The Unbearable Whiteness of Being

As I often do, I’m going to start in an odd place before I get to the actual things I want to talk about. Today, I’m going to start with Jean-Baptiste Joseph Fourier, a French genius (1768 - 1830) and end up with Queer of Colour students, whose genius is being suppressed by whiteness.

Fourier should be loved by the ‘woke’. He promoted the French revolution and is credited with being the first to propose the greenhouse effect at a planetary level.

Sadly, however, he was white. And Male. And is dead. The perfect trifecta of bad things to disqualify him as anyone we should honour or praise.

The only picture I could find of him does seem to indicate he’d not been sufficiently introduced to the pleasures of testosterone.

So, let’s just re-write history, because that’s the done thing these days, and suggest that he was, in fact, Queer. He never married, so that’s further evidence he wasn’t a champion of the cisheteronormativepatriarchosystemicaloppression that was in operation back then (as it is today - only it’s worse now, allegedly).

If you’re a student doing one of those STEM things, particularly if you’re into engineering or physics, you will almost certainly have to learn how to do some Fourier Analysis at some point.

We’re not going to learn how to do it here, but it’s a cool idea. We’re all kind of familiar with it anyway. Think of “cranking up the bass” which is something many of us might have done to annoy our neighbours in the past. We recognize that the lo-frequency components of the music we’re listening to are exciting for us, but intensely annoying to anyone else within earshot.

What we’re doing here is amplifying the low-frequency bits. If you like a bit of screeching with your bass, you might also tweak the treble knob and amplify the high-frequency components.

So we’re familiar with the idea that the music we listen to contains bits of different frequency. This is, crudely, the entire idea behind Fourier Analysis. It’s a way to break down a ‘signal’ into its fundamental ‘frequency’ components.

It turns out that if you have some ‘signal’ that varies in time, you can reconstruct the entire signal by adding together ‘pure’ oscillations like sines and cosines of different frequencies.

I don’t want to get into any of the real details, and it will come as no surprise that I’ve left rather a lot out of my ‘sketch’ above, but one further neat thing that came out of this was an understanding that (a lot of) functions can be thought of as vectors and that you can build up a general vector (a function) by adding together fundamental basis function vectors (like sines and cosines). This is exactly analogous to the way in which you can re-create any arrow on a piece of paper by adding together, in appropriate combination, just 2 arrows of unit length; one of which points north and one of which points east. The north and east arrows act as fundamental ‘components’ for the whole space of arrows we can draw on a sheet of paper.

Now, in general, you have to add an infinite number of these fundamental function components in order to be able to reconstruct the function you’re interested in. So, we have to know how to do that. We also have to know whether we can do that - because not all functions can be expanded like this. You have to have some idea of something called convergence. When we add an infinite number of things together does it converge to a definite value?

If we add 1 + 2 + 3 + 4 + 5 + . . . (etc) we can see we’re never going to converge to a specific value - the sum just keeps getting bigger and bigger. But what about something like 1 + 1/2 + 1/4 + 1/8 + 1/16 + . . . (etc) does that home in on a specific value as we add more terms? Yes, it does. You get closer and closer to the value of 2 as you add more terms in¹.

This is what happens with Fourier Series (Fourier Analysis applied to periodic functions); as you add in more and more sines and cosines you get closer and closer to the function (the ‘signal’) you’re interested in.

It’s at this point I have to profoundly apologize to any Queer of Colour people who may be reading because I have, undoubtedly, caused you undue emotional labour² by the sketch explanation I’ve given because it is steeped, just drenched, in whiteness.

Even my ham-fisted attempt to make it more culturally relevant by talking about “cranking up the bass” probably wasn’t enough to overcome the decades of intergenerational intersectional interplanetary trauma you must have faced.

You think I’m just joking, don’t you?

This was the Spectra Lavender lecture of 2023 which is

an honorary lecture to be given annually at the Joint Mathematics Meeting to recognize and highlight the contributions of LGBTQ+ mathematicians. This event seeks to honor an LGBTQ+ mathematician who has made significant contributions to the mathematical sciences, mathematical education, or the mathematical community at large.

According to the abstract of this lecture I’ve been doing it all wrong, all this time.

