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M y fourth-grade fantasy was to have five older brothers and one twin brother; in reality, I had two little sisters. Sometimes in public I would slur my sister Debbie’s name so it sounded like “Danny.” Boys got to have more adventures and therefore more fun; pretending to have a brother was the closest I could get to both.

Having read many books for kids over the years with my now-teenaged daughter and son, I see that a similar belief about the relative potential for girls and boys to have adventures still holds true in children’s literature, regardless of strides made in the nonfictional world. While awareness of gender gaps is nothing new, I want to talk specifically about an issue in children’s chapter books I’ll call “the golden gender ratio.” Hearkening back to the ancient Greeks, the golden ratio is a mathematical relation deemed pleasing in art, architecture, and design. When a line is divided into two parts in the proportions of this ratio, the length of the longer segment divided by the length of the shorter segment is equal to the length of the whole line divided by the length of the longer segment, a ratio of approximately 1.618:1. Classic examples can be found in the layout of the Parthenon and Da Vinci’s The Last Supper.

Applying the ratio to middle grade children’s literature, we derive the following formula: For every smart/brave/adventurous fictional heroine, the author must supply 1.618 boys.

Applying the ratio to middle grade children’s literature, we derive the following formula: For every smart/brave/adventurous fictional heroine, the author must supply 1.618 boys. Rounding to the nearest whole number for human purposes, we see that adventurous trios must be 2:1 male: female. Or, to retain our original mathematical precision, novels for children must contain one smart/brave/adventurous girl, one smart/brave/adventurous boy, and one somewhat lacking boy, i.e., 1.618 boys.

While this pronouncement is based on the books brought home for and by my own two kids, an admittedly small and idiosyncratic sample, it was validated by a recent analysis of the hundred most popular children’s picture books of 2017, which revealed gender disparities along similar lines. Reporting on research conducted by the Observer newspaper and Nielsen market research company, Donna Ferguson notes in The Guardian that main characters with speaking parts were twice as likely to be male, and, “on average, there were three male characters present in each story for every two females featured.”

The article goes on to quote a picture book publisher as saying, “If anybody wanted to put a weak girl in one of our books, I’d whack them over the head.” The problem, however, is not that girls are portrayed as weak — in fact, the opposite is often true — but rather that they are not portrayed enough. The example given of “new titles which break with tradition” serves only to underscore this fact: Julia Donaldson’s The Detective Dog, 2017’s bestselling picture book, features “a brave female dog [who] helps out a male sidekick and a male teacher.”

The problem is not that girls are portrayed as weak — in fact, the opposite is often true — but rather that they are not portrayed enough.

Of course, not every recent popular adventure series for kids follows the male to female golden ratio (Lemony Snicket’s A Series of Unfortunate Events series and Michael Buckley’s The Sisters Grimm series both feature two girls and a boy) but focusing more on girls is unusual enough that authors who do so, at least male authors, will be asked about it. Daniel Handler (Lemony Snicket’s given name) says in his essay, “The Righteous Anger of Girls,” that he writes more often about girls intentionally, because girls face more obstacles, which inherently makes a story more interesting. He writes, “A man walking alone down a road at night may or may not be a good story; turn him into a 12-year-old girl, and it’s already gripping.” Buckley, on the other hand, said in an interview that he is “often called a writer for girls” despite considering himself “a writer for kids — boys and girls.” Even so, he notes that “hands down,” his boy character, the fairy Puck in human form, is “the most popular character in the series. I get more fan mail about him than anyone else.” Let’s hope it’s because of Puck’s retractable wings.

The prime example of a series that embodies the golden gender ratio is, yes, Harry Potter. Though it seems unfair to pin the establishment of the literary gender gap on J.K. Rowling, is it plausible that the overwhelming popularity of the Harry Potter books set the ratio in stone? Or are these books merely emblematic of a larger, preexisting cultural bias?

