Noncommutativity

  by F.C. Zeri

Do not to take things for granted. My mother used to warn me. She mostly meant the small family gestures harbouring scripts in their texture: there are people who lay the table, people who clean the kitchen, people who stay up late working or stay up late scribbling rhythms and figures in worn-out notebooks, steering clear of housework. Still, they’ll wake up rested to clean dishes and folded clothes and finished problem sheets neatly packaged into a backpack.

When I was five, I learned about commutativity. From the Latin “muto, mutas, mutavi, mutatus, mutare”: to change. An operation is as commutative when the order of the factors can be changed.

2 plus 3 is equal to 3 plus 2

Three plates on the table plus two in my hands, two plates on the table plus three in my hands: both meant there were five of us eating. Commutativity in addition and multiplication is spelt in elementary schools and left unbothered for the rest of standard education, so unbothered it may seem an axiom.

Then, university classes in abstract algebra. Lo and behold: commutativity can be disrupted. There are mathematical geographies where order matters.

x times y may be different from y times x

A new axis added to inner mappings, enough to squander previously established rhythms. Torn and crumpled papers. Migraines and late nights and paracetamol-drenched mornings and brains scrambled by insomnia. Unwashed dishes in the sink and unfinished problem sheets, whispering hey, look, you’re missing something.

There are people who first notice the table is laid and only then start eating. There are people who eat first and only realise the table is laid afterwards. There’s guilt in the borders of my hindsight as I notice it. Noncommutativity, carved in the eyes of my loved ones.