The quarrels of popes and kings, with wars and pestilences, in every page; the men so good for nothing and hardly any women at all – it is very tiresome.
Jane Austen
It took about two hours for Daina Taimina to find the solution that had eluded mathematicians for over a century. It was 1997, and the Latvian mathematician was participating in a geometry workshop at Cornell University. David Henderson, the professor leading the workshop, was modelling a hyperbolic plane constructed out of thin, circular strips of paper taped together. ‘It was disgusting,’ laughed Taimina in an interview.1
A hyperbolic plane is ‘the geometric opposite’ of a sphere, explains Henderson in an interview with arts and culture magazine Cabinet.2 ‘On a sphere, the surface curves in on itself and is closed. A hyperbolic plane is a surface in which the space curves away from itself at every point.’ It exists in nature in ruffled lettuce leaves, in coral leaf, in sea slugs, in cancer cells. Hyperbolic geometry is used by statisticians when they work with multidimensional data, by Pixar animators when they want to simulate realistic cloth, by auto-industry engineers to design aerodynamic cars, by acoustic engineers to design concert halls. It’s the foundation of the theory of relativity, and ‘thus the closest thing we have to an understanding of the shape of the universe’.3 In short, hyperbolic space is a pretty big deal.
But for thousands of years, hyperbolic space didn’t exist. At least it didn’t according to mathematicians, who believed that there were only two types of space: Euclidean, or flat space, like a table, and spherical space, like a ball. In the nineteenth century, hyperbolic space was discovered – but only in principle. And although mathematicians tried for over a century to find a way to successfully represent this space physically, no one managed it – until Taimina attended that workshop at Cornell. Because as well as being a professor of mathematics, Taimina also liked to crochet.
Taimina learnt to crochet as a schoolgirl. Growing up in Latvia, part of the former Soviet Union, ‘you fix your own car, you fix your own faucet – anything’, she explains.4 ‘When I was growing up, knitting or any other handiwork meant you could make a dress or a sweater different from everybody else’s.’ But while she had always seen patterns and algorithms in knitting and crochet, Taimina had never connected this traditional, domestic, feminine skill with her professional work in maths. Until that workshop in 1997. When she saw the battered paper approximation Henderson was using to explain hyperbolic space, she realised: I can make this out of crochet.
And so that’s what she did. She spent her summer ‘crocheting a classroom set of hyperbolic forms’ by the swimming pool. ‘People walked by, and they asked me, “What are you doing?” And I answered, “Oh, I’m crocheting the hyperbolic plane.”’5 She has now created hundreds of models and explains that in the process of making them ‘you get a very concrete sense of the space expanding exponentially. The first rows take no time but the later rows can take literally hours, they have so many stitches. You get a visceral sense of what “hyperbolic” really means.’6 Just looking at her models did the same for others: in an interview with the New York Times Taimina recalled a professor who had taught hyperbolic space for years seeing one and saying, ‘Oh, so that’s how they look.’7 Now her creations are the standard model for explaining hyperbolic space.
Taimina’s fundamental contribution to the study of the hyperbolic plane does not, of course, close a data gap that directly relates to women. What this story shows instead is that the case for closing the gender data gap extends beyond women’s rights. Closing the data gap, as we’ve seen from the impact women have in politics, in peace talks, in design and urban planning, is good for everyone. Even mathematicians.
When we exclude half of humanity from the production of knowledge we lose out on potentially transformative insights. Would male mathematicians have come up with Taimina’s elegantly simple solution on their own? Unlikely, given how few men are keen crocheters. But in Taimina the traditionally feminine skill of crochet collided with the traditionally masculine sphere of maths. And it was this collision that led to the problem that many mathematicians had given up on as a lost cause finally being solved. Taimina provided the link the male mathematicians were missing.
All too often, however, we don’t allow women to provide that link. And so we continue to treat too many of the world’s problems as insoluble. Like Freud, we continue to ‘knock our heads’ against what seem like riddles. But what if, like representing the hyperbolic plane, these problems aren’t insoluble? What if, like the problems in broadcast science competitions, all they are missing is a female perspective? The data that we do have is unarguable: as we continue to build, plan and develop our world, we have to start taking account of women’s lives. In particular, we have to start accounting for the three themes that define women’s relationship with that world.
