# Blog

What I'm curious about right now## Inner and Outer Critics: the Power Dynamics of Imposter Syndrome

I don’t have *an* inner critic.

I have at least ten of them.

Their voices are shrill, thundering, hissing quietly. They say things I’d never say to another human being. Frankly, they’re a bunch of verbally abusive jerks.

They tell me all kinds of things – things that mostly aren’t true, though they’re laced with enough *truthiness *that they often get to me. At their heart, my inner critics are fear embodied. Fear embedded within my mind, nervous system, muscle memory. Disdain internalized.

I’ve written before on how I work with my inner critics – how to work with imposter syndrome when it crops up, minimize its hold, move past the obstacles it has set in my path. I’ve taught others how to do the same.

What I haven’t written about before, but have been thinking about a lot, is where the inner critics come from.

They don’t come purely from within. Not everyone has inner critics – at least, not the obnoxious, and frequently paralyzing kind I’m talking about here.

Inner critics come from outer critics, seen and unseen.

They might come from your father. *(He’s never satisfied.* Oh man, Prince is on repeat in my head right now, but I’m gonna forge ahead here.)* *Your big sister. A shitty teacher. You might hear echoes of their voices in your mind when you’re working on stuff that matters, or just going about your day.

But they might also come from the environment you grew up in – and here, I mean the water you swam in, almost invisible to you:

- The educational system that rewarded privileged kids and punished the ones who came to school hungry, tired, or distracted by the chaos at home.
- An economic system that might not show you a whole lot of people like you rising to the top of the financial heap.
- A culture that uplifts “normalcy,” whatever that might be, and tells you that any part of you that doesn’t fit the mainstream mold should be hidden, reshaped or disowned.
- A society that has demonstrated again and again that
*you are not safe*– that your body, your voice, the work of your hands can be used and stolen from you at any moment, for the pleasure, profit, and amusement of others.

These are the outer critics. They are as real as real can get.

The outer critics say: *You are worthless. (Or at least, worth less.) Your idea would be more valuable if it were spoken by someone whiter, straighter, able-bodied, male. You could sell more books if you had a Ph.D. after your name, no matter that you can’t afford grad school. *

The outer critics are sometimes very, very quiet. They can afford to be, because they are everywhere. They don’t need to be loud because they are The Way It Is: indisputable, seemingly monolithic, nigh impossible to topple.

And sometimes they’re loud and proud: the trolls online who threaten you for daring to work in a male-dominated field. The music professor who told me, with no trace of irony, that the reason her syllabus featured not a single woman composer was because there *were *no great women composers. Justice systems that repeatedly perpetrate violence against people and communities of colour without facing repercussions.

When you grow up in a world where the outer critics have power – and let’s be clear: the outer critics *are *the power. If they didn’t have power over us, we could brush them off, twirl on them haters, and move on – it is a completely rational response to internalize their criticism. Because the consequences of ignoring it are real.

What we call imposter syndrome often reflects the reality of an environment that tells marginalized groups that we

shouldn’tbe confident, that our skills aren’t enough, that we won’t succeed—and when we do, our accomplishments won’t even be attributed to us. Yet imposter syndrome is treated as a personal problem to be overcome, adistortionin processing rather than a realistic reflection of the hostility, discrimination, and stereotyping that pervades tech culture.

(I would add that this is true everywhere, not just in tech culture.)

So we internalize the outer critics, turn them into inner ones, thereby doubling down on the forces standing between us and our chosen paths.

I’ve been reading some excellent writing on what imposter syndrome is, and is not. Alexis Hancock argues that we dedicate way more time and energy to talking about imposter syndrome than we do to addressing the structural inequities that are at the root of it, and to that I say Amen. And it’s no surprise that we lean that way. The powers that be will always be happier paying for imposter syndrome workshops for all their marginalized employees than facing up to their own privilege and biases. And at least here in North America, where individualism is the altar at which we worship, most of us would rather take on a self-help project than join a social movement. We’d rather tackle the problem we think we can fix within ourselves, than the one that’s systemic.

