far as physicists are concerned, the human body has no place in physical theory (Barad 2006a). Ultimately, feminist science scholars do not argue against experiments demonstrating physical phenomena but point out that viewing such items in isolation does a disservice to historical, anthropological explanations for things that cannot be modeled.

Math in a Vacuum

Feminist science studies face even more pushback for its examinations of mathematics, which is considered the fundamental cornerstones of scientific research. Mathematics is seemingly more “reproducible” than the life or social sciences, which have open-ended epistemological structures (Schiebinger 1999).

The “data” is assumed to be quantitative and thus “hard” not “soft” like the qualitative data that is stereotypically associated with the life and social sciences. It is assumed to be purely “logical” and “subjective”. Indeed, some basic math also translates to geometric phenomena. For example, 2 x 2 = 4 corresponds to a rectangle of 2 width and 2 length resulting in an area of 4. Even “negative numbers” can be translated to downward movement other concepts like imagery numbers are not.

However, such reasoning ignores that much of physics and mathematics research is “applied”. It characterizes biological phenomena with such books written by mathematicians and physicists as “Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering” by mathematician Steven H. Strogatz (1994), “Mathematical Aspects of Heart Physiology” by mathematician Charles S. Peskin (1975), or “Biological Physics” by physicist Philip Nelson (2020).

Indeed, mathematical conventions, scientific facts, equations, symbols, and principles are inherently meaningless until we apply some sort of meaning to them (Harding 1986). Often such “meaning” is assigned through metaphor (Lakoff and Núñez 2000). There is a rich history of mathematic symbol development, tied to Latin, alchemy, and physics. The plus sign likely derived from the Latin “et” meaning “and”. The square root symbol (√) originated from the Latin word radix (“root”). The modern integral sine an elongated S, refers to the Latin term for summa for sum. Indeed, there was sort of a ‘war’ over the development of the integral sign. Modern integral signs stem from Gottfried Wilhelm Leibniz while Isaac Newton developed his notation (dots over variables).

Math’s feminine/masculine dichotomy

Now this is where things get crazy. A 1921 article attempted to read erotic meaning into current math symbols. Another 1957 manuscript provides interesting insight into the development of sex, gender, and mathematical symbols.

It is also of interest to note that in ancient times all odd numbers were regarded as male, and all even numbers as female. This may be connected with the fact that modern logicians have found that all of mathematics can be deduced from three basic concepts, “1,” “0,” and “+”. In ancient times, these symbols represented the male and female principles, along with the symbol of eternity, or copulation—the joining of these sexual principles. (p54-55).

The article further links the concept of “divine justice” to a key influence on early mathematical development by drawing on readings of Pre-Socratic, Platonic, and Neoplatonic philosophy. It also connects developments of geometry and mathematics in antiquity to practical concerns, such as the fair measurement of land and the quantification of goods for trade:

The intimate connection between the quest for all-explaining logical or mathematical formulae and problems of sexual harmony is also indicated in the fact that in ancient times the universe was believed to operate according to moral principles. What we now call “scientific laws” were then identified with moral laws immanent in the universe. That is to say, the cosmos was believed to be ordered by a divine justice (p55).

If we follow this interpretation, mathematics can be understood as a striving toward order, fairness, and a form of “divine” justice. If “feminine energy” is conceptualized as a form of “lack,” in Freudian interpretations then the development of “imaginary numbers” can be read as a way of addressing or compensating for this absence. Beyond Freud, however, it appears that broader cultural conceptions of masculinity and femininity in mathematics may have influenced mathematical development dating back to ancient times.

(The imaginary number is supposed to represent a “hidden dimension”, necessary for a system to function—often used in electricity applications in physics.)

The French psychoanalyst and philosopher Jacques Lacan frequently read sexual meaning into other commonly employed mathematical and symbolic notation, including Greek letters, to formalize aspects of his theory of desire. In Lacan interpretations, the uppercase Φ (Phi) [used to represent magnetic flux in physics equations] is often used to denote the symbolic phallus, r. In contrast, lowercase φ (phi) [often used in waves and optics equations in physics] is sometimes used to represent the imaginary or partial phallus, associated with a perceived lack.

The most famous Lacan interpretation though concerns the imaginary unit, defined as i= squareroot(−1​). Specifically, the imaginary number has been symbolically linked to the male erectile organ. Imaginary numbers lack geometrical equivalents and cannot be visualized like say the square root of four which can be represented via rectangles in rectangles.

