Flattening the Curve Too Much

There's been a lot of talk, during the 2020 virus pandemic, of the need to flatten the curve. The reasoning, which is valid up to a point, is that hospitals don't have enough equipment (e.g., ventilators; Galion hospital for instance has two of them) to treat as many people at once, as would need to be treated if the virus ran its natural course. This is true up to a point, as you can see in places like Italy, which didn't flatten the curve nearly enough and have consequently seen a disturbingly high mortality rate. The American medical care system would be more difficult to overwhelm than that of most other countries. American culture is obsessed with medical care; on an average day, something like 10% of the population receives medical care of some kind, and that's if you don't count prescription drugs as medical care; if you do, it's more than 50%; so our medical care industry is pretty substantial. It's expensive (and Americans spend a disturbingly large amount of money on medical care), but it's substantial. Nonetheless, we don't want to be in the boat Italy is in. We want to flatten the curve —up to a point.

But there is such a thing as flattening the curve too much.

I live in Crawford County. It's difficult to get an exact population figure, because population changes over time, but the 2018 estimate is around 41 and a half thousand. (This is down from almost 44 thousand in 2010. The population is on a long-term decline since the mid twentieth century, because most of the graduating students who go away to college, never come back. There are very few jobs suitable for college graduates here, and an employer would be mad to locate here if they need that kind of workforce, which creates a vicious cycle. What, if anything, we could be or should be doing about that, is an interesting question, which I will not attempt to address today.) It's now 2020 and we're due for a new census, but meanwhile I will be conservative and estimate that we have at least 40 thousand people in Crawford county.

We've had, according to the latest figures, which are about a day old at the time of this writing, 37 known cases of the virus. Being generous and assuming that only one case in twenty is confirmed and known (bearing in mind that some people never show symptoms), we could guess that perhaps as many as 750 people in the county have been exposed to the virus and are no longer in danger of catching it, either because they already have it, or because they are immune. (The difference between already having it and being immune may be of great personal importance, but for the calculation we are about to do, it actually doesn't change the figures, so it's something we don't need to distinguish in our estimates.) The true figure is probably markedly less than 750, but I'm being conservative here.

We started canceling stuff back on March 6th, and at that time we had 0 cases in Crawford county. (Some people were already being tested; but those early tests ended up coming back negative.) Our number-of-cases figure is from April 20th, a difference of more than six weeks. If the curve were linear, this would mean we'd need to stay home for about six more years. The curve is, as the word "curve" suggests, not linear. Technically, it's still an exponential growth curve. But we've flattened it so much, that the difference from linear is not nearly as dramatic as you'd normally expect. For the last month, the only time the statewide increase in reported cases has been noticeably different from linear, was in the last few days, when comprehensive testing in the prison system confirmed a large number of already-suspected cases. Prisons are a particularly problematic environment, for a variety of reasons (nursing homes aren't much better), so you expect a higher curve there. For most of the state, and especially for smaller communities, the curve is effectively so close to linear as makes no practical difference. Maybe we won't have to stay home for six years, but if something major doesn't change, it's going to be months and months and months. Which is really not ok.

We have flattened the curve too much.

We cannot, realistically, all remain cooped up at home for even one year. Inevitably, at some point, we are going to have to start going out again. And then the curve will be less flat, possibly a lot less flat. The natural shape of this curve, when people aren't all staying home, is very steep. I propose that we would have been better of with a curve somewhere in between these two extremes. Flattened, but not so completely flattened.

What were "pocket protectors" anyway, and why are really old people always talking about them?

We've all been in this situation: you're talking with an old person, and through one circumstance or another the fact comes up that you know something about computers, or at least use them, or that you have studied a little math, or science, or accounting, or business, or pretty much any other subject that the old person doesn't know anything about.

Anyway, as soon as they find out that you know something about anything, they immediately make some kind of remark about "pocket protectors".

Huh? What does that mean? What's a pocket protector, and what does it have to do with the differential equations class I'm taking?

Having heard these "pocket protector" remarks all my life, a couple of years ago I did some research and found out what it's all about, so now I can share that knowledge with you. The short version is that what these remarks really mean is that the old person hasn't really caught on to the fact that they're old and the world has changed since they were in school. Okay, so you probably already knew that part. The details, however, are interesting...

