Math as a Flexible Substance
Math as a Flexible Substance
Not long after the start of the Pandemic, I identified a reemergence of my affinity towards sensical equations. A particular longing for the math of my past. I was always slightly embarrassed about being good at math as a kid, because I wanted to be an artist and artists aren't supposed to be good at math. I liked doing my math homework and lining up the numbers methodically on the page with a perfectly pointed pencil, checking each answer in the back of the book, and feeling intensely validated when the answers matched up. Sometimes I would compose nonsense lists of things just so I could feel organized and productive by seeing the numbers lined up at the left hand margin, always slightly annoyed when I got to 10 because the extra digit would make things look uneven. What a relief when I understood that adding a zero in front of a single-digit number didn't change its value! Finally my numbers could be lined up perfectly.
Like so many of us, I haven't engaged much in basic arithmetic since a teenager, but suddenly, in the overwhelming uncertainty of the Pandemic, the comfort of a reliable right and wrong sounded somewhat like a prayer or a meditation: so comfortingly stable. While 3 days became 3 weeks, become 2 months, became 32 weeks, $350 of unemployment every 7 days, the oven constantly on preheat to 375, long hair grew longer while short-tempers grew shorter, checking the clock over and over and over, what I thought I wanted was reassurance that 1 + 2 still equaled 3. What I was unaware of was that 1 + 2 never did equal 3 100% of the time. And that's why math becomes beautiful long after we discount it as irrelevant in high school. So many of us never get to appreciate the fluidity, and for some, the spirituality, of math unless we are directly in the field.
Personal Equations:
Is this a universally satisfying thing, this feeling of one's brain clicking into order upon seeing numbers in a recognizable pattern? The matching up of identical pairs, the positioning of things in a visually sensical order? I observe the satisfying phenomenon of same-height humans in a line when I pass a daycare of two-year-olds out for walk on a hold-a-ring rope. This particular rope doesn't have to snake upwards and downwards like it might at any other age; it can remain perfectly horizontal, all the little hands grasping from an almost-identical height.
How does the brain know how many steps to take to cross the street if I'd like to step up on the curb with my dominate foot? I don't have to stall and recalibrate when I get to the curb; I gradually prepare for the mission step by step, in an uninterrupted gait so that I can seamlessly complete the task upon reaching the curb. Additionally, I don't have to deeply consider this calculation in real time. My body and brain do the work while I'm thinking about any number of other complex things, or listening to my friend walking beside me who is calculating his own set of complex equations in some tucked-away part of his own brain, as we carry on our conversation about squirrels.
As for me, I consult an analogue clock most days. As part of my recent pursuit of increased groundedness, I've started mediating for 20-minute intervals. To note the time I will stop mediating, I look at the clock face, observe where the minute hand is (spatially, not numerically), then visually fold the clock in half, calculating a 30 min interval, then subtract 10. It is unknown if my clock ritual illustrates some sort of faulty time-telling comprehension as a child, or merely a preference for visual-problem solving. Either way, this method has become streamlined in my head, not needing to use actual numbers, it's instead based solely on diameters of circles and distances between shapes in space.
Mathematical Fluidity + Spirituality
My renewed interest in Math led me to Mathematician Dr. Eugenia Cheng's book "X+ Y". It is a misconception, Dr. Cheng states, that math is mostly about numbers. Numbers are tools of math, but math is a lot more about relationships. A 2 is only a 2 because of 1 and because of 3. We can call 2 anything we want, its twoness is only observable when it's in relationship to other numbers. Instead of thinking about intrinsic characteristics of things, it's more helpful to instead think about relationships with those things around them. And in terms of 1 + 2 not always equalling 3 100% of the time, we see how 11 + 2 can equal 1 if we return to the clock: 11 + 2 hrs = 1. All this to say, there is plenty of room for these things that we hold onto as truths to be sometimes incorrect. It seems that in higher math, there is not so much a right or wrong. Instead scenarios are presented in which something is right alongside other scenarios which could present another conclusion. The key is to remain flexible, fluid, open.
One of the most meaningful outcomes of my research is my ongoing correspondence with an infectiously enthusiastic and recently retired Rabbi called Rim Meirowitz. Rabbi Meirowitz described to me a curious obsession with the Fibonacci sequence after his cancer diagnosis. Thankfully, he is now cancer free, but over the course of his treatment, while contemplating his own mortality, he found himself replacing recitations of traditional Jewish prayers with mathematical calculations. The Fibonacci Sequence as Guided Meditation became a cornerstone of his recovery, focusing and grounding his mind. His approach was not just to recite the numbers in the sequence 0,1,1,2,3,5,8... but to add up each sum of numbers in his head, remembering which number to carry forward into the next equation:
0+1=1
1+1=2
2+1=3
3+2=5
5+3=8
and so on. As he dug further into the Sequence, he noticed that the pattern represents deep aspects of reality, appearing in the natural world, determining things like the number of petals on flowers, spiraling on shells, the construction of pinecones. The number of leaves on stems, for example, tend be a Fibonacci Number, which is why 4-leaf clovers are so rare.
There are so many great examples of personification in Number Theory. The field is packed with terms like Friendly Numbers, Amicable Numbers, Perfect Numbers, Irrational Numbers. In this case, the numbers in the sequence are Exact Numbers. 1 is 1, 5 is 5, the sequence is unwavering. "So in the midst of the confusion of cancer", Rabbi Rim Meirowitz writes, "exact numbers are a way of expressing confusion in exact terms--which is both poetic and paradoxical. How can confusion be expressed exactly?" "Through more and more reading about physics," he writes "and then moving into mathematics--I found meaning in the story of the basic structure of the universe which is expressed in mathematics. I am only at the beginning of using the structure of the universe to express spiritual ideas such as gratitude, joy, surprise, to impose order on disorder. " "It seems to me that the world and what it means to be human needs communities built around rituals and beliefs, and poetry to describe nature, and Math to describe the truth of reality"
Crumple Theory:
Earlier this year, I ran across an article in the New York Times about Crumple Theory. Yet another example of mathematics--geometry, finding its way into the emotional centers of my brain. A piece of crumpled paper, the articles explains, in all of its messiness and chaos of creases, suffers from "geometric frustration". Even without any knowledge of geometric frustration, it's somehow hard to not immediately relate. Is it geometric frustration that I experience when I cram into an over-crowded subway car? Or is it what I feel when the remaining Chex cereal at the bottom of my bowl doesn't tesselate properly in the milk? Or perhaps it's when I look at my calendar and can't imagine how I'll fit everything into one week, those seven little squares seeming to collapse into one another with the weight.
It turns out that the formation of a crease in a paper is how the stress is relieved, it's a way of protecting the paper from further damage. Is this a kin to soles toughening on feet that run barefoot all summer? Or crows feet?
"Given the finiteness of the human life," Rabbi Rim Meirowitz writes, "how many languages can we use to describe life as we experience it? How does each language enable us to see another aspect of reality? Can they all connect us to the underlying aspect of reality which is eternity: something beyond ourselves?"
I don't fully comprehend most complex mathematical theorems or formulas, but that doesn't take away from the comfort I feel by their existence. Reassuring proof that things tend to grow the way they should grow and time tends to pass exactly how it ought. Not to deny the messiness, because there's also something about the messiness being factored into the equation from the beginning: our reminder to remain open.