Heteronormativity and binary gender assumptions

Recently quite a number of questions have been posted that contain heteronormative assumptions or assumptions about binary genders, e.g. questions about married couples that assume that these consist of female wives and male husbands, or questions about gender distributions in families that assume that all children are either male boys or female girls.

Recently a new code of conduct was adopted, and while I was strongly critical of other aspects of the code, I just as strongly supported its focus on banning all forms of discrimination. To my mind, using language that assumes the non-existence (or non-marriedness) of people who are not heterosexual and/or don't identify with a binary gender is a form of discrimination (though certainly often not a conscious or deliberate one).

The code of conduct states in relevant part:

We don’t tolerate any language likely to offend or alienate people based on race, gender, sexual orientation, or religion — and those are just a few examples. When in doubt, just don’t.

It would seem likely to offend or alienate people to talk as if they didn't exist. I would therefore hope that we can agree that posting such questions without a critical reflection of this aspect violates the code of conduct (again, often not consciously or deliberately). I'm well aware that existing books are full of such examples, and I wouldn't want to go so far as to say that these cannot be used or referred to here in any way (after all, people may have gotten them as homework against their will); but I do think that they shouldn't be used without mentioning this offensive aspect and clarifying that the author of the post doesn't endorse it.

(I'm aware that this is also a more general issue beyond the math site, but it also has a math-specific aspect in that there are so many of these kinds of problems in math texts (there's even a theorem whose name implies heteronormative assumptions, Hall's marriage theorem), so I think it makes sense to discuss this here specifically.)

P.S.: Interestingly, there's no tag that contains “code” or “conduct”.

• There is a tag be-nice-policy which until rather recently was the term used instead of code of conduct, which I applied. I am not sure what is "interesting" about the lack of a code of conduct tag given that it is a rather recent introduction. You could've created it. Pointing out the lack in this form could be seen as trying to imply a lack of consideration for it, which might go against said CoC. Further, it's not something to be included in the body of the post. – quid Sep 24 '18 at 0:42
• A question related to this came up on MESE What's a replacement for “married couples” in combinatorics problems? – quid Sep 24 '18 at 0:45
• Is the following a problem? "We are seating 5 married couples around a circular table (the seats are identical). Let {m1,m2,m3,m4,m5} be the set of men and let {w1,w2,w3,w4,w5} be the set of their wives. In how many ways the man 1 will be seated next to his wife and the man $3$ will not seat next to his wife?" – quid Sep 24 '18 at 0:58
• If a poster states "Assume that the probability a child is born male is $49\%$" without stating the probability a child is born female, I can understand if some people are offended by the implication. But what if a poster states "Assume that the probability a child is born male is $49\%$ and the probability that a child is born female is $51\%$"? Is this good enough (in the sense that the probabilities were explicitly stated and not implied)? If not, then what could be done to make it acceptable? – Joel Reyes Noche Sep 24 '18 at 1:25
• I upvoted because I learned a new word: Heteronormativity. I rely on my colleagues to leave a Comment when something I say offends, giving me the chance to edit or delete as appropriate. – hardmath Sep 24 '18 at 1:55
• @quid: Yes, I think that's in fact a rather typical case of the problem. It introduces married couples and then talks about "the set of men" as if a set of $n$ married couples necessarily corresponded to a set of $n$ men and about "the set of their wives" as if married men necessarily had wives. – joriki Sep 24 '18 at 4:21
• @JoelReyesNoche: The fact that the probabilities add up to $100\%$ in the second case carries the same implication as leaving out the $51\%$ does in the other case, namely that there are only male and female children. If it works for the problem, the percentages could be reduced; if not, another example (e.g. red and green apples) could be used; and if for some reason boys and girls with probabilities that add to $100\%$ absolutely must be used to make a point, it could at least be mentioned that this is a hypothetical example in which non-binary genders are not being taken into account. – joriki Sep 24 '18 at 4:26
• @joriki thanks for the clarification. If ever the community decides on an acceptable way of handling these cases, I think there should be a place where examples like this are clarified. – Joel Reyes Noche Sep 24 '18 at 4:29
• Binary apple assumptions – en.wikipedia.org/wiki/Golden_Delicious – Gerry Myerson Sep 24 '18 at 13:24
• The underlying challenge is that particular fields - combinatorics is one - have particular gender assumptions intertwined with historically significant results. Consider Hall's marriage theorem, Kirkman's schoolgirl problem, etc. One might hope that current combinatorialists will use different language for new problems, but that leaves an enormous collection of existing problems in textbooks. I don't think we can expect to see a wholesale change in terminology on MSE until there is a larger revolution in which combinatorics textbooks adopt different ways of phrasing problems. – Carl Mummert Sep 24 '18 at 14:40
• At the same time, I think that in many cases it would be possible to re-write problems to remove some of the unfortunate wordings. I don't think we can expect student to do this for their own homework, but others could rephrase questions in equivalent ways, for example by matching two different kinds of marbles instead of two different groups of people. In this way we have identical mathematics, without unnecessary nonmathematical assumptions or stereotypes about gender. – Carl Mummert Sep 24 '18 at 14:47
• joriki; there is also a different way to see it though, which is why I chose that example. These five couples happen to be of this form, and this is explained. There is no implicit assumption in this case. (There may be in some other examples, but not in this one.) – quid Sep 24 '18 at 15:22
• Somewhat related what should be do about these types of problems? " There are 7 girls on a bus. Each girl has 7 backpacks. In each backpack, there are 7 big cats. For every big cat, there are 7 little cats. Question: How many legs are there in the bus (minus the driver)? " – quid Sep 25 '18 at 17:19
• One thing that may not be obvious, given the even balance of votes, is that 40 users cast votes on this post. At this point in time, we have 20 upvotes/20 downvotes. The net votes have vacillated between +a couple and - a couple. I think it's important to note this, because I think it's important to note that half the voters do not think the post is nothing more than nonesense. Also, have the voters disagree with the suggestions in the post, for varying reasons, only some of which did because they think the post is nonsense. – amWhy Sep 25 '18 at 19:37
• I would also venture a guess that the people who find themselves on the farthest ends of the issue would probably not have guessed that the vote would be split so closely. Kudos on voter participation yielding an interesting insight into the proportion of voters' feelings. – rschwieb Sep 25 '18 at 20:02

