Identity: Math and Myth

What does it mean to have an identity?

If you don’t look too closely, you might think that you can simply adopt a set of labels, slap them on yourself, and go forth into the world as a sequence of nouns. But that’s not how it works in practice. And socially constructed reality is all about how things work in practice.

Who Gets To Decide?

What kind of thing are you?

When put that bluntly, this is clearly a rude question, yet it is one that we are asked and ask of others moment by moment, all day long. As we wander the world, we project our models upon the surfaces of the people we encounter, classifying, scripting, assigning roles. One of my meditation teachers highlighted this beautifully when he said, “Now, everybody look around the room, and if you see anybody about whom you have no opinion, raise your hand.” We all looked around, dutifully, and started to laugh.

Identity Theory – The “Is A” Construction

I am a mother.

This is one of the overriding identities in our culture. It puts enormous constraints on my life, both real and imagined. Or rather, it places constraints upon my expected actions, some of which are comforting and I accept, and some of which are imposed from outside and are not relevant to my capacity as a mother. “Mother”, although it is, in principle, a word that describes a particular familial relationship, is freighted with more baggage than any seven letters are due.

This is a math-like identity, one that I have previously considered using the more innocuous barber paradox. In mathematics, the identity operator is one which says A = B, or A is exactly identical to B, or logically A is B.

Seonaid is a Mother. Seonaid = Mother.

It does not follow, however, unless you are one of those three people in the world, that Mother = Seonaid. And thus, the analogy breaks down. Mathematically, A = B implies that B = A.

Yet effectively, that’s how it works in the mind on the run. Not only do we apply our existing maps to the people we encounter, each individual becomes the representative of the whole category, a sort of involuntary synecdoche.

It’s even worse than attempting to use labels to define our selves, because in that moment we see not a complex multi-faceted human but only the single label. What is worse in many cases, we have defined the other as nothing more than a not-us (whatever “us” is most salient in that moment). It is an appallingly bad model of the world.

And it is what our minds work with as their default, navigating the system moment by moment.

This is what is meant by “objectification”. It actually has nothing to do with sex. It is the process of turning an agent with moral positions and independent existence into an object in your own story. That person is no longer a person, they are a thing to be moved around according to the laws of your own existence. (1) They become, not who they really are in the world, not another small piece of a conscious universe, but merely the identity you have projected upon them. (2)

Identity Theory (B) – The “Is a Member of” Construction

Functionally, most identity discussions are more analogous to set theory. We assume that there is a valid identity to which somebody could, in principle, belong. And then, the “fun” starts. Because once the identity is established as a valid category, the question of who is, and is not a member begins. (Spoiler: It’s not much fun.)

Chuck Wendig tells us how to find out if we’re writers.

This is a pretty simple example, right? Are you a writer becomes the simple question, “Do you write?” Excellent.

But let us consider how many people would disagree with this. That “Do you get paid to write?” side would be considered by many to be the estimate of the “real” writer. Sometimes, they would restrict it to people who write books. Or novels. Or short stories. Not poems (poets) and certainly not mere blogs. (3)

Let us consider a model of this type of identity that considers the process by which the identity is defined. That is, how do we know whether somebody belongs to a particular group of somebodies?

I was thinking about using a “real life” example… I’m tempted to write about feminism, but that conversation always gets derailed. It will get its own post for derailing, on the off chance than anybody ever notices my work. For the purposes of this discussion, let us create a new category… Foopy. (4)

In principle, as I pointed out in The Problem of Naming, the goal is to divide the world neatly in two. Some people are in Foopy (p ∈ F), and all the other people are not contained in the Foopy category (p ∉ F). Clearly not everybody belongs in the Foopy category, or there would be no need for the division.

Let’s also say that there are advantages and disadvantages to being a member of the Foopy category. Maybe they have a particular flair, and access to some neat bands, and generally seem to have a good time. They like one another, and enjoy thinking of themselves as Foopy. But perhaps (to some non-members) they’re oddly dressed and loud and therefore tend not to get hired except as baristas at particularly fancy coffee shops (owned by other Foopy people).

(These people may, in fact, be Foopy. I think I want to become Foopy… but I could never carry it off.)

Apparently they are wearing Swants. If you, too, wish to join them but need a tutorial on how to make such a garment from an old sweater, they have kindly provided one.

Stay with me. This is a serious conversation about how identity policing works. Sociology happening here!