During the second half of the lecture, I apply my framework and research findings to argue how undergraduate mathematics education operates as a white, cisheteropatriarchal space that limits learning opportunities affirming of queer of color identities and experiences.

And here’s me thinking that my job was to develop an understanding of maths when I should have been trying to affirm the identities of my students.

I was not sufficiently concerned with “justice”. That’s my whiteness, see. Those of us infused with this terrible, terrible affliction just don’t care about justice at all. But the good news is that we can do better. The author tells us how :

. . . by re-imagining undergraduate mathematics education with structural disruptions that advance justice for learners marginalized across intersections of race, gender, and sexuality. This re-imagining accounts for ideological, institutional, and relational forms of disruption that interrogate dominant forms of knowledge production as well as expand access to learning opportunities and departmental support that affirm queer of color identities.

I just didn’t put enough of those structural disruptions into my lectures. What a wasted opportunity. I unreservedly apologize to all of my former students.

The upshot of all of this sesquipedalian loquaciousness is that we must hang our heads in shame as lecturers. In another of the author’s papers

we learn that our traditional way of doing things, just focusing on the maths, has a negative impact on the Queer of Colour and other marginalized entities, like women, because we have

. . . limited faculty consciousness of how students can experience instruction in oppressive ways and thus potentially reinforced racialized-gendered harm through their practice. I conclude with implications for instructional practice that confronts systems of power preserving mathematics as a white, masculine space and expands equitable learning opportunities in undergraduate calculus.

All that racialized-gendered harm I’ve been doing by just trying to get them to understand a bit of Fourier Analysis. My white guilt is threatening to overwhelm me.

All of that oppressive instruction. I will accept that my grading was oppressive. I oppressed the hell out of those who got it wrong when I should have been effusive in my praise for their ‘imaginative’ working, however bizarre or incorrect.

Can’t expand a bracket? I’m sorry, that’s because you’ve been steeped in a White Cisheteropatriarchal Space that has prevented you from learning how to do it. I have some structural disruptions up my sleeve that might help.

As ever, the question of how (TF) did we get here?, rears its ugly white head.

One of the ‘classic’ papers that purported to ‘analyze’ how ‘white supremacy’ (aka whiteness) operates in organizations is simply titled “White Supremacy Culture”. It lays out certain organizational behaviours that are said to be all examples of white supremacist ways of doings things.

Some of the things on the list are a bit strawmanny and others do, indeed, represent negative practices in a workplace. Others are just silly.

What’s fascinating, however, and where there is no analysis at all, is the identification of these things with whiteness. This is just assumed. It is far from self-evident. Any moron can make a list of stuff they, personally, don’t like and just call it “whiteness”.

I don’t like sprouts. Or mushy peas. Must be all that whiteness involved in food prep.

There’s no attempt to justify the equation

purported bad stuff = whiteness

It’s just an axiom wholly plucked out of thin air that we’re expected to nod along to.

Bugger that.

And this is claimed as some kind of ‘foundational’ paper in subsequent writings. It’s, academically speaking, a joke - it should have been laughed the fuck off the stage and ridiculed to Andromeda and back. And yet it was taken seriously.

Once you’ve nodded enough times you’ve severed your spinal cord you can then write papers about how all this white stuff pervades entire systems and works against marginalized folk - like the Queer of Colour.

It’s all built on the sweetest most sickly dollop of Fuck All.

It’s a well known result in maths that if you are prepared to accept as true some logical absurdity (like 2 + 2 = 5) you can basically ‘prove’ anything.

We can justice and intersect and disrupt and equity and queer our way through the teaching of maths as much as we like, but none of it changes the fact that, at the end of the day, the students are just going to have to learn (and hopefully understand) how to do Fourier Analysis.

That’s just the way the Oreo crumbles.

Fourier must be examining high-frequency rotational motion in his grave.

1. If you want a nice pictorial way of seeing this then draw a square. Halve it and shade in one half. Take the unshaded piece and halve that, shading in one of those halves. Keep doing this process. You can quickly see that you’re never going to go ‘outside’ the original square and that each time you do it you shade in more and more of the original square.

2. “Racialized and gendered labor in students’ responses to precalculus and calculus instruction”