I share the sentiment but disagree with this being classified as a violation of the code of conduct.

Marriage equality is absent in most countries of the world and I found only six countries in which gender assignment at birth is not binary (the latter information was from 2013, much can have changed since.) At places where the law enforces heteronormativaty or gender binariness, using these categories might be simply acknowledgement of the legal situation without it being an endorsement.

Moreover, and I'm aware that this is a rather problematic argument, as far as gender issues are concerned this is probably not the issue to focus on. I don't want to put marginalized communities against each other, but it is already hard but proably more feasible in the current situation to keep reminding users that a user of unknown gender need not be male and that humanoids fitting in the binary scheme should probably not be classified as "men" and "girls."

Finally, it should be clear that one can offend without trying to offend ("Grandpa, you really shouldn't use that word.") but it is also much more effort to enforce rules about unconscious offenses. Let's improve the world in small steps.

Please note that this answer refers to enforcement of rules only. I do encourage pointing out implicit biases in formulations of questions and answers in comments. I would also like to point out that this is my personal opinion and not something that emerged as a consensus among site moderators.

• Agreed; treating this as a code of conduct violation means mods having to say, "This is your second question in which the probabilities of having a boy and a girl child added to 1, so have a one-day suspension." This would be a better response if someone were being deliberately offensive. Here, asking "Could you rephrase this as a problem about flipping coins, to avoid alienating people that don't identify with either gender?" leads to better outcomes for all. – Misha Lavrov Sep 24 '18 at 18:42
• MichaelGreinecker I agree to a large extent, that "one can offend without trying to offend." This isn't about blame on most folks, especially when they are working with a question from a text making inappropriate associations. I didn't see Joriki's post as calling for punishment for missteps. They merely called for discussion, which is a good thing. But it is entirely reminiscent of the struggle woman have had to fight to be considered valid, full-fledged human beings with voting rights and the right to work, etc. The ideal way to deal with widespread exclusion, ... – amWhy Sep 24 '18 at 19:44
• ... is to correct the language where it is. If that means editing a question, or making a polite comment to a user, I support it. I think this question was asked with reference to the "spirit" of the code of conduct. And that may encompass education, and day to day suggestions for alternatives to "he, him, his, sir," or just as important, alternatives to $\forall p, (m(p) \oplus w(p))$ ("all people p, are exclusively male or else female"), and such. Is that a bad thing? – amWhy Sep 24 '18 at 19:48
• @amWhy Well, my answer states my support for comments; I'm less sure about editing (that might generate more anger than insight.) Given that joriki disagrees with much of the code of conduct, I read his question as relating to site policy (as in policing) and that is what I answer. As for pronouns, I'm very conservative. What was good enough for Woolf, Shakespeare, and the King James Bible is good enough for me, so I use the gender-neutral pronoun "they." – Michael Greinecker Sep 24 '18 at 20:04

Let's just stick to common sense and not attempt to find all possible reasons to get offended when it is rather obvious that no offense has been meant. We have had enough of liberal extremist nonsense in this world recently (recall the Tim Hunt story, to mention just one) to drag it to the mathematical sites. The common politeness and respect to "alternative lifestyles" is one thing and censoring the language is quite another.

