Mathematics moves in mysterious ways... spells of arithmetic forged with sigils, numeric and operative. These are the keys and the battering rams used to pass new gates of knowledge. As we unlock and annihilate the mysteries of reality, in turn we learn new spells. If only we knew just how vicious this cycle could become.
See, when Story was eight she was riding her bike once, alone. It was one of her favorite things to do, in the late afternoon, just before twilight really set in, when the whole apartment complex was indoors and it felt like a ghost town... to ride her bike alone. In this solitary silence one day she had a thought, something sharp and clear as a crystal knife cutting through the relative thick soup of eight year old consciousness. She thought: "I wish I could just disappear."
The thought did not come alone. It was, like a thunderstorm at the head of a cold front, trailing something behind it. The doctors would call it "depersonalization" which she guessed was a nice word for it since before that she called it "that feeling that you are not real, that you can't possibly exist." Or that's what she would say that she called it from her adult perspective, but then memory is tricky. It's hard to know if our child selves really had the grasp of language we ascribe to them, or if we put words in their mouths confabulously to try to express what we feel sure was their mind. In any event, that was the front that was blowing in behind the storm of vanishing: a lesser talked about dissociative disorder.
These two became her constant companions through her childhood: the feeling of wanting to disappear and the feeling that she did not and could not possibly exist. They might each come alone or they might come together, but both came and went as they pleased.
One rainy spring day when she was fifteen, she scribbled this in her diary:
When I was young, I already knew where this was going. On the way home from my counseling appointment today I zoned out watching the raindrops sliding around and combining. I always did that when I was a kid, until I would be shocked when we arrived at our destination. The raindrop ballet had become the world and when I was snapped out of it and into another one, it was... just wrong.
When I tried to tell my mom about raindrop world, she never understood. My therapist doesn't understand this "depersonalization" stuff. It's not her fault. It's hard to describe a feeling that defies logic. It's hard to define a feeling that makes logic twist around itself. It's a mental paradox, a kind of singularity, and the only way to understand it is to have that same black hole in your head.
I read a thing on the internet once about metacognition. I think that's involved somehow. I feel that my own existence is impossible, that I do not exist, but I know that I must, because I can think about the fact that there is a me feeling and thinking that. I think I read about solipsism the same day. Either that, or I just always associate the two. I can't imagine what that's like, to think everything else is just a projection of yourself. It's myself that seems less than real, not other people.
I people watch, I raindrop watch, I feel the ground beneath my feet... they are all so real. And even though, yes, I hear my own thoughts and not the thoughts of others, it's my own thoughts that seem like poor evidence of reality.
A friend told me once, "you are just zen, is all." I guess I know what she meant, but I wanted to shake her and tell her she didn't know what zen was or she didn't know what this was or she didn't know anything at all.
I never tell my therapist about wanting to disappear. She would think I was suicidal and that is just not right. She might lock me up somewhere. I don't want to die. I want to not exist. And only sometimes anyway. And maybe not forever. It's as involuntary as the feeling that I don't exist and as contradictory too, but when I feel it, I need it. I want no thoughts and I want no sensation. I want to see not seeing and hear not hearing. I want to experience not experiencing.
I tried to fill the hole with sleep, but I dream too much. I tried to meditate but I get so bored. I get so tired of being bored.
I've decided it would be better
To disappear forever
When she was eighteen she found it, the way to do the thing that had captivated her since she was eight. She found out how to disappear. It was in a book in the downtown branch of the public library, in the 512s. The book was called The Nullity, and it was this old deep black cover, not sporting any dust jacket, with gold embossed lettering on the front, and filled with yellowed pages. It was thin and small and smelled like a dream, like old books turning back to wood pulp always do, ancient tobacco smoke damage unsoured over years to a sweetness.
Holding it, she could could feel her thoughts quiet. She could feel a weight to the book, but not so much a mass as a conceptual weight that she could somehow feel as a physical property. She looked down at it and could feel the world swim for a moment as if she was looking into a bit of that world that had warped in the rain. Her mind tried to race, tried to send thoughts a mile a minute to grasp what was happening, but all she felt was the absence of those racing thoughts. She looked away and all she could think about was that ending card she had seen in a cartoon once, one that imitated films she had never seen herself, a trope learned only from the stories that lampooned it. A field of black with white letters that said "Fin."
