I’ve always been told that everybody, eventually, will encounter math almost too hard to overcome. For some this happens in high school. Others in college. Others in their doctoral studies. But it happens for everybody.
Hell. It even happened to me. First year of grad school.
But through all this time, even when I got there myself, no one ever told me what to do about it. And sure as hell no one told me how to help my students who hit that well themselves.
Or how to help them when they hit that wall as early as third grade.
This last week in class we covered sequences and series. This is a strange unit: It looks little like anything else students have seen, yet mathematically it resonates not only with many things we’ve learned, but with many things we could only dream of ever teaching in a high school class bounded by deadlines and curricular standards.
If you’ve ever counted or made a to-do list or put things in order, you know innately what a sequence is: it is merely a list of numbers, with a specific order: 1 2 3 is a different sequence than 1 3 2. Some sequences seem patternless (sunshine Monday, snowstorm Wednesday, downpours Thursday, a blizzard today) while others are so set in stone we hardly take notice: Sunday always precedes Monday, and April follows March.
Now suppose you look at that to-do list you made and count all the things you’ve got to do (that infinite list that seems to always grow two more items when you knock off the first–how hydraen life tends to be!) then you know, too, how a series differs from a sequence: simply take all the things and add them together. No more complex than that.
But what does any of this have to do with identity or politics?
I fell headfirst from the pages of my linear algebra textbook into another classroom. It reminded me of calculus, but was of no building I’ve ever stepped foot in: the walls were white and discolored at the edges, darker greys and burnt yellows that made the corners stretch into oblivion. Low white tables sat in clusters of four or five around the room, but I was the only student held between its four walls. And hanging at its front, two large projector screens hung, covered in a PowerPoint slide as simple as text and a link.
But I said I dreamed of fantasy, and here the portal lay.
I haven’t been sleeping well since I got back from Alaska. The time change was easy heading west: All I had to do was stay up late. Coming east wasn’t as easy–it feels like midnight at four in the morning. So today’s fiasco actually began last night: I didn’t get to sleep till five. In the morning.
So waking up at nine? Didn’t happen. Ten? Not even then.
About a year and a half ago, right after Amendment 1 passed, I wrote about walking through Walmart hand-in-hand with my boyfriend at the time and the woman who changed everything–who was, in that brief moment between aisles, the unending image of hope.
It’s ironic how life, the year turned by, returns us to where we began–wholly changed, mind you, but wholly the same.
I was once told all of calculus, and by extension all of mathematics, was built upon an assumption, and that should this assumption prove false, everything we know about mathematics, physics, the world as a whole would just crumble into nothingness and we would be left to flounder in a world of unknown possibilities and frightening realizations.
The truth is that was all before I became a math major and learned this is just a staple fact of axiomatic math: We make initial assumptions, build systems upon them, but acknowledge that they only hold when those foundational axioms are true. (That’s why there’s multiple geometries–such as Euclidean and hyperbolic, etc.) So the world won’t come crashing down in fire and brimstone. We just know the rules won’t always apply.
The point of any of this is not at all mathematical–but factual. Like Tolkien posited, a reader will only believe so long as the writer has sufficiently sowed a willing suspension of disbelief in the reader–the notion that, for a moment, we will ignore the rules we know in favor of the rules we wish to believe. For a brief few moments, dashing from word to word across the page, we forget that reality has bounds and for a moment become limitless.
I’ve lived my own life as both reader and writer: I’ve laid a foundation of beliefs upon basic axiomatic assumptions, and as I write these words, I fear I’m losing hold of my own willing suspension of disbelief.
We all know the saying that we are each greater than the sum of our parts, but I like to expand this by saying I am greater than the product of the factors in my life. It’s funny because of the mathematical parallelism between sums and products, but it also changes the focus from the internal to the external.
When I think of the parts that make me up, I think of the roles I fill and the things I am. I’m a writer, a brother, a friend, a leader. I was homeschooled, graduated from a community college, and now I’m attending an awesome university. But when taken together, I am greater than any one of these things.
When I think of the factors that have brought me here, I think of the outside forces that have shaped me: My parents are divorced, I’ve grown up depending on government assistance, and I’ve only been able to make it through school because of the challenges I’ve overcome. Yet I am greater than each of these things, and I am greater than merely taking them all together.
It’s hard to say which came first–the outside challenges or the changes inside–but all of these elements have brought me here and made me who I am, and because of the extraordinary opportunities I’ve been given, I’ve finally realized where I want to go in life.
Today officially began my semester. I woke up before the sun (but not as early as yesterday) and trudged out to my first course. I left earlier than I actually had to and therefore was almost an hour early.
I took my seat casually, somewhat thankful I wasn’t the first one there. I withdrew my iPad to fiddle with for a bit, eager to distract myself, yet still eager for classes to begin.
Had I known what the day would bring, I’d have felt differently.
Endurance training is pretty basic. It simply involves proper pacing, commitment, and determination. Through continued exercise, stamina and endurance are increased accordingly. But how does one make wisdom enduring? Last time we spoke about reverence and how it roots our wisdom, and this time we’re going to continue the narrative.
After all, if we are enduring, we’re practically immortal.
Yesterday was part of an epiphany. I realised I’m giving far too much importance to the location of the universities I’m looking at than I should. Yes, location is important, but relevant to the other factors I’ve been including, it doesn’t carry as much weight as might be intended.
As for today, I’m hoping for some similar epiphanies in the fields of academia.