• let's just do math! – Paprika Sep 24 '18 at 4:55
• A post labelling a post about discrimination "liberal extremist nonsense" has received more up than down votes. I find that very disappointing. I've flagged this post as "rude or abusive". – joriki Sep 24 '18 at 5:05
• Being offensive doesn't require an intent to do so, especially when it is inherent in the mere action or words used. – Nij Sep 24 '18 at 6:12
• This post states an opinion, clearly and arguably quite provocatively. However, I do think this is well within the boundaries of what should be tolerated in such a discussion. I do not intend to suppress it. At the same time, fedja, if you could find a less confrontational way to state the same point, I'd appreciate it. – quid Sep 24 '18 at 7:59
• I disagree, @quid. It is rather preposterous that you would comment: "I do think this is well within the boundaries of what should be tolerated in such a discussion." So I'll leave a comment, based on your decision, which follows. – amWhy Sep 24 '18 at 13:38
• Let's stick to common sense and recognize a sense of inclusion is paramount to the development of a true community. We have had enoughright-extremist nonsense and conspiracy theories in this world already, so it's time to push back when we encounter it in our daily lives. – amWhy Sep 24 '18 at 13:40
• While I agree with @quid and am generally against any form of censorship, this post pushes the boundaries. Not because the term "liberal extremist nonsense" is by itself offensive, but because the OP has injected a political viewpoint into a discussion about math.SE. (I made the mistake of injecting political humor - not even a viewpoint - into this forum and I will not do so again.) So while I agree with the OP's overall sentiment and his right to post it here, the OP should know that by his provocative language, he has shown his cards. Not a good look here. – Ron Gordon Sep 24 '18 at 13:43
• In a discussion like this one about boundaries and censorship, I think we need to be prepared to let posts like this stand. After all, if you remove it, you are also obliterating the fruits of opposition to it. I don't mean to say that there is no boundary in discussions like this, just that we should probably move our normal limit out by another standard deviation. Outside of a discussion like this, I agree such a statement could be considered to cross a line. My two cents. – rschwieb Sep 24 '18 at 14:47
• Perhaps you didn't mean it this way, but statements like "[Let's] not attempt to find all possible reasons to get offended when it is rather obvious that no offense has been meant" are exactly the issue. I think you're trying to dictate what other people find offensive, and being so totally dismissive of someone's concerns (and especially calling it "liberal extremist nonsense")… well, that means that you are part of the problem. – user296602 Sep 24 '18 at 15:19
• @quid A post about "liberal extremist nonsense" is not a post that "calls for politeness and respect." – user296602 Sep 24 '18 at 17:54
• @amWhy no such implication is suggested in my comment. However, whether a user is competent on the subject of the site is, I think, directly relevant to whether it is a loss if they are avoided on the site. This is what I said. I am not sure why you see fit to ask this question in this form. It contains an unwarranted implication. The user find this particular suggestion non-sense. Maybe we could all focus on whether the suggestion is good or not. – quid Sep 24 '18 at 18:41
• @quid If you didn't mean to make such an implication, then I fail to see why you brought this user's mathematical competence into the discussion at all. Are we applying the same standards to everyone, or are we giving a pass to those who show they're really good at math? – user296602 Sep 24 '18 at 18:44
• oops, you left out "liberal extremist" before you referred to the user's suggestion that the post is nonsense, @quid. They said, specifically, that the questions is promoting liberal extremist non-sense. I merely called this answer like I see it: it is nothing more than conservative extremist nonsense xenophobia. To try to change the subject is something I am not sure why you see fit to suggest your interpretation. – amWhy Sep 24 '18 at 18:45
• You are merely echoing, dear @quid, the attitude when women sought the right to vote, to hold jobs, to attend college, and called on others to challenge the gendered language of default "he", "his", etc. where woman who sought inclusion were told, this has no bearing in higher education, certainly not in mathematics. We need always to keep our minds open to acknowledge how our sometimes-behind-the-times languages can reinforce the exclusion of folks who may currently be treated as non-existent. I won't discuss this further with you here. If you want the last word, be my guest. – amWhy Sep 24 '18 at 19:58
• I don't echo anything. I explained what in my understanding is in the answer @amWhy – quid Sep 24 '18 at 19:59

I think this is a problem that we are ill-equipped to deal with, in that our actions (whatever they are) are unlikely to make a significant impact. The primary sources of these problems are professors, textbook authors, and practice problem websites, and while they produce these problems, we are going to get them on our site.

I don't think we should interpret these problems as a violation of the code of conduct. There is already a high bar for quality of questions, and an enormous volume of questions that do not meet this standard and have to be closed or deleted by the community.

Moreover, treating these problems as a violation of the code of conduct will punish the poor student who is just trying to get some help with their homework, and will have absolutely no effect on the aforementioned sources of these problems.

However, despite this, I'd prefer not to do nothing. If a question comes up that implicitly assumes binary gender or heterosexuality, I think we should try to make it an explicit assumption. We can use comments to ask for clarification, something along the lines of

Are you assuming every person in the problem is a man or woman?

or

Are you assuming that every marriage in the problem is between a man and a woman?

or something like that. If you get a positive response, then edit the question to include the assumption explicitly, e.g.

Assume, for the sake of the problem, that each person in consideration is a man or woman.

Not only is it clearer mathematically, but it demonstrates that we, as a community, recognise the queer community, and that while we host these problems with simplifying assumptions, they do not reflect our own assumptions in real life.

Everything in the second paragraph of Theoretical Economist's answer is true and important, and I could write a great deal about it from personal experience, including how it has severely affected my mathematical education.

On the other hand, were it not for its unfortunate use of the inflammatory phase "liberal extremist nonsense", I would also agree with every word of fedja's testy answer!

I do not feel the slightest bit personally offended or exluded by heteronormative or binary gender assumptions in mathematical word problems. [Is that the right term?] I don't even feel offended or hurt by this question (originally entitled "Preventing billiard ball mental patients from committing suicide"), even though I have attempted suicide and been a mental patient. It is genuinely amusing, and quite harmless. (As indeed are most of us loonies!) :)

More than that, I think it makes life worse, not better, for those of us in various marginalised groups if everybody is made constantly fearful that some abstract other individuals are liable to take offence at even the most innocent and natural assumptions, just because those assumptions are sometimes mistaken.