So, there are people who clearly identify as Foopy, and there are people who adamantly do not. But then, there are some others, who might want to be considered Foopy, but either they aren’t sure, or the other Foopy people aren’t sure, or the not-Foopy people aren’t sure… and the boundaries, and particularly the fuzziness of the boundaries, becomes evident. (See how hard it is not to use the “Is a” construction? I’ve edited this five times, and I still can’t come up with a natural language approach that doesn’t sound contrived and exclude using Foopy as an adjective.)

Individual or Political Social Mobility

This is intended to be a trivial case, since I invented the Foopy people. There is (as far as I know) no existing category of people who are limited by social constraints to live out their years as (if they are successful) coffee shop owners and (if they are unsuccessful) baristas. Not only that, but there is nothing intrinsic about this group of people that sets them apart from others. In principle, they could simply dress differently and change what music they listen to and cease to be a member of F. (More about that later.)

But let us posit that somehow Foopiness was maintained as a stable identity for a period of generations. Let us also posit that, because of general expectations around this socially constructed identity, social mobility, intermarriage, musical comfort etc. that they came to form a recognizable Culture. And let us further suppose that one of their children, having been raised wearing Swants, wanted to don a different outfit and pursue another line of work. Would they be permitted to? By their parents and/or the other members of their tribe? By people hiring outside the community? What would be the barriers? What strategies could they employ? What might be used against them? Conversely, is it possible, by means of learning and changing one’s way of being, to become a member of the Foopys? What actually defines membership or non-membership?

These are not academic questions; they are questions of practical importance upon which people’s lives depend.

Now, policing happens in both directions, and from both sides. There are power moves which push people into identities that they don’t accept, and also to exclude them from identities with which they are attempting to become affiliated. I’ve come up with seven “moves” to be made in this situation, depending on the position of the actor, but there may be more. Let us be clear: each of these is undertaken by an agent.  They may be purporting to speak on behalf of some identity, but at this point, I am considering the ways in which individuals interact at these boundaries. I will address collective outcomes later. Probably in another post, given how very long this has become. (I also have examples of each of these, but I don’t want to get into the details Right Now.)

Subject = S Individual whose membership is in question
Member = M Member of the culture who is generally accepted by other members of the category
Outside = O non-member of the culture whose outsider status is generally non-ambiguous according to both members and non members

Outsider Strategies

1. Excluded identity. Perhaps the most aggressive means of identity policing is the outright refusal by an outsider to accept the existence of the category.
2. Pathologized identity. Perhaps the category is accepted, but it is constructed as a problem to be solved, rather than a valid way of being in the world.
3. Enforced identity. The category is imposed on all individuals having some set of key features, whether they self-identify as a member of the category, or whether it is relevant to the current situation.

Member Strategies

1. Circling the Elephants: attempts to exclude subjects from membership in an identity from the inside.
2. Big tent (or maybe Borg): Attempts to assimilate and claim anybody who might possibly be members of the category, and also to universalize the category. The statement is, in effect, that “this is the proper identity for all members of the defined class to adopt”, whether they agree or not. It is related to “enforced identity” as it is an imposition of an identity, rather than the adoption of one.

Subject Strategies

1. Claiming identity due to a felt affinity. There is not necessarily an external characteristic that draws this person into a particular group, but a desire to be accepted as such either by members of the group, or by the broader society.
2. Refusing/distancing oneself from some other identity which may be imposed by either members or outsiders using the above moves.

Rather than attempting to define the rightness and wrongness of these approaches, let us restrict ourselves to considering each a strategy for negotiating structures, which comes with particular consequences. (5) It also gives us a generalized path into the notion of privilege, because the ability to police somebody’s membership in a category which either guarantees or restricts their access to the necessities of life is part of the the knowledge/power phenomenon to which Foucault was referring.

Identity Theory (C) – Identity as Performance

One of the criticisms of postmodernism makes reference to the “playfulness” of identity, because of the ways that it ignores the very real structural problems addressed above. People’s lives depend upon their affiliations. A socially isolated human being is a human being who isn’t going to last very long. And playing your role as assigned (we perceive) is key to gaining support from the other members of an identity group. It really matters who accepts you as “one of them”, and that means that you need to be able to follow the rules of what it looks like to be “one of them”. This is where myth comes in: the stories that we tell about it what it means to be a member of an identifiable group effectively defines the group. This is more obviously true where there is no intrinsic (biological, readable) characteristic around which the identity is formed, but the policing of gender expression should provide an immediate suggestion that there is more to it than that. Biologically female people are expected to perform “femininity”, which is equated with particular ways of walking, moving, dressing, thinking, entire ways of being. The precise nature of these gendered behaviours are culturally dependent and localized, but the construction of masculine and feminine roles along biological lines is a repeated cultural form.