The first of these themes is the female body – or, to be precise – its invisibility. Routinely forgetting to accommodate the female body in design – whether medical, technological or architectural – has led to a world that is less hospitable and more dangerous for women to navigate. It leads to us injuring ourselves in jobs and cars that weren’t designed for our bodies. It leads to us dying from drugs that don’t work. It has led to the creation of a world where women just don’t fit very well.
There is an irony in how the female body is apparently invisible when it comes to collecting data, because when it comes to the second trend that defines women’s lives, the visibility of the female body is key. That trend is male sexual violence against women – how we don’t measure it, don’t design our world to account for it, and in so doing, allow it to limit women’s liberty. Female biology is not the reason women are raped. It is not the reason women are intimidated and violated as they navigate public spaces. This happens not because of sex, but because of gender: the social meanings we have imposed on male and female bodies. In order for gender to work, it must be obvious which bodies elicit which treatment. And, clearly, it is: as we’ve seen, ‘the mere sight of a woman’ is enough for the viewer to ‘immediately elicit a specific set of associated traits and attributions’.8 To immediately class her as someone to speak over. Someone to cat call. Someone to follow. Someone to rape.
Or maybe just someone to make the tea. Which is where we run into the third trend, which is perhaps the most significant in terms of its impact on women’s lives worldwide: unpaid care work. Women are doing far and away more than our fair share of this work – this necessary work without which our lives would all fall apart. And, as with male violence against women, female biology is not the reason women are the bum-wiping class. But recognising a child as female is the reason she will be brought up to expect and accept that as her role. Recognising a woman as female is the reason she will be seen as the appropriate person to clear up after everyone in the office. To write the Christmas and birthday cards to her husband’s family – and look after them when they get sick. To be paid less. To go part-time when they have kids.
Failing to collect data on women and their lives means that we continue to naturalise sex and gender discrimination – while at the same time somehow not seeing any of this discrimination. Or really, we don’t see it because we naturalise it – it is too obvious, too commonplace, too much just the way things are to bother commenting on. It’s the irony of being a woman: at once hyper-visible when it comes to being treated as the subservient sex class, and invisible when it counts – when it comes to being counted.
There is one more trend I kept coming across while writing this book: the excuses. Chief amongst these is that women are just too complicated to measure. Everyone was saying this, from transport planners, to medical researchers, to tech developers: they were all knocking their heads up against Freud’s riddle of femininity and coming away baffled and defeated. Female bodies are too unharmonious, too menstrual and too hormonal. Women’s travel patterns are too messy, their work schedules are too aberrant, their voices are too high. Even when, in the early twentieth century, influential Swiss architect Le Corbusier was devising a standard human model for use in architecture, the female body was ‘only belatedly considered and rejected as a source of proportional harmony’,9 with humanity instead represented by a six-foot man with his arm raised (to reach that top shelf I can never reach).
The consensus is clear: women are abnormal, atypical, just plain wrong. Why can’t a woman be more like a man? Well, apologies on behalf of the female sex for being so mysterious, but no, we aren’t and no we can’t. And that is a reality that scientists, politicians and tech bros just need to face up to. Yes, simple is easier. Simple is cheaper. But simple doesn’t reflect reality.
Back in 2008, Chris Anderson, then editor of tech magazine Wired, penned an article headlined ‘The End of Theory: The Data Deluge Makes the Scientific Model Obsolete’.10 We can ‘stop looking for models’, Anderson claimed. There is now a better way. Petabytes [that’s 1,000 million million bytes to you and me] allow us to say: ‘Correlation is enough.’ We didn’t need to hypothesise about anything, we just needed to crunch the numbers – or, more accurately, ‘let statistical algorithms’ crunch the numbers. In the era of Trump, Brexit and Cambridge Analytica, this seems Pollyanna-ish to say the least, but even before these data scandals it should have been obvious that his claims were hubristic, because back in 2008 we had even less data on women than we have now. And when you’re missing out half the global population in the numbers you feed your statistical algorithms, what you’re actually creating is just a big mess.
Anderson holds up Google as an exemplar of what he dubbed ‘The Petabyte Age’, singing the praises of its ‘founding philosophy’ that ‘we don’t know why this page is better than that one: If the statistics of incoming links say it is, that’s good enough. No semantic or causal analysis is required. That’s why Google can translate languages without actually knowing them (given equal corpus data, Google can translate Klingon into Farsi as easily as it can translate French into German).’ Except, as we’ve seen, Google actually can’t translate very well at all, even ten years later. That is, if you care about women being erased from language.
So. Not so simple after all.