Within the Lacanian psychoanalytic configuration, any image, in particular visual image, of the erectile organ, including that of an “erectile organ,” can only be an image of the signifier […] This signifier itself is fundamentally, irreducibly non-visualizable. At the limit, this signifier – that is, its ultimate structure of, once again, the signifier designated as the erectile organ – may be inconceivable by any means, which epistemology or de-epistemization, and specifically de-visualization, are crucial to most of Lacan’s key concepts. Indeed, this signifier is in fact or in effect unnameable, for example, again, as the erectile organ, or the phallus (page 150-151)

Arkady Plotnitsky, however, argues that Lacan was not directly referring to the erectile organ, since he does not use math to ‘prove’ this.

First – the structural analogy – the erectile organ, as a signifier, or indeed the signifier (in Lacan’s sense), belongs to and gives rise to a psychoanalytical system different from the standard one or ones (based on misreadings of Freud, conceivably to a degree by Freud himself), and to a different formalization – “algebra” – of psychoanalysis, a formalization that is more effective both conceptually and in terms of the ensuing practice. Second – the epistemological analogy – the erectile organ, as a signifier, or again, the (Lacanian) signifier of this system, while and in a sense because it governs the economy of the system, can only be approached by means of tentative, oblique and ultimately inadequate metaphors. It is ultimately inaccessible, along with its signified and its referent, at the limits inaccessible even as that which absolutely inaccessible but definable in terms of independent properties and attributes (154-155)

The Pythagorean Table of Opposites

The Pythagorean Table of Opposites (Aristotle) associates the “feminine” with “feared” concepts such as “infinite” and “oblong” and “evil”. The discovery of irrational numbers (which cannot be expressed as simple fractions, such as √2 ≈ 1.41421…) disrupted earlier notions of “divine” mathematical order and was, in some interpretations, associated with the feminine.

Conclusion

Math theories, equations, and symbols were developed in a long line of male dominated fields. Often, they assume ideal conditions that are rare in the real world. Because they assume ideal conditions, historical neglect of sociological variables in many research applications has been rampant.

While Freudian readings may interpret mathematical developments like chaos theory and imaginary numbers as compensating for a “missing piece”—a masculine response/rationally ‘imposed’ solution to perceived feminine chaos—modern mathematical interpretations may instead suggest an embrace of this so-called feminine mathematical “energy.”

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References

Barad, Karen. 2006a. “Agential Realism: How Material-Discursive Practices Matter.” In Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning, Durham & London: Duke University Press, 132–85.

———. 2006b. “Diffractions: Differences, Contingencies, and Entanglements That Matter.” In Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning, Durham & London: Duke University Press, 71–94.

———. 2006c. “Meeting the Universe Halfway.” In Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning, Durham & London: Duke University Press, 41.

———. 2006d. “Niels Bohr’s Philosophy-Physics: Quantum Physics and the Nature of Knowledge and Reality.” In Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning, Durham & London: Duke University Press, 97–131.

———. 2006e. “Spacetime Re(Con)Figurings: Natural cultural Forces and Changing Topologies of Power.” In Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning, Durham & London: Duke University Press, 223–46. 978-0-8223-8812-8.

———. 2013. “Posthumanist Performativity: Toward an Understanding of How Matter Comes to Matter.” In Women, Science, and Technology: A Reader in Feminist Science Studies, eds. M. Wyer et al. New York: Taylor & Francis Group., 473–94.

Bug, Amy. 2003. “Has Feminism Changed Physics?” Signs 28(3): 881–99.

Desmonde, W. H. (1957). Eros and Mathematics: Some Speculations. American Imago, 14(1), 53–56.

Goldberg, Stanley. 1970. “In Defense of Ether: The British Response to Einstein’s Special Theory of Relativity, 1905–1911.” Historical Studies in the Physical Sciences 2:

Harding, Sandra G. 1986. The Science Question in Feminism. Ithaca and London: Cornell University Press.

Lakoff, George, and Rafael E. Núñez. 2000. “Introduction: Why Cognitive Science Matters to Mathematic.” In Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being, New York, NY: Basic Books, 1–11.

Panek, Richard. 2020. “How a Dispute over a Single Number Became a Cosmological Crisis.” The Scientific American.

Schiebinger, Londa. 1999. “Physics and Math.” In Has Feminism Changed Science?, Cambridge, MA: Harvard University Press, 159–233.

Sherwood, Steve. 2011. “Science Controversies Past and Present.” Physics Today 64.