For a long time she was silent, merely slumping to the ground and leaning against her backpack, The Nullity held out as far away as she could, front cover pressed to the ground, but gripped tightly by its sides, her fingers gone white. She could not let go, even though she was afraid. She would not let go.
She thought for a moment that she had had another "episode" as her mother called them. But that was wrong, she quickly realized. Depersonalization was the opposite: constant thoughts that contradicted the feeling, even conviction, that she did not exist. When she looked at this book, her mind had gone silent, but she felt sure that she would have fallen in if she wasn't careful. She had felt so strongly that there was a self to lose.
She took it to the counter, and if the librarian had the same experience looking at the book, he sure didn't let on. He made cheery small talk as he checked her out, which she participated in with full willingness for maybe the first time in her life.
When she got home she placed the book on top of her bookshelf and layed down into a dreamless sleep.
One James ADW Anderson invented what he called "transreal arithmetic" as a computer science professor at the University of Reading.
The idea of transreal arithmetic was to solve a "1200 year old problem" in Anderson's words: division by zero. He claimed that solving this problem would make computers faster. There were also more grandiose claims about solving quantum gravity, for example, and so as not to bury the lede too deep in this sucking silt bed of a story, transreal arithmetic was rejected by the mathematical and computer science communities as: a. not solving anything that was an actual problem, b. not actually providing any unique solution to the "problem" presented, but merely swapping old terms for new ones, and c. actually creating more grave problems in its own system by attempting to oversimplify the way that undefined solutions are dealt with. (Incidentally, b. means that it should not make computers any faster even if it could actually be implemented on one.) That is of course, as best as I understand it. I'm neither a mathematician or a computer scientist.
(Author's Note: Maybe it was a dream, or from some less than reputable source, as I haven't been able to find any evidence of it again, but I once read, on a cheap looking website, about a cult in India called the Nullists who believed that what was behind the veil of illusion was so infinitely terrible that we should always try keep our hold on the veil. The way I was raised, especially since it had really only been a few years out of that headspace, maybe something about this rang true to a little voice that still says you're going to hell for having your doubts about something someone told you. Maybe something rang absolutely terrifying in weaker moments. Hells bells...
Supposedly, following the cosmological argument to its logical conclusion, you get infinite regress. I think this is probably true of most things though. You have to set an arbitrary place to stop. Like in addiction recovery circles, there is talk of "hitting bottom." You know about this because it's become part of the pop psychology lexicon. "Everyone's bottom is different." True! In fact, the vast majority of people never really find one. Or put another way, their bottom is death. Maybe a lot of people have the same bottom after all.
The argument could be made that death is "true bottom." After all, death is some people's bottom, and everyone gets there eventually, even people who aren't addicts (by whatever narrow-ass definition you think such a class of people exists.))
In Anderson's transreal arithmetic, you have the normal line of real numbers with the addition of three more: plus infinity, minus infinity, and the nullity. We're used to hearing about "infinity." We've talked about it like it was a number since we were kids. In standard arithmetic infinity is decidedly not a number though. Think of it like this: what are the digits of infinity? And to the smart ass in the back who said "well, it's a one and then infinite zeros," the mathematition says, "what happens if you add one to that?" Infinity is certainly often a useful concept in mathematics, but as far as the author knows, it's never treated as a number. Well, maybe sometimes but... we'll get to that.
(Author’s Note: Not one but both infinites treated as numbers is an extremely interesting thing if you ask me, but the thing that drew me to this, I’m not going to lie, was the Nullity.
The Nullity is the sort of poem-written-in-blood of a concept that the best metal albums should be named for. The Nullity is the most nothing that nothing can be. When anything interacts with the Nullity in any way, the result is the Nullity. Nothing escapes the Nullity.
This black hole nature pulls me in, pun intended, whenever I encounter it. Black holes themselves are a great example. I am always fascinated, kind of obsessed really, when I find evidence of a hole in things which sucks in anything that comes near. A lot of spiritualities, religions, and other poetic descriptions of life include a void. But most voids you encounter are infinitely big emptinesses. They are characterized by nothingness. What fires the more morbid parts of my imagination is the abyss which is really a hungry maw, the void with teeth. These voids don’t just gaze back; they will eat you if you get too close.