It’s simpler (or so we believe). It’s smaller. And in the case of the corporate workshop, it’s something we can buy once, and then feel good about ourselves. *We’ve done that work, *we can say. *We *feel *more empowered.*

Changing our collective mindsets, addressing our biases and prejudices, addressing inequities – these are hard tasks. They’re deeply uncomfortable, and they’re endless. They resist a simple line in the budget, a date on a calendar, or a metric on a quarterly report. But to quiet our inner critics when the outer ones are still raging has limited value. Even I, who have written and taught and coached on imposter syndrome, freely admit that.

Don’t get me wrong: it’s wildly liberating to learn to outsmart your fears. I still believe it’s meaningful work. But I never supposed it was the whole picture, or a complete solution.

There’s also a fabulous piece by Alicia Liu outlining the differences between imposter syndrome and simply recognizing your limitations.

Before jumping to self-diagnosing with Impostor Syndrome, get objective evidence of whether you are really valuing yourself too low, or whether it’s a more or less accurate assessment of where you are right now. It’s okay to be a beginner, and feel inadequate. Keep learning and growing, and the circle of what you know will naturally grow.

In a related post, she writes, “Impostor Syndrome instilled in me a deep fear of failing. I was afraid to speak up or ask questions for fear of saying something stupid, and people would find out I didn’t really know my stuff… I quietly avoided doing things I didn’t think I’d be good at, even though the only way to get better is to do them.” Here, she connects the dots between imposter syndrome and a fixed mindset, as defined by Carol Dweck.

Fear of failure, coupled with a belief that aptitudes are innate rather than learned – which is, of course, exacerbated by stereotype threat – is a recipe for stopping yourself from stretching. And if you don’t stretch, you’re never going to feel fulfilled by your successes.

So this is the piece I’ve been trying to tackle with my work on imposter syndrome. Not to suggest that it gets at the root of the problem, but that where we *have *internalized structural inequities, fear of failure, and fixed mindsets, we *can *intervene and change our internal narratives. We can choose to act differently, choose differently, than we might if we choose to believe the defaults our culture dishes out to us.

This is not a perfect solution. It is, in some ways, a band-aid. But a band-aid has its uses. It can help you heal in the places that hurt, even if it doesn’t shield you from ever getting hurt again.

I don’t take back my work on imposter syndrome. I stand by its value for addressing the inner dimension of this work: managing one’s inner critics. But I do believe that, as with everything, there is also an outer dimension to this phenomenon. *There is a reason you experience imposter syndrome, and it’s not all your fault.*

And there is deep and wide structural work to be done, here.

I have said before that imposter syndrome affects people who are both “ambitious and conscientious**.**That is, they want to do great work in the world, and they care greatly about that work being done with integrity.”

Ambitious people focus on the outer world; conscientious people, on the inner. The solution to feelings of being an imposter is both an outside *and *inside job.

Let’s roll up our sleeves.

Postscript: I realized after publishing this post that I failed to credit another article that inspired my thinking on this subject: Sarah M. Seltzer’s piece for Refinery29, which argues that imposter syndrome has its roots in systemic problems. “Once you become less insecure,” she writes, “you may end up becoming more pissed off.” And later: “Imagine waking up every day and going to work in a country with more humane policies, like paid sick and family leave, longer vacation time, universal basic incomes, occasional sabbaticals, or anything else that would allow us to pursue our intellectual and career ambitions in a healthier way — without feeling like they were the only things that mattered… In that country, which would look a lot like every *other *industrialized nation, I think a lot fewer of us would feel like impostors, and a lot more of us would feel like people.”

## Adventure and Grief on the Road to New England

Last night, in the deep darkness that comes at this time of year, I got in the car and drove to an empty parking lot outside of a shopping mall. I circled around until I found the row of large metal donation bins in the corner farthest from the mall entrance; parked; opened the trunk of the car, lugged three heavy bags of children’s books to one of the bins, and tossed the books by handfuls into the clanging interior.

I estimate that I’ve read some of those books hundreds of times, talking to my young sons about the pictures, savouring the rhymes and alliteration, laughing at slapstick humour and hoping for the baby animals to be reunited with their mothers. (If you haven’t read children’s books lately, that’s a staggeringly common theme .)

We’ve set aside the books we’ll be shipping to Boston in a few weeks. Some are treasured gifts from family and friends; others are simply too delightful and beloved to part with.

*(Kinda skipped over that move to Boston, didn’t I? I’ll get to that in a minute.)*

When you’re moving across both a continent and a border, every single item gets evaluated. Is it worthy of shipping? Of packing into storage? Either way, you’ll be paying for the privilege of holding on to your possessions. So there’s a new calculus that gets invoked, beyond that wonderful KonMari question – d*oes it spark joy?* – and beyond its monetary value.