In mathematics, it's a damn nuisance, and pointless, to worry about putting the arguments of a binary operation in a certain order when the operation in question is known to be commutative. Of course one has to be prepared to treat noncommutative operations properly when they occur. I don't think mathematicians, of all people, need educating about this sort of thing!

The advice quoted from the code of conduct, "When in doubt, just don’t", is simplistic, wrong, and harmful. I'd much prefer people to be relaxed and commonsensical about the whole business. Again, I think fedja said it well.

Of course, as a self-confessed very odd bird indeed, I'm not representative of any class (marginalised or not), and I'm very much open to correction from any reader of MSE who belongs to some such marginalised group and does feel offended, excluded, or hurt by the kind of casual false assumptions in mathematical "word problems" that are being discussed in this thread.

[I've edited this, in the forlorn hope of preventing any more misunderstandings of what I meant!]

But is there actually any such person here?

Excuse me if I have missed something in this thread. (I think I read it all, but the subject understandably makes me nervous - I'm really going to regret posting this, by the way! - and my concentration may well have slipped.)

But my impression is of a lot of well-intentioned people worrying themselves to death (or angrily refusing to worry too much) over whether someone else might be offended. I think that much the best advice is "DON'T PANIC!" :)

• "X doesn't bother me, so X shouldn't bother anyone" is a pretty harmful point of view. And I mean that in general, not just in the realm of human interaction. (e.g. it comes up in software design -- developers don't fix serious issues with their product because they've learned to tolerate the issues and refuse to believe that it bothers others so much) – user14972 Sep 27 '18 at 17:59
• I'm familiar with the worry over people making a big deal over imagined slights, but it had never struck me how much more serious such worries would be for someone who is already in a tenuous social position. If nothing else, I've learned that from this post. – user14972 Sep 27 '18 at 18:22
• @Hurkyl That is why I was at pains to point out that I am an odd bird, not representative, and open to correction, and asked for anyone else in the affected classes to step up and contradict me. I may be a bit of an Uncle Tom, and that may be one of my most grievous faults, for all I know. [This is in reply to the first of your comments. I'm not sure I understand the second comment, but give me a moment.] – Calum Gilhooley Sep 27 '18 at 18:27
• One of the most important freedoms, surely, is the right to articulate one's individual point of view, as a member of a marginalised class, without being automatically presumed thereby to be speaking for all other members of that class. I thought I had forestalled any such misunderstanding. It is said that "hard cases make bad law", and I'm definitely a "hard case", in that sense, even if not in any other! :) – Calum Gilhooley Sep 27 '18 at 18:34
• @CalumGihooley: My second comment was to remark that your fourth paragraph highlights an issue and made me realize it's more serious than I thought. – user14972 Sep 27 '18 at 18:37
• @Hurkyl Ah - OK, I thought that might be what you meant, I just wasn't sure. – Calum Gilhooley Sep 27 '18 at 18:38
• Re whether this is harmful: It took me years to come to terms with my sexual orientation, mostly because every single part of society was constantly telling me that straight = normal. I would not wish that experience on anyone else and it troubles me that people are so quick to sweep this problem under the rug. Heteronormativity does cause material harm to specific individuals. The question is whether you want to do anything about that harm. – Kevin Sep 28 '18 at 0:23
• @Kevin I'm relieved that someone else is addressing this from their own experience. About the harm: I acknowledged this in my first paragraph. If I didn't labour the point, it was partly because TE's answer had covered it so well, and partly because I cannot adequately express the harm done to me. I was tempted to write at length about it, but judged that this would be unwise in several ways. Perhaps I overcompensated! I have certainly been complicit in my own oppression, but that topic, belonging as it does to the field of "mental health", is even harder to write clearly and relevantly about. – Calum Gilhooley Sep 28 '18 at 3:32

I can do no better than to quote Pere's answer in the Math Educator's Stack Exchange thread:

The issue is not making problems about heterosexual married couples. The issues are:

• Implicitly making the assumption that all married couples are heterosexual.
• Making problems about heterosexual marriages but not about other kinds of couples.

Both points are [alienating to]* people following other types of marriage, but they can easily be solved while keeping the problem clear and interesting. We just need to make all assumptions explicit (thus acknowledging that they aren't universal while making the statement unambiguous) and making a wider array of problems (which can be useful to teach different tools).

Therefore, I do not think that posting a problem about heterosexual marriage requires a disclaimer that the author recognizes the problem is offensive. This is because it is easy to reword these problems so that they are not offensive by including language that makes it clear that heterosexual marriage is not the norm.

There are 10 men and 10 women. How many ways are there for these 20 people to form 10 married couples?

Then if the intended answer is $$10!$$ rather than $$19!!$$, change the problem to

There are 10 men and 10 women. How many ways are there for these 20 people to form 10 heterosexual married couples?

*I rephrased this part, original wording was [unengaging for].

• Or, even better, find a context that doesn't require exclusionary implications or force-fit conditions, like "A Widget requires two parts, a Zig and a Zag. If there are ten of each type of part available, how many unique Widgets can be made?". – Nij Oct 19 '19 at 12:06

Regarding the fact the term "marriage" has two inequivalent common usages, I am inclined to treat the situation much like how we treat other terms with the same problem: infer meaning from context, clarify when needed, and maybe advise the author that the term is ambiguous.

