# 'Being a Programmer, I Decided to Build a Mathematical Model for the Decay of a Shower Curtain'

A rigorous anthropology of the humble bathroom accessory

When my wife and I were shopping for houses, it never occurred to us to look at the curtain rods for the showers. They’re all the same, right? As it turns out, the ones we inherited when we bought our house are extravagant things—high-mounted, metal, two-sided poles with hooks on both sides for a decorative outer curtain and a functional inner liner. The hooks are actually embedded within the pole, meaning the only way to replace them would be to get a new pole entirely. This would kick off a long chain reaction involving paint and wallpaper, something we weren’t ready to face. Five years later, the same poles and the same wallpaper still hang there, waiting.

It was obvious right away that the first shower curtain we bought was too short, but a shower curtain is not the type of thing you can go too long without. It’s the best feeling, the first time you hang a shower curtain. The excitement for the newness of a home is fresh—manifest destiny on a much smaller scale. The distance between space colonies and science fiction is slowly shrinking over time, but here on Earth we’ve pretty much run out of things to colonize. We make do with filling our houses with stuff. You’re not merely hanging a shower curtain, you’re bringing order to chaos. Hanging a shower curtain tames the wild within the domestic: you transform a potential shower into an actual shower.

We replaced the old, short curtain with an extra long liner. Installing a shower curtain is trivial enough. Match the hooks to the holes, just like buttoning a shirt. I took down the first curtain one hook at a time, neatly folded it, and placed it in the basement to be forgotten. Then I wondered: without my intervention, how long would it have taken for the first hook to come out on its own? It has something to do with bunching, perhaps. Somewhere in the opening and closing of a shower curtain, there seems to be a small chance that a hook will work its way free of a grommet, causing a slight imperfection in how the curtain hangs.

A standard shower curtain has twelve grommets and a standard pole carries twelve hooks. How did an even dozen come to be the standard?  There are twelve months in a year because of the lunar cycle. The Egyptians and Sumerians we inherit our clocks from were fond of base-12 systems. A standard bathtub is five feet long, but a standard shower curtain is six feet by six feet. If the curtain and the tub were the same length you’d have to pull it taut every time. The extra space gives us a little slack. Is one grommet every six inches some mathematically perfect way to distribute the weight of the curtain? Add more grommets and they’d tangle more often. With less you’d be adding more weight to each tiny plastic hook, increasing the risk that one might snap through the course of everyday curtain opening and closing.

In our house, we seem to average about two years between shower curtain re-hangings. That’s twenty-four months from perfectly strung shower curtain to disheveled mess in need of a total do-over. What else runs in two-year cycles? Onions and carrots are biennials. The Martian year is roughly two Earth years. When we first moved in, my wife was still my girlfriend. We were engaged by the end of the first shower curtain cycle, married by the second, and entered the third cycle as we had our first kid. Will we have a second child before I change the curtains again?

If we assume that the breaking point—the moment when ignoring a failing shower curtain no longer supports showering—is somewhere around 50% loss of hooks, that averages out to one hook every four months. Four months seems a little low, though. Between total replacements will come several bouts of mild frustration and demands from my wife to “fix the curtain!”

Is it sexist that I’m the one who always has to fix it? Or maybe just practical—I’m tall enough to reach them without a stool. These minor fixes are delays—grab a single hook and place it through an available grommet. Functionally, it’s simple patch-job to make it through that one shower. No care is given to whether it’s the right hook for the right grommet. Like an old wooden ship that’s been patched so many times that it no longer contains any original wood, the shower curtain’s march into final disarray is an organic process. I don’t set out to create a mismatch, but neither do I bother to take the time to do a proper fix.

The end hooks seem oddly immune to this pattern. Though no less likely to pop out of their holes, having the two end hooks attached to the tension rod is paramount to a properly functioning shower curtain. Lose a few hooks in the middle and you’ll get a saggy curtain, but drop a hook on the end and the curtain will no longer close all the way. Dangling end pieces are fixed immediately. Is this an extremely mild case of obsessive-compulsive disorder? No matter how many hooks are missing in the center, if you squint a little the shower curtain looks to be in order. Without a solid frame, though, the whole thing falls apart pretty quickly.

It makes me wonder if psychologists have ever run experiments on the effect of a messy shower curtain. Imagine if, unbeknownst to you, someone came into your house every day and made sure your curtains were perfectly hung. Would this extra bit of order each day impart some sort of calming benefit? Or, conversely, what if someone patched over some of the grommets with sturdy fabric to prevent the shower curtain from ever hanging properly? How does a messy shower curtain create anxiety? Maybe because it would be easy to fix and we just choose not to do so.

Re-hanging the shower curtain seems like such an adult task. Throughout college and the immediate years after, I never stayed in one apartment long enough to run into this problem. During those years a shower curtain was a decorative object, trimmed with the kind of bright patterns that you used to only be able to find at Target. The decorations are gone now (it’s harder to find extra-long curtains with patterns), and we never even bothered to get a pretty outer curtain to go on the second set of hooks. Every time I re-hang mine I’m reminded that I’ve lived in this house for longer than any other in my adult life.

Plenty of other grown-up tasks are cyclical. Change the air filter. Change the water filter. Change the oil. Pay the bills. Water the grass. Cut the grass. The shower curtain is different because it decays slowly. It would be trivial to fix it every time I notice a hook missing—an ongoing maintenance cost, to be sure, but one that would keep the curtain in perpetual perfect or near-perfect state. Somehow I never bother until the shower is in such a terrible state that I can’t stand it any more.

Being a programmer, I decided to build a mathematical model for the decay of a shower curtain. Start with twelve digital hooks perfectly aligned in twelve digital grommets. Begin a shower by closing the curtain and end it by opening it up again. Each time the curtain opens, assign a small chance that a single hook will pop loose. Now assume two adults will use that shower once each day, every day. This pace should put us at about double my one-every-four months estimate.

Minor repairs should also be allowed. If a corner hook comes out, fix it immediately. If there are three empty grommets in a row (causing an unfortunate curtain sag), grab a nearby hook and put it in the middle hole. I can define “disheveled” as a condition missing half of the hooks and having only four hooks stationed in their proper grommets.

Running the simulation 10,000 times, I get an average of 724 days between getting fed up enough to re-hang the curtain, not so far off from my two-year real-world cycle. Of course, relying on random numbers, the simulation endures wild extremes. One simulation took just under four months to go from order to chaos while another took seven years—over 5,000 showers!

Is a cold simulation an accurate representation of reality? Pondering further additions shows us how deep we can venture into the seemingly shallow world of the shower curtain. Perhaps we should model the velocity we use to open the curtain. Am I more likely to knock hooks out of place than my wife, perhaps due to my height? What if an interruption like a phone call cuts a shower short? What about seasonality? I’m much more likely to tamper with the shower curtain in colder months, trying valiantly to create a perfect seal to keep cold air from intruding into my steam.

I tell myself that this love of steam is the primary motivation for remodeling one of our bathrooms. Instead of just refinishing the tiles and the fixtures, I had a steam generator installed. You can’t put a shower curtain on a steam shower, which means at least one shower curtain in our house will be replaced by the calm sanity of a glass door. With this, the cruel entropy of the shower curtain is extinguished—but along with it, my ability to commune with it as a living creature amidst the cold tile.

 An ongoing series about the hidden lives of ordinary things