It doesn’t always matter how much you paid for it, and how much joy it sparks; if it won’t fit in the shipping container and it’s going to cost you an extra fifty bucks a month to store it, **you will confront the question of how much it’s worth to you right now.**

(This isn’t another ode to living minimally, by the way. It’s simply a letter from this moment in my life to this moment in yours.)

**So about this move to Cambridge:** my partner David has been offered a totally amazing job. He’s going to be teaching at Harvard. That’s particularly amazing because David isn’t an academic – so we didn’t see this coming. It was definitely not in the plans. But it is a what-what-omg-can’t-say-no opportunity. So we are moving, with our two young kids, to a new city.

And we’re working every day to focus on the adventure of it all, and the possibilities it presents, and not get swept away by the grief of saying a thousand goodbyes, of giving away our sons’ baby clothes, of leaving our beloved home.

I’m trying not to be swallowed by sorrow when the books our children teethed on clang into an echoing metal bin in a dark corner of an empty parking lot.

Not because I won’t allow myself to be sad. I will. But because **the aching beauty of this experience is that it is bringing me face to face with the passage of time.**

Face to face with the present.* (This is what transition looks like. This is how not-knowing feels. This is the best use for this object right in this specific moment, no matter what it meant to me last week or six months ago. This is the sound of books falling into a bin, no matter how much my mind wants to fashion it into a leitmotiv of nostalgic farewells.)*

Face to face with the transitory value of all material things.* (The boys have outgrown the baby clothes. Those books will be better loved elsewhere. And still, the grief is here.)*

And for that, I am thankful.

**This is a letter from this moment in my life to this moment in yours. **What does this moment hold for you?

What are you holding on to because it matters enough to keep investing in it?

What are you holding on to that has served its purpose and is ready to be released?

What do you need to grieve in the cold dark? What memories will keep you warm forever?

Where is the not-knowing that makes you so uncomfortable that you reach for your soothing balm of choice again and again?

I’m listening.

*Photo credit: RebeccaVC1 on Flickr.*

## How likely is an all-male speakers list, statistically speaking? A mathematician weighs in.

If, like me, you *still *find yourself shaking your fist at the abysmal numbers of women speakers at your average STEM conference, and you enjoy a bit of geeking out over math, then today’s post is going to make your toes curl in delight.

A few months back, my mathematician friend Greg Martin at the University of British Columbia invited my feedback on a paper he was writing on how to increase the number of women speaking at math conferences. One bit in particular jumped out at me:

**He used statistical probability to disprove the notion that underrepresentation of women on any given speaker’s list “just happens.” **

(Picture me bouncing in my seat with glee. Take *that, *sexist STEM-ers!)

If you’ve ever followed a debate about why an event has so few women speakers, you’re likely familiar with the argument that gender was not a factor (AKA “we chose the best speakers, regardless of gender”), and that speakers were chosen in an unbiased fashion, on merit alone. Well, if I understand the math correctly, the odds of that assertion being true are next to nothing.

It delights me to no end that Greg has found a way to use the master’s tools to dismantle the master’s house. So naturally, I asked if he’d be willing to share a little more about how he arrived at his calculations.

What follows is, to be sure, a fairly technical read—but it’s an accessible and engaging one, too. I hope you’ll follow along, even if math isn’t your most cherished subject, and share this with your favourite stats nerds.

Over to Greg:

In a recent article, I made the following statement regarding the genders of plenary speakers at the International Congress of Mathematicians:

The appropriate null hypothesis is “the ICM speakers were selected independently of gender from among the pool of people who have received PhDs in mathematics in the last 25 years”. Under our conservative 24% assumption from above, the observation of nineteen male plenary speakers and one female plenary speaker rejects ( ) this null hypothesis. Indeed, it is 18 times as likely that we would have seen an “overrepresentation” of female plenary speakers (five or more, since ) by chance than to have seen at most one.

Clearly the gist of this statement is that having one female speaker out of twenty is really unlikely to be the result of chance or bad luck. But how were those exact numbers, 0.031 and 18, determined? How can we calculate analogous numbers in similar situations? It turns out not to be that hard, once we know the formula to use; the purpose of this post is to supply that formula and give some examples of how to use it.