In the Harry Potter series and subsequent books featuring adventurous trios, if the alpha male is masterful in some traditionally male way — for example, in terms of bravery or skill in battle, as is Harry — then the second boy should be less so, as is Ron. In other words, one of the two main male characters should have qualities traditionally associated with the feminine, perhaps to soften or camouflage the overtly unequal nature of the ratio — and, according to my theory, to make the ratio more approximately approach 1.618:1. For example, in Rick Riordan’s The Lightning Thief, Grover, a sensitive satyr, establishes, of all things, an “empathy link” with the protagonist, Percy Jackson. (What could feminize/reduce someone to .618 of a boy more than that?) Grover also cries and stress eats and is less brave than both Percy and Annabeth, who happens to be the demigod daughter of Athena and thus exceptionally smart and skilled in battle. Likewise, in Nicholas Gannon’s The Doldrums, Adélaïde is the boldest of the three main characters, the most embracing of adventure; Archer, descendant of explorers on his father’s side, is also brave, though limited in what he can actually do by his overprotective mother; and Oliver, Boy Number Two, is simply afraid.

An astute reader might reasonably wonder: What is the role of the smart, brave girls in these books? Often the girl’s strengths are somehow distinct from the boys’ and thus vital for the team to be able to embark on their adventures at all — and ultimately to succeed — but Boy Number One is nevertheless the protagonist, the one for whom the outcome of the trio’s quest matters most. Archer, Adélaïde, and Oliver plan to rescue Archer’s grandparents from an iceberg (though .618 Oliver isn’t so sure). Brave, smart Annabeth nurses Percy back to health both before and after the trio’s quest — that is, Percy’s quest — to retrieve Zeus’s stolen lighting bolt and prevent a war between Zeus and Poseidon, Percy’s father. Before they set off, Annabeth tells Percy, “I’ve been waiting a long time for a quest, seaweed brain… If you’re going to save the world, I’m the best person to keep you from messing up.” Is the girl character merely the strong woman behind the successful man — the child version of putting one’s husband through dental school? Are the girl lead characters mostly there to support the boys in having their personal growth/epiphany so their manly courage can finally be revealed?

Is the girl character merely the strong woman behind the successful man — the child version of putting one’s husband through dental school?

Kate, the female lead character in Trenton Lee Stewart’s The Mysterious Benedict Society, consistently leads the way in all things physical and daring, but toward the end of the book the author points to how well the boys, Reynie and Sticky, are coming along. When Kate is captured by the evil Executives, her physical strength and combat know-how can no longer save her or the team; meanwhile, up in a tower with the main villain, “despite his terror, in the face of the Whisperer’s irresistible power, Sticky had resisted with all his might. He would never have done that if not for Reynie’s urging.”

Here we approach an interesting divide, wherein some female lead characters are both smart and brave (such as Adélaïde and Annabeth), while others are allowed to be smart and brave but not the best at both, in the way that Hermione is smarter than Harry but less skilled in battle, as if to ensure the girl’s magnificence approaches but never surpasses the lead boy’s magnificence. For example, Kate is by far the bravest, strongest, and most physically adept of the main trio of older kids, but she is by no means as brainy as Reynie and Sticky. (A fourth child, a toddler girl, seems mostly extraneous until the end, though she goes on to play a key role in subsequent books.)

And yet, despite his allotted magnificence Boy Number One often has some kind of deep-seated wound he battles internally in addition to the external menace the trio is battling. Most of these characters, girls and boys alike, have been orphaned, abandoned, or otherwise failed by their parents, and though the lead girl has often also endured hardship, the emotional impact of the lead boy’s ongoing struggles tends to trump hers. The aforementioned picture book publisher’s threat to whack creators of weak girls on the head notwithstanding, a de facto ban on weak girls in children’s books has resulted, however unintentionally, in a narrowing of possibilities and emotional development available to girls.

A de facto ban on weak girls in children’s books has resulted in a narrowing of possibilities and emotional development available to girls.

If girl characters must now be smart and brave and skilled, if they must start out strong and remain strong, then they are allowed only the slimmest of margins for personal growth, the traditional raison d’être of character-based literature. M.K., the little sister in S.S. Taylor’s The Expeditioners series, is not only “one of the best inventors of the New Modern Age,” according to the three siblings’ late father, but bold enough to bean two menacing government agents on the head with a wrench, thus instigating the trio’s escape into adventure. How could such a brilliant, badass ten-year-old possibly improve from there? Though boys in real life may have limited opportunities to explore and express emotions, boy characters, on the other hand, regardless of their strengths at the outset, seem to have more opportunities to grow and change than do girl characters.