• I agree in principle, yet tangentially, there are more meanings than this. For one thing, all these examples seem to be based on a monogamous notion of marriage. This can also be seen as problematic (Eurocentrism etc). – quid Sep 27 '18 at 11:01
• Following up on @quid's comment, I think a larger issue in these problems is that they often include other gender assumptions or take agency from particular genders. Hall's marriage theorem, in the classic formulation, was about finding brides for men based solely on the men's preferences - the women had no agency at all. The theorem could be renamed "Hall's arranged marriage theorem" with tounge in cheek. – Carl Mummert Sep 28 '18 at 13:04
• If we reverse the roles of men and women, as in the [Wikipedia article] (en.wikipedia.org/w/…), then the men have no agency. There are certainly other situations that could be used that would not have these issues. – Carl Mummert Sep 28 '18 at 13:04

I agree with your statement to some extent, but (paraphrasing one of your answers you linked to) I think it takes an extreme position that I believe would be harmful. It would mean that hardly any posts mentioning humans would be allowed at all.

For example, take this recent tweet (I replaced 'mathematicians' by 'guests' - see comments):

At a large dinner party, $$n$$ guests hang their coats on the coat rack as they enter. At the end of the night they leave in a drunken stupor, each one randomly putting on a coat without checking that it's their own. In the limit as $$n \to \infty$$, the probability that none of the guests staggers home in their own coat approaches $$1/e$$.

Clearly, this is "using language that assumes the non-existence of people" who do not wear coats, do not drink alcohol (e.g. many Muslims, recovering alcoholics, etc.) and/or cannot walk (e.g. have to use a wheelchair).

Or take this version of the dining philosophers problem (I replaced 'philosophers' by 'guests' - see comments):

A group of dinner guests sit around a table and eat spaghetti, each using two forks. However, only one fork is placed between each pair of adjacent guests. Each guest alternately drinks and eats. To drink, a guest puts down both forks, pours some wine into a glass, and drinks it. To eat, a guest picks up the fork on the left and the fork on the right, and eats. If one of the forks is not available, the guest waits until it becomes available. Will the guests be able to finish their meal?

How would you phrase this problem in a way that makes no implicit assumptions and does not exclude anyone, for example people who don't have two hands or for some other reason cannot use two forks, cannot eat food using their hands and mouth, cannot sit in a chair around a table, don't eat pasta, don't drink wine, and so on? (Stephen Hawking couldn't have been one of the dining philosophers, but I'd guess he wouldn't have felt excluded by the problem.)

Are problem statements like these "a form of discrimination", though "not a conscious or deliberate one"? Should "posting such a question without a critical reflection of this aspect violate the code of conduct"? I don't think so.

