The Axiom of Equality

On axioms, annotations, and the way we return to ourselves

I have a copy of A Little Life that looks as though it’s lived several lives of its own. The spine is cracked in a way that suggests it has been pried open and held too tightly, the weight of its pages pressing against hands that refused to let go. More pages are dog-eared than not—reminders to return to them, even if I can’t remember why I wanted to. Entire passages are underlined as if I were trying to etch them into myself, as if the ink might seep through the pages and into my skin. There are boarding passes and MetroCards hidden between the pages, holding a place for a former version of me—a version that was reading but didn’t finish, that didn’t yet get to the end. The pages have yellowed and softened, but maybe that’s just what happens when something has been held too many times, when it has absorbed the weight of every place it’s been carried.

I’ve finished the book. Many, many times. I read it for the first time within three days, absolutely unable to look away from the words before me, even when they made my chest ache with something heavy and unnameable. I’ve lost count of how many times I’ve read it since then, but I know the number will only continue to grow. I know how it will end every time. I know it will be tragic and heartbreaking and sorrow-inducing, and yet I still open the book and read it anyway. As if the devastation is something I need to revisit. As if I expect it to end differently, or at least I hope to find something different within it. The ending never changes—at least not in plot or words. Sometimes, the way I look at it does, though.

It’s a devastating book, but maybe that is why I love it so dearly. It holds some of my favorite words I’ve ever read, ones I return to when I need them and ones that return to me when I need them—even if I don’t want them to. It is a book that seems to exist outside of time, in that sense.

A whole section of the book is dedicated to the axiom of equality—the concept that x is equal to x and always will be.

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“The axiom of equality states that x always equals x: it assumes that if you have a conceptual thing named x, that it must always be equivalent to itself, that it has a uniqueness about it, that it is in possession of something so irreducible that we must assume it is absolutely, unchangeably equivalent to itself for all time, that its very elementalness can never be altered. But it is impossible to prove.”

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Admittedly, I am not a very math-oriented person. I took my last required math class last semester and could not be happier to be free of the subject. And yet, this part of the book continues to stick with me, three years after I read it for the first time.

I find myself thinking about Jude—the book’s main character. He takes the axiom to mean that he will never be anything other than what he has been. That the past is the only truth of who he is. That no matter how the world changes around him, he will remain the same: damaged, incapable, unworthy of love. Now, regardless of the falseness of his self-perception, the axiom, for him, is not comfort. It is a sentence.

I think about this often. What is x? Am I x? If I believe the axiom, does that mean I am fixed in place? And, if this is true, what does that mean for me? Like Jude, do I accept that as an inescapable and tragic fate? Or is it the opposite—is my only proof of constancy found in my ability to come back to myself, to who I was, and to who I’ll always be? I guess I don’t really know what the answer is here.

Maybe that’s why this axiom haunts me. It forces me to wonder if anything is truly irreducible, if anything can remain unchanged. I think about it when I consider who I was when I first read the book versus who I am now, and I wonder: am I equal to myself? Am I now the same person I was then? My gut reaction is to say clearly not. But is there a part of me that is so unique that it will always be a part of me? Do I remain the same at my core, or am I merely a collection of versions, each one slipping away before I can grab hold of it?

Honestly, I realize I've written more question marks in this than periods. I'm at a point where I don't have concrete answers to most of this. But, the axiom is about believing something that can't be proven. And so, I'm also at a point where I want to believe that there is something so immuteably special about me that it will always exist within me. That no matter how many years go by, that I will continue to be me. I will have grown, but I can come back to who I am. To who I was, and to who I will always be. I guess it's a bit like my copy of A Little Life. The pages are worn, creased, written on. But the text is still the same. I may read it differently, and it may have a new meaning for me as I get older, but the words themselves don't change.

I have a bit of a fear of aging—of the slow accumulation of years and time and loss. But as Yanagihara’s novel (and all life experience) so devastatingly shows, the alternative is so much worse. Jude’s life is a study of survival, but it is also a question of whether survival is enough. I don’t think it is. I’ve realized that life isn’t just about getting through but about finding meaning—about holding onto the things that make it worth it.

I’ve found a lot of those things this year.

I turned 19 a few weeks ago and with birthdays always comes the inevitable existentialism of growing older. Of feeling exactly the same and yet somehow completely different. Of embracing the newness of the year to come and yet being cognizant of all the things you’ve left behind in the year passed by.

19 is a weird year for me. When I was little, it always felt like 18 was the thing to look forward to; I was excited for 7 (my golden birthday), 10 (double digits!), 13, 16, and then 18. It meant graduating highschool, moving out and going to college, being able to vote—all the things that seemed very ‘grown-up’. But now I’ve done all of those, and I’m in college, and 18 has come and gone. Now I’m 19 and it’s like I’m not really a kid anymore but I’m not actually an adult either. It’s this weird in-between stage that I haven’t yet figured out how to navigate—but maybe that’s what 19 is all about. I don’t know.

Anyway—this past year, I moved to New York City. The very place A Little Life is set. A city I once only knew through words and imagined streets is now the place I walk through after classes or on a weekend afternoon. It’s the place I have laughed and cried, the place I have found a home in, and the place I have met people who feel like they’ve always been in my life.

A Little Life is, in many ways, about the endurance of friendship—about how it can be the closest thing to salvation. JB, Jude, Malcolm, Willem—each of them finds in their friendships something that holds them together even as their world frays at the edges. The friendships I have now (new and old) remind me of the ones in the book. The way we cling to one another, how our lives intertwine in ways we don’t always recognize at first. There is an intimacy in knowing each other so well, and in growing to do so.

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“I know my life's meaningful because" - and here he stopped, and looked shy, and was silent for a moment before he continued - " because I'm a good friend. I love my friends, and I care about them, and I think I make them happy.”

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I think being a good friend is one of the greatest things I can be.

Friendship is so often the thing that makes it all worth it. The love and the companionship and the ability to walk through life side by side because you’ve chosen to walk together. The knowing someone so well that you’re clearly aware of their faults but loving them regardless.

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“Why wasn’t friendship as good as a relationship? Why wasn’t it even better? It was two people who remained together, day after day, bound not by sex or physical attraction or money or children or property, but only by the shared agreement to keep going, the mutual dedication to a union that could never be codified.”

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There’s a quote from A Little Life that I love very much and that I’ve read aloud to nearly all of my dearest friends—the people in my life I adore greatly and who this quote makes me think of (or maybe who make me think of this quote?), when I’m feeling particularly sentimental.

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“You won’t understand what I mean now, but someday you will: the only trick of friendship, I think, is to find people who are better than you are—not smarter, not cooler, but kinder, and more generous, and more forgiving—and then to appreciate them for what they can teach you, and to try to listen to them when they tell you something about yourself, no matter how bad—or good—it might be, and to trust them, which is the hardest thing of all. But the best, as well.”

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I think, no matter how else I change or evolve or become a new version of myself (three ways of saying the same thing, I suppose), those I am lucky enough to call my friend are there to bring me back to myself. And I turned nineteen a few weeks ago and time keeps moving and keeps asking me to become someone new—and maybe I am. But maybe becoming someone new isn’t really about shedding who I was, it’s just adding on to her. Knowing that I can always come back to her. Knowing that it isn’t about losing myself, but rather adding onto myself. Knowing that no matter how much I change, there will always be a place where I remain—dog-eared, underlined, maybe held too tightly. Very loved throughout.