A difference between books for middle-grade readers and young adult novels is the sex — which translates, as far as the golden gender ratio is concerned, into the two boys having sex and the girl feeling left out. In a non-representative sample of YA novels — ones my daughter liked enough for me to want to read — we see some interesting twists. In Andrew Smith’s Grasshopper Jungle, for example, the 2:1 ratio allows the main male protagonist to have sex with both his girlfriend and his male best friend when they’re trying to survive the imminent end of the world. (He does feel bad about this, though not quite bad enough to stop.) In Jandy Nelson’s I’ll Give You the Sun, a twin sister and brother both secretly like the same boy, their new next-door neighbor. He — spoiler alert — eventually reveals he is gay and therefore, at different stages of the book, appears to be a possible romantic partner for both twins.

So, where are the lesbians? That gay characters for teen readers seem to be predominantly male (my daughter also recommended Bill Konigsberg’s Openly Straight) appears to be another corollary of the golden gender ratio’s tacit notion that teens as well as younger children are more inclined to read about boys. Theories abound as to why teen girls enjoy reading about gay male characters, including that gay boys are seen as more sensitive and less threatening than heterosexual boys — like a boy but also like a girl’s best friend, somewhere between a girl and a boy — perhaps, dare I say, .618 of a boy.

I repeat, a little louder this time, where are the lesbians?

So, I repeat, a little louder this time, where are the lesbians? To find them I turned to the internet, which offered up lists of books with lesbian and bi characters — though obviously the need for such lists highlights the problem — which led me to more questions. Why do so many of the lesbian or bi characters have male-leaning or gender-neutral names (Cameron, Colby, Charlie, Taylor, Alex, Trout, Jamie, Louie)? Is this reflective of real life, or yet another nuance of the golden gender ratio, even in books clearly marketed to girls?

I often think about how we are teaching children to see the world. Back in second grade I remember being shocked when my teacher explained to the class that we must use the pronoun “he” if a group contained even a single boy. (Even when you had one hundred girls and one boy? Yes.) Only recently, in an era in which what pronoun to use is surfacing as a significant identity issue, has the “singular they” been finally ruled a legitimate replacement for yesteryear’s “he.” Even so, apart from biologists and entomologists, well-meaning people routinely refer to insects and amphibians and hermaphroditic sea slugs as “he” — “he” in our culture and language representing the default — particularly when simplifying the world for young children.

The golden gender ratio raises an important question: To what extent do girls count? It’s accepted that girls will read novels about boys but boys won’t read novels about girls. But why is this the case, and why do we think that’s okay? And is it also the case that by the time they reach high school many boys won’t read fiction at all, becoming less willing to enter the realm of the imagination and emotions — and so authors and publishers are merely doing whatever they can to lure them in earlier? A high school English teacher friend tells me most of her classroom sets of books focus on males, such as Lord of the Flies, one of her least favorite books. Maybe the problem, she says, is that adults (publishers, teachers, parents) choose books they think “everyone” will enjoy.

To what extent do girls count? It’s accepted that girls will read novels about boys but boys won’t read novels about girls. Why do we think that’s okay?

Back in second grade I came to recognize that though girls could wear both dresses and pants, the notion that girls had more choices was a hollow one — who wanted to wear dresses? Likewise, I see now that the current crop of over-the-top fearless genius girl characters represents an improvement and yet only partly so; options for girl characters — and the concomitant options that readers see for real girls — need to widen still further. The current choices seem to be either being invincible or not existing at all. While one might wish for the arts to lead the way to a more egalitarian future, that mission has not yet been accomplished for children’s literature. While it’s great that adventure books are now routinely featuring smart, strong, dynamic girls, we’ll know girls have truly achieved parity with boys when they can be not only as strong but as wounded and vulnerable — and more to the point, when they are as numerous, when they abundantly populate books both as leaders and regular kids.