Damian G. Kelty-Stephen, Assistant Professor at Grinnell College lifts the lid on gender science research, including the work of Anne Fausto-Sterling and the role of multifractal geometry in predicting the development of a gender stereotype
Gender science epitomises the complexity of goal-directed experience: it exemplifies nonlinear interaction across many scales of space and time. Nonlinear dynamics provides a particularly good geometry – called “multifractal” – for quantifying, modelling, and predicting such interactions across scales of space and time. That sounds complex which I regret, but I think multifractal geometry is complexity that gender science needs.
Introducing gender science
For what it’s worth, simplicity in scientific advertising has rarely been good news for gender science. First, developmental science tried to boil gender down into “nature” versus “nurture” probably because the science did not know better. Next, it continued boiling gender down into nature to protect gender diversity against bigoted appeals to unlearn or opt out of non-heterosexual and non-cis identity.
Now, taking oversimplified “born that way” defences of gender to dangerously literal extremes, the Trump administration wants to enact a legal definition tying gender to biological sex. My piece here is about gender, so I will just recommend Sarah Richardson’s book Sex Itself for readers interested in how sex is not a simple function a so-called “sex chromosome.” Generally calling for more nuance in our discourse about gender, I write this piece specifically to recommend multifractal geometry as one of many tools that nonlinear dynamics has to offer an account of gender respectful of gender’s complexity.
The current wisdom in development psychobiology is that nature and nurture are completely entangled. They interact at many scales, to such a degree that they are not even separate. Genetic “nature” exerts no effects separate from experiential “nurture.” Epigeneticists in the tradition of Gilbert Gottlieb have shown any simple accounting of “what genes do” separate from “what you learn” absurd, rendering weary statements that “nature and nurture interact” meaningless. Whereas developmental psychology once only envisioned maturational unfoldings of a genetic programme, it now respects the “active child” driving its own trajectory, a bustling organism reaching out to design its own experiences.
And intuitive as it is to imagine an “active child” exploring the playground and leaving a charming path of exploratory destruction in its wake, developmental psychobiology has struggled to make as clear the epigenetics wrapping everything we thought was “natural” in experientially produced constraints. But epigenetics has been very clear about its complex truths: genes only do what cellular contexts prompt, and behaviour has cascading effects rippling across time and down from the full-body organismic scale, traversing physiological terrain, to the finest systematic changes in gene expression.
The research of Anne Fausto-Sterling
Gender science is at the forefront of researching this developmental tangle wrought by the active child. Anne Fausto-Sterling explores the rich pattern of touch-based experiences and interactions that children have with their caretakers long before children learn the social codes of gender. With such rich haptic experiences crafting all other aspects of organism development, it becomes less tenable that genetic codes should proceed so smoothly – through the creative chaos of a developing child’s activity – to cleanly transmute into gender outcomes.
Fausto Sterling aligns her work with the expectation that gender emerges from the necessarily intersectional experience of a developing organism. Intersectionality refers to a pattern of several overlapping constraints at very many scales, from the cultural to the biological, and gender is no simple sum of these constraints – gender is rather the result of the interaction these multi-scale constraints. Gender is neither coded by genes nor a fluke of nurture, and it is instead emergent from the self-same interactions governing the rest of organism-wide development.
Multifractal geometry – predicting a gender stereotype
To unlock the creative chaos of this active child, Fausto Sterling and Adrienne Harris have both pointed gender science towards nonlinear dynamics. Nonlinear dynamics offers mathematical lenses for modelling interactions across scales. One such intriguing lens is multifractal geometry. Nonlinear interactions across scale generate “multifractal structure.” When development follows from nonlinear interactions across scale, developing systems exhibit very many large slow changes and progressively fewer and smaller fast changes. Using what mathematicians call an “inverse power law,” we can quantify progressive decay in the relationship between size-of-change with speed-of-change.
Intriguingly, power-laws are “scale invariant,” meaning that the decay of size-of-change with speed-of-change is the same throughout, suggesting widespread permeability of entire organism to epigenetic-like interactions from grand-scale behaviours to finest gene expressions. Power laws are “fractal” because power-law exponents are often not integers but fractions. Now, nonlinear cross-scale interactions do not just produce one power law but multiple power laws. So, if we study development with an eye to how many and how strong these power-laws we find in time-series of measured fluctuations, then we might get to test the hypothesis that the variety of power-laws (i.e., the multiple fractal patterns: multifractality) could predict the gender outcomes.
Surely, mathematizing gender sounds like a fool’s errand. However, the mathematics that speaks to the convolution and complexity of subtle constructs like gender can speak to interactions across scales even in a brief span of time. You may only need a 2000-word narrative with just enough information to suggest a gender stereotype about an ambiguously-named protagonist and then measure how long people take to read each word. I did just that with collaborators Hannah Brown, Chase Booth, Lizzie Eason, and Sebastian Wallot. We asked whether multifractality geometry in word-reading times could predict the development of a gender stereotype.
When readers reached the 1000th word with a plot twist thwarting the cued gender stereotype and showing the ambiguously named protagonist having an unexpected gender, readers slowed down to gather their startled thoughts before pressing forward again. Multifractal geometry of word-readings series up to that point predicted individual readers’ differences in how much and how long readers slowed down. After almost as brief a text as appears here, multifractal geometry allowed us to predict the development of a gender stereotype. Interestingly, the startled readers went on to read the remaining text with markedly increased multifractal structure.
Certainly, learning new math sounds dreary and intimidating, and maths seems too harsh and unfeeling a thing to reveal the heart of our experience of gender. But simplicity is cheap. Nonlinear-dynamical complexity respecting the known intersectionality of gender may reap quicker insights.
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Damian G Kelty-Stephen
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