• In the "drunken mathematicians" problem and the "dining philosophers" problem, assumptions are made only about a particular set of (fictional) people. Neither scenario presupposes the truth of any dubious assertion about the set of all people, such as "everyone is either male or female". Therefore a hypothetical rule that outlawed all problems of this kind would be [even!] more draconian than a rule against the use of problems that do in fact sneak in false assumptions about the kinds of people that do or do not exist. So this is a bit of a straw man (even though straw men don't exist). :) – Calum Gilhooley Nov 22 '19 at 18:13
• @CalumGilhooley in a way I agree. However the questioner specifically also found problems problematic that in fact do not make an assumption about all people. See the comments on the main post. – quid Nov 22 '19 at 19:45
• Your first example doesn't state explicitly that each of these married couples consists of a man and a wife, therefore it relies on an implicit assumption that every married couple does so. It would be very different if it had begun, "We are seating five men and their wives around a circular table ...".. I wouldn't have even the mildest objection to that. (But I'm braced for someone to protest, "Why not five women and their husbands?", and/or "How dare you use the possessive pronoun!" That's even if no-one protests that the example is presented as if it were typical!) – Calum Gilhooley Nov 22 '19 at 20:10
• Actually, someone could rationally object that in some cultures a man may have more than one wife! Damn, life is complicated. I think I'll stick to mathematics. – Calum Gilhooley Nov 22 '19 at 20:17
• Our four ... no ... Amongst our weapons ... Amongst our weaponry ... are such elements as fear, surprise ... I'll come in again. – Calum Gilhooley Nov 22 '19 at 20:26
• The way I first heard the "coats" problem, many years ago, it was a careless coat-check girl who was giving out coats at random. I think we're making progress. – Gerry Myerson Nov 22 '19 at 22:37
• @CalumGilhooley I am convinced it does not rely on that assumption. If I say "We are seating ten persons around a table. Let $\{m_1, m_2, m_3\}$ be the set of persons from Montana." Does this rely on the assumption that every collection of ten persons contains some from Montana? – quid Nov 23 '19 at 0:18
• @CalumGilhooley I'd mostly concede that the assumption that couples are disjoint so to say is implicitly needed. As chance has it I actually had thought of that. One could also argue it relies on the assumption that when we say let {m1, m2, m3} be the set of something then often the elements are implicitly assume to be distinct, and assumption of distinctness of all the mi and wi in my example suffices at implicit assumption I think. – quid Nov 23 '19 at 0:27
• @CalumGilhooley on the point that I constructed it as men and their wives, I do not recall the reason. I will not exclude some subconcious bias but actually I think I started out with m and w alphabetically and then went along, but I really don't recall that. On the possessive pronoun, hmm, thinking about it I recall that some do not like this but I really never understood this objection. There just is not necessarily a hierarchy or property implied. The argument I'd give is that say "my father" and "my son" are both possible and common. Or "my superior", "my president", "my king", etc. – quid Nov 23 '19 at 0:31
• @quid It would be clearer and more natural to write "We are seating ten persons around a table, and three of them are from Montana", and only then introduce the notation $\{m_1,m_2,m_3\}$. As it stands, the reader must either supply this interpretation her/himself ... :) ... (an unnecessary burden on her/him), or else draw the absurd conclusion that what you mean is that every group of $10$ people contains exactly $3$ from Montana! Coming back to your actual example: the only natural inference is that the number of men and the number of wives are necessarily equal to the number of couples. – Calum Gilhooley Nov 23 '19 at 0:37
• @CalumGilhooley - I don't understand your distinction regarding assumptions about a particular set vs. about all people. Is it because the problems I mentioned are about mathematicians / philosophers? How about the following variation: "At a large dinner party, 𝑛 guests hang their coats on the coat rack as they enter. At the end of the night they leave in a drunken stupor, each one randomly putting on a coat without checking that it's their own. In the limit as 𝑛→∞, the probability that none of the guests staggers home in their own coat approaches 1/𝑒." Does this problem make ... – jcsahnwaldt Reinstate Monica Nov 23 '19 at 0:47
• @CalumGilhooley "or else draw the absurd conclusion that what you mean is that every group of 10 people contains" no not every group, just this one I happened to consider, which is the point, and in my mind is the very same point you raise related to the example in the answer here. Like "Let $A$ be a set and let $p$ be a positive integer in $A$." does not imply that every set contains a positive integer. – quid Nov 23 '19 at 0:49
• ...assumptions about all people? If that was your point, then I'll be happy to edit my post to clarify what my actual point was. Because I feel that your objection is a bit of a straw man. :-) – jcsahnwaldt Reinstate Monica Nov 23 '19 at 0:51
• In case anyone else is confused: quid posted 2 more comments while I was still replying to his[/her??] first, and then quid and jcsahnwaldt both posted comments while I was mentally collecting my wits and composing a reply to quid's third comment. And I see another comment (a continuation of jcsahnwaldt's) has been posted while I was composing this one. In response to quid's third comment: we are in heated agreement! Please recall that I wrote "I wouldn't have even the mildest objection to that." As an afterthought, I then anticipated how other people might still find some cause to object. – Calum Gilhooley Nov 23 '19 at 0:55
• @CalumGilhooley: I edited my post. If I understand your objection correctly, the problems as stated now presuppose the truth of several dubious assertions about the set of all people. Do you think posting such a question without a critical reflection of this aspect should be said to violate the code of conduct? – jcsahnwaldt Reinstate Monica Nov 23 '19 at 1:16

I'm of the same line of thinking as the OP. Personally I try to use "They", "Them", and so on in my answers, and in everyday conversation. I think it's important not to assume roles (I saw a post on MSE about a farmer that repeatedly referred to "him"), and generally it isn't too hard to be gender neutral.

HOWEVER, I do think that in historical problems such as the Hall's Marriage problem, and other similar combinatorics problems, we can take the assumptions of binary genders and heterosexual couples as given in the question as outdated and just move on with the maths.

In answer to the original question, there is no need to make this a breach on the code of conduct, but it is something we can all work on to make MSE less hetero-normative/binary. This could only be a good thing.

• Discussing heteronormativity and binary gender assumptions in mathematical problems is considerably different from discussing the usage of gender-neutral pronouns. You are conflating both. – Aloizio Macedo Sep 26 '18 at 14:06
• @AloizioMacedo I am not conflating the two. The OP brought up the issues surrounding both, and I shared my opinion primarily on gender neutral pronouns but also touched slightly on heteronormativity. In my opinion the best way to avoid making binary gender assumptions is to use neutral terms (which in one fell swoop don't assume roles, and don't force gender into being binary). Notice that using the term "Parents" instead of "Mother and Father" challenges both issues. – MRobinson Sep 26 '18 at 14:16
• As far as I can see, there is no allusion whatsoever to defaulting to male in language when a gender is unspecified, and this is one of the main reasons as to why there are people who think one should use they/them etc, and this all revolves around the concept of grammatical gender, and is another discussion completely. For instance, the title mentions "Heteronormativity and Binary gender assumptions": Heteronormativity is another issue altogether. Binary gender assumptions is not the defaulting to male: it is assuming that people are either male or female. – Aloizio Macedo Sep 26 '18 at 14:31
• To give examples: "A couple went on vacation. There, the man bought socks and the woman bought snickers." is worlds apart from "Every new employee should be treated as if he were already part of the family!". The later is also worlds apart from "There are two forms that can be filled. If you are a man, fill this form. If you are a woman, fill the other one." – Aloizio Macedo Sep 26 '18 at 14:31
• @AloizioMacedo again, you aren't wrong, but I highlight my previous point that using neutral language does a double job of both not reverting to male, and not assuming binary gender. – MRobinson Sep 26 '18 at 14:43
• I agree with that. The point is that there are people who think one is a problem, and the other isn't. So you are proposing a solution which solves a problem$^{(1)}$ while changing something else which some people do not perceive as one, and which requires people to change how they use the language for that. – Aloizio Macedo Sep 26 '18 at 14:53
• $^{(1)}$And it is not clear to me that it solves the specific problem at hand: binary-gender/heteronormative exercises use the binary aspects with effect. If one were to get rid of them, the exercises can change dramatically. So a better solution for this specific problem under discussion, in my point of view, if there must be one, would be to change the context to some other thing entirely, as some people have suggested. – Aloizio Macedo Sep 26 '18 at 14:56
• @AloizioMacedo I agree with what you're saying. Often if you talk of pairing pegs and holes, or keyboards and mice (mouses?) you get the exact same question but without the heteronormativity. I just think the question posed by the OP goes beyond that, and that is what I am mainly referring to. Maybe I am wrong to do that, and apologies for that, but I do think my answer has relevance and that by and large we are agreeing with each other! – MRobinson Sep 26 '18 at 15:03

