Math Isn't Real
This week, I'm finally graduating with my bachelor's in applied math. It seems like many are drawn to math by some notion of it's objectivity, myself included at some point. Using pure logic to prove theorems, it seems like it must be some sort of truth, some part of reality itself. In reality, math is terribly, terribly subjective. To its benefit, of course. And thinking about the subjectivity of math, both applied math and pure math, can yield some perspective useful to other fields, such as queer theory.
Applied Math isn't real.
All models are wrong, but some are useful
Applied math is specifically concerned with applying the tools of math to practical applications, typically involving some sort of mathematical model. Newton's three laws of motion are an easy example, they're decently accurate for most human-scale physics and simple enough to be taught in grade school. Phrases like "an object in motion stays in motion" or "every action has an equal and opposite reaction" have burned themselves into the English corpus. The mathematical formulations of these laws are often used in some of the first application problems anyone sees in a calculus 1 class, and are likely to be the only way most people are presented classical mechanics (everyday physics) in a high school or introductory college physics course. The entire field of physics itself provides interesting insights into applied math because the two are so interlinked. Oftentimes, math is invented literally just to do physics. Many of the applications throughout my degree had something to do with physics, e.g., heat transfer, vibrations, flow of fluids,
Newton's three laws of motion are wrong. For anything really small, really massive, and/or really fast, they become practically useless. Fortunately, we have other models for physics that describe these more accurately! Special relativity for the really fast, General relativity which generalizes this to also describe gravity and the very massive, and quantum mechanics for the really small. You might be using the theory of relativity daily with out knowing it! (or, rather, your phone is). GPS wouldn't work without Einstein's model. However, these models are wrong too! General relativity and quantum mechanics famously do not cooperate. Attempts to unify these and find a theory of quantum gravity is a wide ongoing field of research. Many seek to unify all of physics into just one "Theory of Everything." Let's assume, for now, that such a theory could be found. Would it be correct? By definition it would account for all physical observations. This isn't sufficient though, because so does the statement "anything could do anything at anytime." We need precision here in addition to accuracy. I'm not a statistician, so let's just assume that current theories of quantum mechanics are wrong and that everything we previously thought was random is actually somehow deterministic. (Or, if you'd like, assume that random processes still exist, but our theory of everything describes their distributions and that our observations always match these distributions to an arbitrary significance). Such a model would be difficult to describe as "wrong." Such a model might even be easily described as "correct." And, it's likely that such a model would be very useful. But it would not be unique, and it would not always be useful.
Let's consider that non-uniqueness. Looking at classical mechanics, there's actually more common formulations than just Newton's method. For example, Lagrangian mechanics and it's descendant Hamiltonian mechanics both formulate classical mechanics with an emphasis on energies and their relationship rather than the evolution of forces applied to objects. Importantly, these formulations make trivial some impossibly difficult to solve problems with the tools of newton's laws. In a practical sense, these formulations become tools in a toolbox rather than attempts to definitively capture some specific phenomena.
A Theory of Everything would probably have some drastic ramifications and enable some new technologies and etc. etc. BUT but but that doesn't make it always useful. Something being more accurate doesn't always make it the best, since usually higher accuracy means it's more complicated. There's always a balance to strike between the accuracy of a model and its simplicity. Physics curriculum starts with Newton's laws instead of general relativity for a reason. And this doesn't mean that we're lying to children about physics, just striking a balance between accuracy and usefulness. This doesn't mean the statement "gravity is a force" is necessarily incorrect, it's a model and it's not necessarily any more wrong than any other model. Sure it may be less accurate, but, often, it is much more useful.
Physics doesn't exist in a vacuum either, there will always be context surrounding it and how we use it, as for any mathematical model. If we learn to describe all there ever is and all there ever was, at the end of the day there will always be a lesbian somewhere crying themself to sleep.
Pure Math isn't real either.
Even in pure math, there isn't some objective truth to be found. Sure, math is built around proving statements using pure logical reasoning. But those proofs require statements that have proofs of their own. It's not proofs all the way down, you eventually arrive at a set of axioms which are simply assumed to be true. There's nothing special about true or false. You could switch your axioms around to be assumed false and it would invert everything while retaining the same structure. It seems like their only real meaning is just not being the other. And when we assume an axiom to be true, we aren't assuming it to be true as some fundamental aspect of reality. Instead, we simply assume it to be true in order to examine what happens when we apply rules of inference. It's a subjective choice. Pure math is not objective.