Zero is like that the first time you encounter it. Multiply anything by zero and get zero. It loses that luster somewhat over time as you discover newer and weirder numbers and concepts, move on to the harder stuff. But give zero its due. See...)
Zero as we understand it today was a mashup of Greek and Hindu ideas about the concept performed by Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī. It relies more on Hindu concepts, being that they were a little more consistent and advanced. To be fair to the rest of the world, there were pretty advanced concepts of zero in the Mayan calendar, which probably actually date all the way back to the Olmecs, and the ancient Egyptians, Babylonians, and Chinese were no slouches on the subject. That’s just history doing what it does and defying a nice, neat, linear story.
(Author’s Note: Works for me: I like my stories complicated.)
For instance, the story can be complicated by the notion, as far as research shows apocryphal, that the Catholic Church declared “zero” heresy during the crusades because it was an “arabic concept” and therefore “the work of the devil.”
(Author’s Note: I can’t find evidence from any real sources of this being true, not that I’ve looked all that hard. It’s a shame too, because I had grown a little attached to the story as a throughline for the one I’m telling here.
I could have just presented it as true. After all, this is fiction, not a history lesson. A good heresy story is always a lot of fun.)
Like Anderson’s story?
(Author’s Note: Make no mistake, Anderson’s story is definitely a heresy story. And we like the stories of the heretic, maybe because they are the underdog. We like them so much that we often exaggerate just how extreme their story was. And we probably shouldn’t forget what else these stories are: tales of gigantic egos. You need one to stand up to everyone and say, “you’re all wrong and I’m right.”
But why is Copernicus a hero and Anderson a joke? You might say, “Copernicus was right and Anderson is wrong.” This is, as far as I know, both a true statement and a good reason. I think there is another pretty important reason though: Copernicus won. The heresy of Copernicus is cannon now, and therefore those who go against it, those who proclaim geocentrism are the heretics now. It would be incredibly naive to think that this means we should now switch allegiances and root for the geocentrists. But it might be a worthwhile practice to think about how rarely we side with the heretics in their time.)
It’s also probably just as important to remember what ridiculous losers a lot of heretics are. So many of them are just edgelords trying to prove how different they are from any entirely misperceived status quo. In the end, I think the most important takeaway is that heretic stories are stories. Fiction.
The most obvious heresy I can think of is already an ancient and tired cliché: what I am doing right now, butting in for a long time as the narator and ranting stream of consciousness about the influences of the story itself, with emphasis on little factoids that the author’s brain obsesses over, that makes the author think they sound clever, put in the mouth of the narator or charaters. We’re spending a lot of time in poorly organized, non-fiction essay territory. We are edging on the metafictional wall like humpty-frigging-dumpty.
This is still fiction. If you tell an amusing anecdote to a friend, a “true” story that happened to you, it has already become fiction. It isn’t the real event, it’s an abstraction. Memory and imagination are not entirely separate things.
It seems like they actually might be very interrelated. The historian tells you a fiction too. It is an abstraction of reality constructed from little bits of evidence. And when it hits your brain it goes through all kinds of changes, just like any story. You interpret. You are an interpretation machine.
What part of the author’s brain do you think a whole other person comes from? There are no characters here. There’s no protagonist. There’s no narrator. The author tells you an interpretation built out of things they have interpreted and you interpret that. Fiction has no boundary. Every story ever is fiction.
With that out of the way, as the narrator there’s something I need to explain to you. You don’t have to continue. There is no rule that says you can’t just stop a story in the middle and never find the end. They’re not real anyway, right?
You can see there’s a countdown going on here. I’ve kept you here as long as I have by exploiting the very simple fact that between every whole number there is an infinite amount of space.
Think about Zeno’s Paradox, dear Achilles… you need never catch that tortoise.
But let’s be clear, in real life Achilles does catch the tortoise. If you keep going like this you are going to reach zero, and then you are going to reach the end of the countdown. You’re the only one who can actually prevent that. I have no real power here.
Well, nothing but the power of words… a peculiar power to be sure.