Who are these people getting alienated by the premise to a math word problem? Seriously? Meanwhile victims of actual racism/sexism around the world are being denied basic human rights ... some perspective is necessary.

heteronormative assumptions or assumptions about binary genders, e.g. questions about married couples that assume that these consist of female wives and male husbands, or questions about gender distributions in families that assume that all children are either male boys or female girls.

It's obvious to me that the point of a math "word problem" is the actual problem behind the words, not the story/setting created by the words.

Edit: Thanks to Theo for explaining why my comparison to more severe problems was not relevant (strikethrough above).

That said, I think time spent editing questions to be more inclusive can easily instead be spent actually answering the math problem which just looks to me to be orders of magnitudes more important.

I'm open to changing my mind on that as well.

• If we avoid addressing issues just because there are serious issues elsewhere, then progress is never made. The implication that people are somehow not allowed to be offended because there are bigger issues in the world is pretty problematic. – user296602 Sep 25 '18 at 3:49
• If, as you say, "It's obvious to...that the point of a math 'word problem' is the actual problem behind the words, not the story/setting created by the words," why not change the story the be more inclusive? – Xander Henderson Sep 25 '18 at 4:03
• "some perspective is necessary" Perspective is often helpful. Excusing a serious problem because there are even more serious problems in the world is often counter-productive. Unless you specifically plan to use the time that you otherwise would have spent making questions more inclusive on trying to grant people their basic human rights, your argument rings false. – Theo Bendit Sep 25 '18 at 4:12
• If some weirdos are getting upset over something that makes no sense to you, but it costs you nothing to fix it, why not do so? (And, as a corollary: if there's a whole bunch of people that are all upset by the same thing that makes no sense to you, why not discuss the bizarre issue in advance of it actually coming up?) – Misha Lavrov Sep 25 '18 at 4:28
• I think you are right @Theo. Thanks. I'll delete this answer, it's quite unreasonable in hindsight. – Zubin Mukerjee Sep 25 '18 at 4:30
• @T.Bongers Nobody is "not allowed" to be offended by anything... people are "allowed" to be offended by [what I perceive to be] nonsensical reasons and I'm "allowed" to then say that I think they're nonsensical. That doesn't seem problematic. – Zubin Mukerjee Sep 25 '18 at 4:48
• I think my comparison to worse problems was irrelevant, but I don't think I fully understand yet. @misha. and xander, wouldn't time be better spent solving the math problem than editing to rephrase the story/setting? I'm thinking there is an opportunity cost to time spent on rewording questions about boys and girls to questions about coinflips – Zubin Mukerjee Sep 25 '18 at 5:05
• How important inclusivity is to you is ultimately up to you, of course. But, I think devoting some time to it when you can is a good idea. Regardless of whether you sympathise or not, this stuff adversely affects a really large number of people, and I think that is reason in itself to make it some kind of priority. How you rank that priority is, again, ultimately up to you. – Theo Bendit Sep 25 '18 at 5:13
• That makes a lot of sense. If I'm writing some probability question from scratch then I'll be a bit more careful to use coinflips instead of boys and girls, since there is no additional time required. On the other extreme, I won't trawl through a long paragraph of an already-written question on probability with boys/girls, changing everything to coinflips, because the additional time isn't worth it (also the risk of messing up the actual content of the question in the process) – Zubin Mukerjee Sep 25 '18 at 5:20
• I've forgotten the details, but this reminds me of a user on MSE who made hundreds of edits that were all changing something like the font on the $\mathrm{d}x$ in integrals. Many people would think that those edits weren't worth the time, but to some people it is worth the time. I think that's similar to me thinking editing for inclusivity isn't worth much time, while other people think it is. – Zubin Mukerjee Sep 25 '18 at 5:31
• Excuse me, @ZubinMukerjee, but I think your comparison between a user editing to make posts more inclusive for all human beings, and a user editing to replace all $dx$ with $\mathrm dx$ in every integral they see, is exceedingly misguided. They are incomparable. – amWhy Sep 25 '18 at 23:42
• Why? $\, \, \,$ – Zubin Mukerjee Sep 26 '18 at 1:36

I partly disagree with Michael's answer. (Save the downvotes for when you've read the rest of my answer, please.) I believe that posts that use heteronormative language or contain implicit binary gender assumptions are clear-cut violations of the code of conduct.