Anderson is right about one thing though. There is a better way. And it’s a pretty simple one: we must increase female representation in all spheres of life. Because as more women move into positions of power or influence, there’s another pattern that is becoming even more apparent: women simply don’t forget that women exist as easily as men often seem to.
Women in the film industry are more likely to employ women.11 Female journalists are significantly more likely to centre a female perspective and to quote women.12 Female authors do the same: 69% of US female biographers wrote about female subjects in 2015, compared to 6% of male biographers.13 The emphasis by women on female voices and perspectives extends to the academy. Between 1980 and 2007, female history faculty in the US rose from 15% to 35%14 – meanwhile across a similar time period (1975-2015), US history faculty specialising in women’s history rose from 1% to 10%15 – a tenfold increase. Female academics are also more likely to assign female authors to their students.16
Then there’s how women might interpret history: in a 2004 Guardian article comedian Sandi Toksvig wrote about how when she was studying anthropology at university one of her female professors held up a photograph of an antler bone with twenty-eight markings on it. ‘This,’ she said, ‘is alleged to be man’s first attempt at a calendar.’ We all looked at the bone in admiration. ‘Tell me,’ she continued, ‘what man needs to know when 28 days have passed? I suspect that this is woman’s first attempt at a calendar.’17
When Britain’s EU Withdrawal Bill was announced in 2017, the Human Rights Act was explicitly excluded from alteration – but it took a woman, Maria Miller, the Conservative MP for Basingstoke, to force the government to agree to make a statement requiring that Brexit is also compatible with the Equalities Act.18 Without this concession, a whole range of women’s rights could be scrapped after Brexit, with no avenue for legal redress. In the workplace it is often women, like developmental biologist Christiane Nusslein-Volhard with her foundation to help female PhD students with children, who are putting in place solutions to structural male bias – a bias which male leaders have overlooked and ignored for decades.
Women are also leading the way when it comes to closing the gender data gap. A recent analysis of 1.5 million papers published between 2008-15 found that the likelihood of a study involving gender and sex analysis ‘increases with the proportion of women among its authors’19. The effect is particularly pronounced if a woman serves as a leader of the author group. This concern for women’s health also extends to the political sphere: it took a woman (Paula Sherriff, the Labour MP for Dewsbury) to set up the UK’s first All-Party Parliamentary group for women’s health in 2016. It was two rogue female Republicans who scotched Donald Trump’s attempts to repeal Obamacare (which would have disproportionately impacted on women), voting three times against his proposals.20
And women are making a difference in politics more generally. It was two women, Melinda Gates and Hillary Clinton, who spearheaded the UN-backed organisation Data2x that is aimed specifically at closing the global gender data gap. It was a woman, Hillary Clinton, who insisted on going to Beijing in 1995 to make the now famous declaration that ‘Human rights are women’s rights, and women’s rights are human rights.’
And when the worst happens, women are there too, filling in the gaps left by male-biased disaster relief. Researchers found that the ‘masculine and muscular image[s] of relief workers’ that dominated the media post-Katrina were belied by women who were ‘working tirelessly and courageously’ behind the scenes.21 The same thing has happened in Puerto Rico, all but abandoned by the US government after Hurricane Maria devastated the region in 2017. ‘The reality is that when you go to communities, mostly it is women as leaders and as community organizers,’ Adi Martinez-Roman, executive director for a non-profit that provides legal assistance to low-income families, told journalist Justine Calma.22 These women have collected data by ‘wad[ing] into flooded neighbourhoods’ and canvassing the abandoned communities.23 And they have developed and provided evidence-based solutions. They’ve set up soup kitchens. They’ve raised money and rebuilt roads. They’ve distributed ‘solar-powered lights, generators, gas, clothes, shoes, tampons, batteries, medication, mattresses, water’. They set up ‘free legal aid societies to help families navigate the confusing and ill-designed processes required to file FEMA claims’. They’ve even managed to source some communal, solar-powered washing machines.
The solution to the sex and gender data gap is clear: we have to close the female representation gap. When women are involved in decision-making, in research, in knowledge production, women do not get forgotten. Female lives and perspectives are brought out of the shadows. This is to the benefit of women everywhere, and as the story of Taimina, the crocheting maths professor shows, it is often to the benefit of humanity as a whole. And so, to return to Freud’s ‘riddle of femininity’, it turns out that the answer was staring us in the face all along. All ‘people’ needed to do was to ask women.