(To be continued… because otherwise I’ll never publish this.)

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1. OK, sometimes it has something to do with sex.
2. The same thing is happening in the other direction at the same time but that doesn’t mean you came into this as two equal agents, because different stories have different power.
3. Thanks, Chuck Wendig, by the way, for validating my existence. Sometimes, it really does help to have a complete stranger tell you that you’re not delusional.
4. Maybe this particular example could be fun.
5. This is foundational for my broader theory on the interaction of individual mappings. Please don’t take it as a claim that there is no moral differentiation or that each of these strategies is “equally valid”. They may all be effective in maintaining or negotiating structures, but the impacts of the structures so maintained cannot be considered morally neutral. Or at least they can’t in this particular theory. But the point now is to figure out how they work, not their impacts.

The Problem of Naming

“This is a Blarg,” said my partner, placing his glass of wine in the middle of the table.

We were at a friend’s house late in the evening, on a rare vacation without our children. The conversation had taken a turn, as they frequently do in my world, for the philosophical. We had a moment of replaying our undergraduate days.

“What does it mean to name something?” he asked.

We stared at the glass. We were moderately too impaired to do the question justice, having just returned from a family wedding and having thus spent the evening drowning the emotional weight. It was a mellow conversation, no beer-sloshing involved. We came, as we usually do, to no conclusions, having  gone round and round the conversation of what makes a chair a chair so many times over the years, we see no further angles to be explored.

Later, he said, “Could somebody hand me a blarg?” and he was handed a tumbler full of water. He did not object. “So, we agree in principle that it was the glass itself, and not the wineglass or the glass of wine to which you were referring?” “I guess so,” he said, and we went onto other topics.

But the next day, the question reasserted itself in my mind. What does it mean to name something? What does it mean to name something?

Naming Something: creating categories where none existed

Mathematical philosophers are keen on a set of problems that are broadly classified as paradoxes.

These are, in essence, statements about the world which *seem* reasonable on the surface, but which, when examined more closely, result in absurd or impossible conclusions.

Suppose, for example, that there exists a village which has a rule that says, “All men who do not shave themselves are shaved by the barber.” (1) The question that exposes the (extremely famous) paradox is, “Who shaves the barber?” (If he shaves himself, he is not supposed to be shaved by the barber… but he is. etc.) (If you simply must see the detailed proof of the intractability of the contradiction, it’s on youtube… with animation!)

Not to discount the mathematical truth of the paradox, the linguistic example exposes a completely different issue with our thinking… which is to propose that, in becoming a barber, the man acquires a different essential nature. The problem is with the use of the verb “to be”, which functions as an identity operator. In this formulation, “The Barber” is now always a barber, whether he is in the midst of barbering or not. His being is now that of A Barber. In this moment of naming, we divided the world in two, and we created a problem (of maintaining that division) where previously none existed.

New Names, New Rules

Even if you, like me, now wish to dismiss this paradox as arising from a rule too stupid to be considered (more on that later), let us sit with it for just a while longer…

For some reason, this village concerns itself with the regulation of shaving behaviours. Perhaps it is a public health concern, perhaps there is some stricture regarding it as a pleasurable activity.  Maybe a powerful barber cartel runs the political system at the national level. Whatever the underlying cause, men are not permitted to go ’round shaving one another all willy-nilly. It also seems clear that a man cannot become The Barber simply by offering to shave his friend’s face, as there is, apparently, only one in the village. There must be some process by which a man makes the transition from not-Barber to Barber, or by which Barber-ness is conveyed.

Before the rule was written, there were (presumably) just men who shaved or didn’t as they saw fit. Their neighbours may have looked askance at their hairy faces, but they didn’t have the force of law to do anything about it. There may even have been people willing to provide shaves for other people, and they may not even all have been men.

But all that changes with the creation of a formal category (role) called The Barber.

Now the village requires an entirely new set of processes. They require

• a means of selecting The Barber
• a way of enforcing shaving requirements
• regulations regarding frequency of shaving and/or maximum permissible stubbliness
• some means of preventing illicit and/or black-market barbering

A whole new world of social control is opened up by this requirement.