I think we all need to try harder to appreciate how exclusionary and alienating it can be to be misgendered or to be told, even if only implicitly and unintentionally, that an important part of your identity is not normal or not real. This is hard for many of us to imagine, because many of us don't experience it. Moreover, even when we try to imagine the situation, it is difficult for us to imagine it in context. Bear in mind that being non-binary often means that you are deprived of rights afforded to otherwise identical heterosexual individuals. You might live in fear of being victim to violence because of who you are. Sometimes, it's more than just violence. It's no wonder that rates of depression and suicide are much higher among non-binary individuals than it is in the general population. It is this context that can, and often does, make it much more difficult to bear things that would otherwise seem like they would not be a big deal. (*)

However, I also think that strict enforcement of this type of violation is going to be an uphill battle, and likely to be counter-productive. Some of the other answers to this question give an indication of why: it's hard to enforce a rule that carries the penalties of suspension and expulsion when it involves behavior that a non-trivial number of people just don't think is a big deal. It is for this reason that I am personally not in favour of enforcing the code of conduct strictly in these cases.

What do I propose we do? I agree when Michael says that we should try to point out implicit biases in formulations of questions and answers in comments. However, I think we should go a little further than that. In particular, the appropriate help pages should state that we strongly encourage the use of non-heteronormative, gender-neutral language. I think that doing this might make compliance a little more likely. This way, it looks more like it's part of the rules of the site, rather than the appeals of some random stranger on the Internet. We should probably also have a short guide on how to do this. In my experience, this issue is a little tricky to navigate for people who are not proficient in English; a guide will help them do that.

I know it's a little inconvenient to try to rethink the language that you use to conform to what seems like a manifestation of political correctness gone mad. However, I hope that no one sincerely thinks that it is important to them that they not have to do so. On the other hand, the more careful use of language is important to many non-binary people. Let's try to make Math SE a place for them too.

(*) There is also the argument that use of heteronormative language is an important part of what engenders an environment that enables the worst aggressions outlined above, but I'll leave that for alone for now. However, you can read about this argument here or here.

• Thank you for a detailed answer. I think what you propose does not go far enough in that it focuses on this one aspect. You could reply that what the question asked about, but the same remark applies there. I am still waiting for an answer to what we should do about "There are 7 girls on a bus. Each girl has 7 backpacks. In each backpack, there are 7 big cats. For every big cat, there are 7 little cats. Question: How many legs are there in the bus (minus the driver)? " – quid Sep 26 '18 at 23:20
• A solution might be (not my idea, but a good one in my opinion) to discourage combinatorics problems that involve humans as agents in the problem, as there is any number of ways this can go wrong. For example, I am given to understand that there are some problems on the site that some consider as racist. – quid Sep 26 '18 at 23:29
• @quid What you suggest is perfectly consistent with what I propose above, and I am personally in favour of that. Re your example, I personally do not find it particularly problematic, but I can see why there would be some discomfort with the language used. (I would probably try and rephrase it were I to word it myself.) I think in cases like these, it's better to err on the side of caution. One way to do that is to say there are 7 people (or children, if you like) on the bus. Of course, there are even more conservative (in the sense of erring on the side of caution) relabellings of your (cont) – Theoretical Economist Sep 27 '18 at 12:55
• (cont) example, and I'm not opposed to encouraging those either. – Theoretical Economist Sep 27 '18 at 12:55
• It seems you did not understand the problem, as the change you propose does not address the main problem at all. The question is based on the implicit assumption that every girl has two legs (and ever cat has four legs), which is false and thus problematic. – quid Sep 27 '18 at 15:50
• @quid you’re right; I didn’t. Thank you for pointing that out. I should be more careful in the future. I’m happy to have a site policy that encourages more inclusive wording for problems like these, even if that wording makes the problem seem less natural. Though, even assuming it’s not possible to find a satisfactorily inclusive wording for examples of this type, I think there are other examples where there are ways to rephrase the problem, and we should try to do something about those. – Theoretical Economist Sep 27 '18 at 16:01
• I think @quid's comments show that the belief "that posts that [...] contain implicit assumptions [about any humans involved] are clear-cut violations of the code of conduct" means that hardly any posts mentioning humans would be allowed at all. There must be hundreds or thousands of math problems which are expressed as a questions about one or more humans and make certain assumptions, e.g. that the humans involved are capable of rational thought, are able to see, hear and/or speak, have two arms, legs, eyes, ears, etc., have one nose, mouth, etc. etc. – jcsahnwaldt Reinstate Monica Nov 13 '19 at 20:45
• For example, how would you phrase the dining philosophers problem in a way that makes no implicit assumptions and does not exclude anyone, for example people who don't have two hands or for some other reason cannot use two forks, cannot eat food using their hands and mouth, cannot sit in a chair around a table, and so on? For example, Stephen Hawking couldn't have been one of the dining philosophers, but I'm pretty sure he wouldn't have felt excluded by the "ableist" assumptions of the problem. – jcsahnwaldt Reinstate Monica Nov 13 '19 at 20:54