The author has the power to end this, of course. But the author could have not even started this. They intend to finish this with or without you. I’m asking you to save her, the protagonist of the story that is. The author is using her to say something, like most authors probably intended to be about the world but ultimately really just about themself. And as most authors do it, she is probably the author stand in. Really, it’s shameful what this author is going to do to her… it’s akin, if you think about it, to self harm. All horror is kind of like that, isn’t it? I won’t spoil it though. After all, I can really only do what the author allows me to, only know what they allow me to. I’m not an omniscient narrator. Instead, let me tell you one more heresy story.
Gottfried Wilhelm Leibniz (Wilhelm was a popular name once, have you noticed?) was arguably as much the father of calculus as Newton. One of Leibniz’s great contributions to mathematics is infinitesimals. Leibniz’s infinitesimals were criticized at the time on empirical grounds by George Berkely in The Analyst, were banned by the church once, and were for a long time considered an unsubstantiated idea (even as they were still used in many places where they were… well, useful.)
Leibniz passed in 1716, but jump ahead to the 1960s and a new friend, Abraham Robinson, developed nonstandard analysis, giving way to the hyperreal numbers. The proofs for this use set theory, which to a layperson like the author, whose mind I cannot surpass, is one of the more esoteric branches of math. But let’s see if we can explain what an infinitesimal is in the very simple way it was explained to the author.
As I’ve said, in general, we are not supposed to treat infinity as a number. But let’s say that there is a number infinity. Now to be a number, it has to have certain properties that numbers have that traditional infinity does not. For instance, if you add one to it, it must go up. If you subtract one it must go down. What this leaves us with an entire new number line of infinities. What it also allows us to do is find an answer to “what is the fraction one over infinity?” That answer is “an infinitesimal.” This is the smallest non-zero number, the number smaller than all the positive real numbers but still not zero. To put it another way, it is as close to zero as you can get on the number line.
We are in a countdown. The next number is zero and after that is something that, if you’ve been paying attention, does not bode well.
I’m giving you an escape hatch.
Before we reach zero, we will ever so briefly reach the infinitesimal. You can stop there, as close to the last part as possible, but before it really happens. You can always stop. We can always split off on our journey. You don’t have to see how it ends.
I’m going to leave this be now. When you reach the infinitesimal it is the last stop before you hit zero and begin the final downward spiral. The decision is yours. She stands in for the author. She stands in for the world. She stands in for you.
She kept the book for a long time, paying the full fine to the library for a lost book. She wasn’t sure why she hesitated to really use it. Once she learned to get used to the feeling she got just looking at the book, she had glanced at pages, skimmed a little. But she knew, just knew somehow, the secret was to read it, from beginning to end.
When skimming she had gleaned that the book was arranged as a countdown. Rather than starting at the first chapter, it started on chapter three. She had also noticed that it had a chapter zero, but she found it difficult to look at anything past that. It was as if the edge of that chapter were a precipice, and the feeling crept in as she approached it that, over the cliff was a never ending fall, or worse yet, that there was an end of the fall, and it was something she didn’t want to know.
But there is a determination that comes with having made a decision. No matter how it frightened her, she needed to do what she set out to do.
At twenty-three she was in her apartment that she shared with a roommate. She had forgone college to work, to make money, to be free. She had only just realized there was no freedom. One night, she pulled out the book and began to read.
Chapter three was a short, poetic, fearful description of the history of mathematical progress.
Chapter two was a description of an episode in the early life of a person not so unlike herself, the feeling that they had wanted to disappear, and the finding of a book just like the one she held, a hole into which they could disappear.
Chapter one was a long tangential passage of metafictional ramblings ending with an impassioned plea to save the protagonist by stopping the countdown, to preserve the protagonist by not letting them end up where all protagonists do.
And there she noticed the infinitesimal in small print just above the heading of chapter zero.
She read on.
Chapter zero was the end of all things. Chapter zero described the protagonist reading the same book that she was reading and finding they had made their decision.
They decided…
She decided…
You decided it would be better to disappear forever.
You can persevere in many ways. Sometimes there is a kind of perseverance toward giving up.
At the bottom of the fall was a hole in the world.
In the end was the hole, and the hole was with you, and the hole was you.
And the hole was…
Otherwise known as: The End.