Look. Let’s be honest. It is a dumb rule. The “paradox” only arises because of the presence of an unnecessary condition in the definition of barber/not barber. If the barber were simply defined as “The person who shaves other people”, without that strange and unnatural exclusive or, there would be no paradox. If we defined barbering as a process, not an identity, he could shave himself quite happily, because barbering would only occur in the moment of relationship with the other. Any number of possible formulations resolve the practical problem… because no conflict exists in fact. The tension arises purely as an artefact of our incorrectly described (and thus prescribed) reality.

But here’s the thing: we try to live our lives according to equally dumb and contradictory rules all the time. This is the nature of the policed identity, which tells you what you can and cannot do based not upon your abilities or your interests, but upon some category to which you have been assigned. Or which has been assigned to you.

For now, before we get deeper into the problem of identity, let us rest here (possibly sipping at our blargs of wine) in the world of the regulated, perplexed, and hairy barber, not because it is realistic, but because it is unlikely to turn the ire of the world upon us.

Unless there really is a secret barber cartel.

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1. This is the statement as I first encountered it, and it seems a perfectly natural way of expressing a rule. More recent iterations seem to be mainly of the form, “The barber shaves those, and only those, who do not shave themselves.” Which I can’t imagine any non-mathematician uttering in casual conversation.

“Position Yourself,” He Said

(This blog has a glossary. Or it will, someday.)

When I was in grad school the second time, I signed up for a course taught by a radical queer theorist/anthropologist. Because that’s what all physics teachers need, you know?

My very first assignment in this course was to summarize the readings (three full length academic papers) on a single page and then ask three questions that had been sparked by reading them. The questions I asked were about why people are so inclined to categorize one another, whether there is some underlying biological drive to separate ourselves based on physical characteristics. His response was the most useful, if not the most traditional, that I’ve ever gotten. What he said was, “Frankly, I don’t really care.”

“Look,” he continued. “The point of this course is to explore the discourse around race. How does race work as a category? How is it constructed as a valid way of thinking about the world? I need you to pay attention to your reading practices. Don’t write response papers, I’m not interested in your responses. I want to know whether you understand, whether you have grappled with the material. Don’t rush to apply before you really know what it is that the author is saying.”

This, to a room full of graduate students, some of whom were several years into writing response papers for nearly every course. You could hear the panic building. What do you mean, don’t react? What do you mean, don’t respond? Don’t apply? I thought that was the “highest” point of development on Bloom’s taxonomy?

“Look,” he said again (he said, “look” a lot), “Your reaction, your initial response, it’s coming from somewhere, from your position in the world. If you find yourself resistant, that’s important. You need to look at what is going on inside your head, what identity you are coming with that is triggering that reaction.” I wrinkled my brow. He had been kind enough not to share whose paper he was dissecting, but I knew. Specifically, I knew that I had been reading a lot of evolutionary biology recently, and that the questions I asked came directly from that school of thought. I also knew (was able to hear) that it was the wrong knowledge tradition to bring to this classroom.

Over the course of that term, I discovered that I was white, middle class, educated. White, I tell you! Yes, I knew I was white. But I never really thought about it. I didn’t have to. This is the essence of privilege, not to have to be aware of categories, as long as you belong to the default. It grants you unearned power. We don’t have to cover privilege right now; it will be a recurring theme.

He asked us to leave our identities at the door, to enter the classroom with open minds, willing to hear the stories of The Other, willing to accept subjective realities that we had no language to encounter. He had us read Frantz Fanon’s work, and I didn’t understand it, but I mulled it, turned it around in my mind, let it sit, until one day I did understand, and I had to stop the car because I was crying too hard to drive.

Who are you?

Position yourself. How do others see you? How do you identify yourself?

Well, I’m a white, middle class, educated, English-speaking, North American. I am also a feminist, and a socialist, and a bleeding-heart liberal, and a queer-identified, male-partnered mother of three. I have a science education and can read math and source code. (This has its own form of privilege in a culture which so values the rational.) I have a tremendous amount of power and opportunity, and a lived experience of constraints just severe enough to remind me that maybe not everything is possible, that we don’t make it on our own, and that resources are not equitably divided.

But who am I? I am more than the sum of my labels, even if I could pull them all into one place. I am (you are) a time-evolving pattern in the universe, a conscious accumulation of particles, capable of feeling desire, anger, and empathy. I am (you are) the stuff of stars. I am (we are) the universe making sense of itself. One. Human. Interaction. At a time.