On Critical Theory and Fourier Transforms

The Humanities and Mathematics Departments Have More in Common than You Think

Critical Race Theory. Feminist/queer critical lens. Marxist literary analysis. Deconstruction. A collection of leftist mad libs (like the game, not insane liberals… never mind) bound to make any conservative shudder. What is it with these woke social justice warriors using ten-dollar words to make up stories so they can revise history textbooks and ruin our favorite movies? Is it simple elitism? A misplaced sense of moral superiority? Or is it because they’re pushing some nefarious Globalist scheme to take over society and enslave us all?

In a word, no. Sure, find the right (or more accurately, the wrong) online communities, and you’re likely to find exactly the kind of boogeyman you imagine in Alex Jones’ worst (okay, medium-rare) nightmares. More broadly, few are immune to the temptations of intellectual or moral pride. But all of these objections to Critical Theory, however valid, merely point out the bugs, not the feature. Professionals aren’t trying to tell some grand narrative of history or make your beloved franchise into some secret gay propaganda.

To some extent, one could be forgiven for the confusion. Somewhat like the sciences, there exists a gap between the people actually doing the research and the often click-bait-y science communicators disseminating carefully-chosen snippets to the broader public. So you end up with both left-wing Bluesky users confidently overgeneralizing and your conservative uncle quote farming some nonsense from LibsofTikTok. So before we can dive into what Critical Theory actually is, I’mma need everybody to take a deep breath, touch some grass, and try to take “Critical Race Theory” out of whatever mental box they had it in and put it in the same box they store terms like “normal distributions” and “cotangent.”

Because that’s where it belongs. Applying Critical Theory is merely a Fourier transform performed on a complex narrative.

Okay, for the non-engineers out there, here are two great videos explaining what the heck a Fourier transform/Fourier series is:

Okay, if you didn’t watch, here’s the tldr: any complex wave, like a sound wave, can be expressed as a finite number of simple sine waves added together. The Fourier transform enables someone to pull out and isolate a single sine wave from a complex waveform using math. And in the second video, you can see how someone can do the opposite: pick a series of simple sine waves to build an arbitrarily complex wavefunction. Cool. Also, don’t ask me to do it, because I suck at calculus.

Critical Theory is a set of tools and a mental framework for deconstructing a complex narrative into discrete threads as a way to gain a better understanding of the whole. It is, out of necessity, reductive; that’s the point. Try summarizing the whole of history in an intellectually honest way so that a high school freshman could understand it. Heck, summarize just the last five years in a paragraph.

Anyone who’s studied history professionally has figured out pretty quick that history’s too complex to fit inside your head all at the same time as one single coherent thing. To make any sense of it, then, you have to narrow your lens and select what elements are worth digging into.

So Critical Race Theory. Is it some anti-white brainwashing scheme? No. Does it claim that race is the sole explanation for where we find ourselves in this historical moment? Again, no. When somebody studies Critical Race Theory, they pull out the thread of race-related dynamics woven throughout history and comment on that thread’s influence now. It doesn’t explain everything, but it’s there, and and it’s often overlooked. Critical Theory narrativizes a complex tangle of cause and effect so that we can make history comprehensible enough for our tiny little brains.

And if Critical Theory can be used to narrativize history, what happens when we turn its deconstructive lens on actual narratives? This is where you see people revisiting works to, again, pull out a hidden frequency (to extend the Fourier metaphor) and gain a new perspective on the whole. To people who do this professionally, college lit professors and the like, I imagine this process is a bit like a treasure hunt.

Lindsay Ellis—a creator who’s been misinterpreted so much she could almost make a career out of it—does this at length in her critical analysis of the Transformer franchise:

Now, I know what some of you would say. If we can deconstruct a narrative into its component threads the same way we deconstruct a sound wave into its component frequencies, how come the liberals who use Critical Theory only pull out the liberal threads? I’d say that question answers itself. It may be that only liberal liberal arts professors call their analysis Critical Theory, but the truth is that every semi-literate person uses Critical Theory.

That’s right, we all do it, we just don’t call it Critical Theory (and we probably don’t do it that well). Conservatives have become adept in sniffing out “woke” pandering in every new movie that comes out. How is this skill any different from what feminists did in the 60s and 70s to find some form of sexism in all media? I suppose the difference here is that the leftist academics know and acknowledge what they’re doing, while conservative commentators imagine they’re giving the final word on a topic when they make their observations. The latter is exactly the wrong way to use Critical Theory. Anyone—left, right, center, or other—who uses Critical Theory to proclaim what X film or book or historical period was really all about is no different from a guy who performs a Fourier transform on a phone conversation and declares that the whole thing was really just a 172 Hz sine wave; in other words, insane.

To deconstruct a text for a critical analysis, you need to be able to do two things at the same time: focus on a particular motif to an obsessive degree and remember that your analysis does not and cannot explain the entirety of the work. This can be hard to do, especially considering how we judge the veracity of theories by their explanatory power. The more of a story or a historical movement a theory seems to explain, the more dots it connects, the easier it is to make the leap to “the one thing that explains X.” People, even professionals, can and do get stuck up their own butts. But again, this is not a feature of Critical Theory, but a bug.

The only way to work out the bugs is to get better at doing it and hold accountable those who do it incorrectly. We all need to become a little more literate, guys. The average American reads on an 8th grade level, and 8th graders aren’t known for their ability to isolate narrative elements or situate themes in their historical context. At the same time, embrace what you’re already doing and call it what it is. Your fan theories on Reddit may be wild and kooky, but have you read any of the feminist criticism of Pixar films? Your unhinged alternate-history takes on how Germany could have won WWII rely on many of the same tools historians use to emphasize overlooked trends in history; you’re just having more fun with them. Your media consumption may be more intellectual than you realize, and intellectual rigor may turn out to be more fun than you’d expect. The ability to look at a text critically can be a great way to enjoy it beyond that first experience

As a writer, however, I get to see this interpretive mechanism from the other side. In the Smarter Every Day video, Destin describes how you can construct any image out of sine wave oscillations. While that is technically true and can theoretically be done as an impressive mathematical feat, artists don’t make art that way. A musician doesn’t compose a song individually selecting thousands of sine waves of differing amplitudes and frequencies, she picks up an instrument and gets to work. Same for me as a writer; I don’t think about every single letter or every possible angle and lens through which my story could be viewed, and trying to do so is like flooring the gas pedal straight into a brick wall. Except, of course, it’s not that simple.

It’s hard to describe my process as a writer when combined with my training in critical analysis. On the one hand, there are plenty of things a reader can bring with them to read my story in a way I didn’t necessarily intend, and I’m more or less okay with that (just don’t use my work as some weird justification of Nazi nonsense or whatever). On the other hand, I do use critical analysis of my own work quite consciously as a tool to diagnose problems with my writing. Maybe something feels off, like a trained audio engineer picking up on some high-pitched frequency sneaking into the recording. If I tease apart the threads, I might find that an emerging theme I’d initially found compelling is clashing, rather than contrasting, with the main theme I’d built from the start of the story. I can either find a way to reconcile the two threads or decide which one to deemphasize.

So there you go. Critical analysis is a tool to pull at the thread of a more complicated work and discover something new. I encourage you to try it. Just know what you’re doing, why you’re doing it, and when to stop. If you unravel a story so completely you start making an entirely different article of clothing (rookie mistake to introduce another analogy right at the very end), it might be time to try your hand at writing your own story.