Metric spaces, air quality and the poetry of place

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As I write this, I’m sitting behind some hydrangea bushes listening through John Coltrane’s classic album “A Love Supreme” for the first time. I don’t usually sit behind hydrangea bushes when I sit outside, but right now it’s the only place in my front yard with shade. I also don’t usually listen to music when I write. Today, it actually feels disrespectful because music has so much to say, but

John Coltrane’s A Love Supreme released in 1965. (Photo by Cletus Awreetus/Flickr)

it won’t speak unless you listen. Its wisdom, although self-aware of its authority, is a humble, gentle sort of wisdom that captures the dimensionality of moments of being (not doing), and thus always remains somewhat uncapturable — elusive. 

Music creates an invisible world with the moments that it captures. As a math major, there are many weeks where I admittedly spend far more time thinking about what’s going on in invisible worlds than I do thinking about what’s going on in the real world. This past week was one of those weeks. I probably spent a lot more time thinking about metric spaces for a math class than I spent thinking about the upcoming election or rising coronavirus cases. 

Metric spaces are pretty interesting to spend time thinking about. They can be loosely defined as a bunch of numbers and some way of measuring the distance between those numbers. We usually think of the distance between numbers as the positive value of their difference, but with metric spaces, we can think about the distance in other ways that allow us to ask different sorts of questions about that bunch of numbers. 

Metric spaces are another way of defining and measuring distance (Photo by @markuswinkler/Unsplash).

Of course, we can’t just choose anything for the way that we measure distance — we need certain things to always be true about any measure of distance we choose — but it’s surprising how many different ways you can measure distance in a useful way. (When I use the word “useful,” I mean useful to people who spend much of their day thinking about math — not necessarily that metric spaces will improve anything you do on a regular day.) 

Metric spaces is one of many examples of things in math that make you look closer at the assumptions or characteristics of things that we consider quite ordinary and therefore do not think twice about — like how we measure distance, or think (or do not think) about air quality.  

I found myself thinking about air quality this week far more than I ever have in my entire life. Some of that was from thinking about close family members and friends who have had to go back to working in schools and are stuck inside a closed building for several hours a day with questionable air filtration systems, windows that do not open and tiny virus particles potentially floating around. Beyond my own corner of the world, pictures of cities under a blood orange sky from unforgettable fires far away made air quality seem especially pertinent.  

It all made me think back to some lines of a lesser known Wallace Stevens poem that I read this past summer: “Air is air, / Its vacancy glitters round us everywhere.” Poetry, like math, also compels us to ponder ways of defining, measuring and seeing things. It compels us to think about possibility, and not in a way that is boundlessly and baselessly optimistic, but that cogently challenges arbitrary assumptions to refine or create definitions and perspectives that are more meaningful for the spaces we are in. 

“Air is air

Its vacancy glitters round us everywhere.”

I enjoyed reading Wallace Stevens this summer because there are particular insights you gain from poetry saturated with depictions of nature that was written by someone whose natural landscapes are similar to your own. I know that when Stevens writes about trees or the winter, they are not the trees of Bengal or the winters of Kentucky described by other poets; so, my own conjectures and extrapolations that have been shaped by being inside Stevens’s landscape can be refined and added to in very pointed ways. 

Knowing that if I continue to sit here behind the hydrangea bushes writing, eventually I will get to the point when “corridors of clouds, / Corridors of cloudy thoughts, / seem pretty much one: / I don’t know what.” So for now I must stop and go back to trying to listen to the wordless strophes of a music I do not completely understand (but that is entirely fascinating) while sitting here in my front yard behind some hydrangea bushes because it’s the only place right now with shade.  

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