The common set of axioms which forms the foundations for the rest of math are the axioms for set theory, specifically the Zermelo–Fraenkel-Choice set of axioms. These axioms define some basic things, like that two sets are equal if they have the same elements, or that you can combine all the elements in multiple sets to make a new set. The last one, the Axiom of Choice, is a historically contentious axiom that is generally used today. Because it is often useful to do so. It states that given a collection of sets, there's always a way choose one item from each of the sets. Using Bertrand Russells' analogy, this is easy for any collection of pairs of shoes. Even for infinite pairs of shoes, you could always just choose the left one. But if you had infinite pairs of identical socks, there's no obvious method to choosing one from the other. But using the axiom of choice, we can assume such a way to choose exists without actually having to construct it. And I think this line of thinking can apply to identity as well. Out of infinite possible ways to construct human identity, there's no obvious way to pick out which one would be me each time. But maybe I can just assert that I could and move the fuck on with my life.
Set theory underpins the rest of mathematics. We've assumed the empty set
Similarly, we can get integers, rational numbers, real numbers, and define operations between them such as addition, subtraction and multiplication, with just the set operations defined in our axioms. But the thing is, real numbers aren't fucking real. They're a model. And they're wrong. Like, really, really, really broken. Let's say you have a sphere, right? It's got some radius, some surface area, some volume. All real numbers. If we assume this ball to exist, then, by our model using the real numbers, and a theorem known as the Banach-Tarski Paradox, you can split your ball into five pieces, and put them back together to create two exact copies of the original ball. No new points are created, by simply pulled out of the uncountably infinite real numbers already present in the first ball. Clearly there is something wrong with our model of a ball.
With this perspective, it's natural to see why it's so hard to bring general relativity and quantum mechanics together. The former relies on the real numbers, on continuous numbers with relations described with calculus. The latter relies on discrete values (quanta) of all quantities, which can render calculus useless.
Math modeling perspective applied to queer theory
Language fundamentally requires some amount of abstraction, otherwise we would all be speaking to each other in pure unfiltered reality. That would be as pointless as making a map via recreating an entire location atom-by-atom. These simplifications necessitate edge cases, something must always be left behind. While no technology or science is safe from ethical context, the questions of "What is this model useful for," "What does this model not account for," and "What assumptions does this model use/perpetuate" are especially consequential in the context of queer theory. In a math context, it's easy to agree upon when/where models are generally useful, but if we start thinking of more linguistic structures this way, we run into more... implications. It becomes more necessary to consider where these structures come from, who's using them, and why.
What happens when neglecting those edge cases cause harm? For example, defining "gender" as invariant from one's genitalia or one's "sex" casts out anyone who this might not be the case for, and enables systemic violence and injustice against transgender people, non-binary people, intersex people, women, etc. Defining "gender" as something socially constructed yet exclusively performative denies any closeted trans person their gender. Defining "gender" as something separate from "sex" but still of biological origin, say, a matter of neuroscience, essentializes gender into human identity and is still used to perpetuate harm against transgender, non-binary, and gender non-conforming folks. So, is there an accurate way to define gender? You are not going to find a consensus. But you could consider every definition to be wrong, and some definitions to be useful. Or, rather, some definitions to be motivated, to be purposeful in context. This approach to labeling in general could, for some, alleviate much of the discomfort I see around labels in queer discourse. For these labels create both a meadow to describe ourselves in relation to, and a prison to keep us organized and gate-kept. Consider that all labels are wrong, but some are useful.
I will end with an excerpt from Paul B. Preciado's An Apartment on Uranus. He finds himself on Uranus, somewhere beyond these structures, perhaps beyond this notion of a structure or model entirely.
Then, I remember my dream and I understand that my trans condition is a new form of Uranism. I am not a man and I am not a woman and I am not heterosexual I am not homosexual I am not bisexual. I am a dissident of the sex-gender system. I am the multiplicity of the cosmos trapped in a binary political and epistemological system, shouting in front of you. I am a Uranian confined inside the limits of techno-scientific capitalism.