Let’s start by examining an idealized situation divorced from social issues. Imagine that we have a giant bag full of marbles; the marbles come in two colours, orange and green (we like the orange ones better), which are well mixed together. We are going to take 50 marbles out of the bag, one by one, and see how many orange marbles we end up with.

Of course, without knowing whether orange marbles are common, rare, or somewhere in between, we have no idea how many orange marbles to expect! Let’s say that we know that 40% of the marbles are orange and 60% of them are green. On average, we’d expect to get orange marbles in our selection of 50 marbles; but of course, we might get lucky and get more than 20 orange marbles, or we might get unlucky and get fewer than 20 marbles. How likely is it to end up with, say, only 13 orange marbles?

As it happens, the probability of ending up with exactly 13 orange marbles, if we draw 50 marbles from a bag containing 40% orange marbles and 60% green marbles, is^{1}

Here, the symbol is a “binomial coefficient”^{2} (sometimes written as , and pronounced “50 choose 13”).

While it’s not impossible to calculate this on our own, we might as well use WolframAlpha to help out: if we type in

Binomial[50,13] * (0.4)^13 * (1-0.4)^(50-13) ,

we receive the answer , telling us that the chance of getting exactly 13 orange marbles is about 1.47%. We can also go to Stat Trek’s online binomial calculator and enter 0.4, 50, and 13 in the first three fields; we see the answer 0.0147378… appear in the fourth field.

The general version of the above situation is: we have independent opportunities for success or failure (in the example above, was 50, and “success” meant drawing an orange marble while “failure” meant drawing a green marble). In each opportunity, the probability of success is some number (above, ). If we are interested in a certain number, , of successes (above, was 13), then the probability of succeeding exactly out of times is given by the formula^{3}

Now, suppose we suspected that some funny business was going on. For example, maybe our housemate loves orange marbles, and we think that she snuck around one night and pulled a bunch of orange marbles out of the bag before we started taking our 50 marbles. (I guess the bag is so huge that emptying it out and counting all the marbles it holds is out of the question.) She denies it, however, saying “sometimes you get few orange marbles by random chance”. What should you believe?

It seems unlikely to get only 13 orange marbles out of 50 (if there really are still 40% orange marbles in the bag). On the other hand, any specific number of orange marbles is pretty unlikely. Getting exactly 20 orange marbles is the most likely outcome, as we remarked above, but even that has less than an 11.5% chance of happening^{4}. So instead of asking how likely it is to get exactly 13 orange marbles, standard procedure is to ask how likely it is to get at most 13 orange marbles (in other words, how likely it is to get a result this extreme or even more extreme).

There’s no secret here: to get the probability of obtaining at most 13 orange marbles out of 50 (assuming that the bag really does contain 40% orange marbles), we just add up the probability of obtaining 0 orange marbles, 1 orange marble, 2 orange marbles, and so on up to 13 orange marbles:^{5}

Fortunately WolframAlpha can do this for us, if we enter^{6}

the sum of Binomial[50,j] * (0.4)^j * (1-0.4)^(50-j) from 0 to 13 .

The Stat Trek binomial calculator also calculates this for us (the answer appears in the third field from the bottom). Either way, we obtain 0.0279883…; so the chances of getting at most 13 orange marbles is less than 2.8%.

So… what should we believe about our suspicious housemate? Well, there are no guarantees in any of this: while 2.8% is a pretty small probability of getting at most 13 orange marbles out of 50 if everything is on the up and up, it can still happen—in fact, it happens about 1 time in 36. But that low a probability seems unlikely. If this were a statistics paper, our “null hypothesis” would be that nothing funny had happened to the bag of marbles, and we would probably reject that null hypothesis since the standard threshold is 5% (the ubiquitous ” level” of statistical tests). If the only other reasonable hypothesis, in your mind, was that your housemate was stealing orange marbles during the night, then perhaps you should believe that.

More often, though, we get to make similar observations many different times. (I’m not sure what’s going on in this world we’re inventing, but maybe we get a well-proportioned marble delivery every week to top up the bag of marbles, and we draw a 50-marble allotment every week…?) If we consistently see extreme results like this, then we become convinced that something fishy is happening. So each individual calculation becomes a piece of data that we can collect to see if there is a larger, systemic pattern.

