Among mathematicians, if I remember what they’re like sufficiently well from my time in grad school twenty odd years ago, it’s common to describe an idea as “trivial” or “deep.” If a claim is trivial – that’s to say, if it’s nearly obvious and mostly unremarkable – it might be called a proposition if it’s lucky, but if it’s nontrivial or deep it might get to be known as a theorem. But even among theorems, there are those that are trivial and those that are deep. When a claim is sufficiently trivial, you don’t bother proving it, you just mutter that it’s trivial, but if it’s sufficiently deep then its proof attains the status of a holy text.
I don’t blame math for this, but I find that the dichotomy of “trivial” versus “deep” colors my thinking about everyday life. Some things I do are trivial and others are deep. Some tasks I undertake are practical annoyances of no lasting significance, and others are opportunities to do meaningful work that might contribute to “the world” in some substantive way.
To give an example, I had to wait at home the other afternoon for a new fridge to arrive. My old fridge had shown signs of approaching death, and its periodic sputtering and banging sounds had jolted me into a project of finding a suitable replacement. This was not entirely a “trivial” project because the dimensions of my stairway (up through which the new fridge would need to be lugged) were quite narrow.
But the whole issue with the fridge struck me as “trivial,” in that my efforts at fridge replacement had no chance of being memorable to anyone in the long run. No one was ever going to remember me for my prowess at getting a new fridge, nor would the world benefit substantively from my having one. This was not my chance to shine in life, it was just a practical chore that had to be completed.
So I felt a little miffed that the pending arrival of the new fridge kept me in a limbo that prevented me from doing anything “deep.” Expecting the fridge any minute, I couldn’t concentrate well enough to write an essay, which might possibly have a favorable impact on a future reader, or to make a new piece of music which would have a nonzero probability of pleasing some future listener. Making new essays, or pieces of music, or photographs – these are things I characterize as “deep,” even if at the moment, I may be only one who cares that I make them.
So why bother writing an essay about Trivial versus Deep? Because I want to escape the prison that it represents.
Replacing my fridge is not a “trivial” thing if I consider that it’s an appliance I use dozens of times a day and it’s actually the most important object in my life that allows me to eat. To have the option of replacing a fridge when it gets old is a pretty special option that many people don’t have–I’m fortunate. And what is a fridge? The temperature in my kitchen could be eighty degrees but inside the fridge it’s thirty-seven? How is that even possible?
And my efforts to replace the fridge, what about them? No, I don’t expect any award. But I had to do some things to make the replacement happen: taking measurements, researching brands, talking with suppliers, choosing among models, following up with the appliance store, paying, scheduling an installation date, being home on that date – I had to be organized and persistent enough to see it through. But if I think of the task as “trivial” I can’t feel proud about any of that.
It’s like that in math too – a point might be trivial, obvious, unremarkable, but you’re using it in your proof of something deep, and without it, you couldn’t prove that deep thing, so maybe it’s not so trivial after all?
As soon as I think of something as “trivial” I start getting impatient about it. I want to get it over with as soon as possible so I can get to the deep stuff. Since I labeled my new fridge as “trivial” I was annoyed that I had to wait around for it. But if I had thought of the fridge as “deep” my experience would have been totally different. I would have felt lucky, blessed to be receiving it.
As an artist, I should want to make art, right? So it’s natural that I’d want to get through with the trivial things that take me away from art as quickly as possible, right? But there’s a danger in this framing.
Art is deep, but many of the things we have to do to make art might seem to be trivial. No guitarist is going to be remembered for his or her prowess at replacing strings, for example. But if a guitarist is too concerned with deep things to give attention to the practical task of changing strings, then every note will suffer as it’s voiced through those old muffled strings that don’t resonate like newer ones could.
If we’re constantly dividing things into trivial versus deep, then we might be relieved when we finally get to focus on the deep task of creative expression, but then that task will surface practical annoyances, trivial things we have to get through so the expression can proceed. We thought we had escaped into the world of deepness but here comes triviality to rear its ugly head.
Calling something trivial has little benefit but significant downside–it diminishes the satisfaction we can get from completing a “trivial” task, it increases the frustration we feel if a “trivial” effort fails, and it blinds us to the consequences of a “trivial” problem. Deep things can masquerade as trivial but if we call them trivial it’s harder to notice their importance.
It’s really better if we don’t divide things in this way. A trivial thing might compound into a nontrivial thing. Like, the exhaust from one combustion engine is trivial in relation to the vastness of the atmosphere, but if there are enough combustion engines doing their chugging and sputtering long enough, that’s not trivial anymore, right? ■