From a sufficiently abstract perspective, examining the gender of speakers at an STEM conference is the same as looking at how many marbles of each color we get from the bag. The collection of all people who might have been invited to this conference is our bag of marbles; female speakers are our orange marbles (our “successes”) and male speakers are our green marbles (our “failures”—only in the context of examining appropriate representation of women in STEM, that is!). In a world where gender was unrelated to being invited to STEM conferences, we would expect the proportion of female speakers to be (more or less, since things are always a little bit random) the same as the proportion of female practitioners in the field of the conference.

Of course, knowing or estimating that latter proportion can be difficult. In the quote that started this post, I used the estimate 24% (which I called a conservative estimate) for the proportion of women in research mathematics; my reasoning was based on data of PhD graduates in the US over the past 25 years, where women earned at least 24% of the mathematics PhDs in all 25 of those years (and sometimes up to 34%).^{7}

The particular conference I was discussing had 20 plenary speakers, only one of whom was female. The above formulas tell us that the probability of having at most one female speaker by chance is

,

or a tiny bit over 3%. On the other hand, if gender bias were not present in the academic system, then we would expect 20-speaker conferences to have, on average, female speakers. The probability of having women “overrepresented”—that is, of there being at least 5 female speakers—is

or over 54%. Since , it is indeed almost 18 times more likely (under our assumptions) to have an “overrepresentation” of female speakers than to have at most one.

Although it doesn’t show all the numbers corresponding to its calculations, the Conference Diversity Distribution Calculator gives a nice visual representation of how many female speakers we should expect at conferences in a bias-free world.

## Footnotes

- Coders and other detail-oriented folks might raise the following nitpick: if the first marble we draw is orange, say, then the percentage of orange marbles remaining in the bag is then actually slightly less than 40%! While certainly true, the slight change is negligible if our huge bag contains a very large number of marbles. It is common practice to ignore this detail when “selecting without replacement”, as a statistician would say, from a huge number of possibilities.
- For number geeks and other interested rockstars: in general, the binomial coefficient is a shorthand for a quotient of factorials: Here the factorial is just the product of all the numbers up to , that is, See http://en.wikipedia.org/wiki/Combination for more information.
- See http://www.mathsisfun.com/data/binomial-distribution.html for a from-scratch explanation of why this is the correct formula, and http://www.statisticshowto.com/binomial-distribution-formula for a reference to a more concise version.
- As we can see by entering
Binomial[50,20] * (0.4)^20 * (1-0.4)^(50-20)

into WolframAlpha, or the numbers 0.4, 50, and 20 into the Stat Trek binomial calculator.

- In general, the probability of getting
*at most*successes out of tries, if each success occurs with probability , is

which we can write using summation notation (or Sigma notation) as follows: The probability of getting*at least*successes out of tries equals - Or, for lovers of syntax,
Sum[ Binomial[50,j] * (0.4)^j * (1-0.4)^(50-j), {j,0,13} ] .

- As a side note: among all critical responses to the posting of that article, I found that this one detail—the 24% figure—generated the most criticism, much of it (in my opinion) demonstrably misguided. Some people complained that the “correct” figure to use should be much lower, perhaps around 10-12%, because that is the proportion of women among tenured faculty at top-tier mathematics departments. There are at least two flaws in this argument. First, it assumes that being hired and granted tenure at top-tier institutions is done equitably for women and men, but there is ample evidence of systemic gender bias in hiring, one that is more pronounced at top-tier institutions; in other words, it relies upon the assumption that men at top-tier institutions are generally stronger than women at next-tier institutions, which a dubious assumption. Second, my article explicitly discusses all of the obstacles for women in STEM, even after they earn their PhD—implicit bias in evaluations, double standards for behaviour and self-promotion, the impostor phenomenon, and all the usual factors known to contribute to the leaky pipeline—and hence comparing the proportion of female PhD-earners to the proportion of female conference speakers is reasonable. In this context, claiming that the lower proportion of women in top-tier tenured positions should be the measuring stick for representation at conferences is, quite simply, using a symptom of the very problem we are discussing to justify perpetuating the problem.

*Update, 21 October 2015: I interviewed Greg for Quartz, and you can read that interview here (or here, in The Atlantic).*

*Photo credit: PearlsofJannah on Flickr.*