As you are probably aware, technology is constantly improving. If the laptop that was so awesome you couldn't afford it last year is now selling used on ebay for approximately the same price as a discount ringtone, imagine how primitive computers must have been way back in the twentieth century! In fact, you probably can't imagine it, because any degree of primitiveness you can think up would still be a good deal more advanced than what they had back then. But that's okay, because you don't have to imagine: I'm going to actually tell you.

In your great-great grandfather's day, microchips and even transistors simply hadn't been invented yet. Instead they used something much more primitive (and larger) called a "vacuum tube". A single computer filled up an entire room. Several scientists were required to make it work, and it would take weeks or even months to complete a computation that your phone can do in under a second.

Speaking of phones, they had to be wired to the wall in order to work, and they didn't have screens, and you couldn't use them to send text messages or do anything else. All they could do was make phone calls, and that was *it*. Even for that you had to dial them, and I mean actually dial, not select a name from a list. If you wanted to send a text message back then, you had to write it on paper.

Cars in that era were made out of metal, and they didn't have cupholders or power windows, and to pay for your gas (petrol for British readers) you had to actually go INTO the gas station.

They didn't have "pay at the pump", because credit cards hadn't been invented yet. Back then, if you wanted to borrow money to buy something, you had to make an appointment and speak to a person at the bank called a "loan officer", and he would expect you to be able to show that you could afford the payments, or you wouldn't get to borrow the money.

You may already know (perhaps from watching something old with your grandparents) that movies were in black and white back then, and the special effects were really cheesy. What you may not realize is that people couldn't just watch movies whenever or wherever they wanted. If your great grandparents wanted to watch a movie, they had to go to a place called a "theatre", which was basically a dedicated building just for watching movies. (Well, sometimes a building; other times the theatre was outdoors in a sort of parking lot, and you'd watch the movie through the windshield of your parked car. Really.) Even small towns had a theatre (larger towns often had more than one), and people would come from all over town to sit in the theatre and watch a movie. There was only one screen for everybody, so they had to all watch the same thing. At the time, this didn't seem strange or restrictive to anyone, because movies were new and they just thought it was cool to get to watch one.

But it wasn't just the big-ticket technologies like phones and computers and cars and money and entertainment that were primitive. The little things were primitive too. Clothes, shoes, soft drinks, Jell-O (it didn't even come in blue), lunch boxes, and even such basic things as pencils and pens. That's right, pencils and pens were primitive, and that's why they had "pocket protectors". No fooling.

Today, with modern technology, we take for granted that we can just put a pen or a pencil in our shirt pocket and carry it there, and we don't expect anything bad to happen. However, this is only possible because we have modern pens. This is the really interesting part of the story.

You see, back in the dark ages, before a company called Walkman introduced the first rudimentary portable music players, the pens that they had were horrible barbaric medieval things called "fountain pens". Compared to modern ballpoint pens they were much harder to use. (Among other things, it actually mattered which direction the pen was rotated compared to the tilt of your hand against the paper.) Fountain pens were expensive, notoriously unreliable, and a hassle to use. The only reason people used them at all was because they were portable: you could carry them around anywhere. This was a new feature.

The pens people used before fountain pens wouldn't work if you took them away from the writing desk, because they relied on something called an "inkwell", which was built into the desk, to supply them with ink every few letters. The obvious solution to this was to put a supply of ink in the pen so you could carry it around, and that's what fountain pens were: pens that could carry a supply of ink around in them, so you could use them away from the writing desk and its inkwell.

You could use a fountain pen almost anywhere. This was such a useful feature that people wanted to carry the pens around everywhere, just like we do today. (It was even more important back then, because they didn't have portable computers or phones, so everything had to be written on paper.) The only problem was, the companies that made the pens hadn't really figured out how to do it right yet. The pens were unreliable, but the worse problem was that they leaked. Frequently. People wanted to carry them in their pockets, but they knew that if they did, they'd get pockets full of ink.

And that's why they needed pocket protectors. Anybody who wanted to carry a pen around in their pocket needed to protect the pocket from leaking ink. Scientists had recently developed a totally new kind of material called "plastic", and although it wasn't nearly as good as the plastic we have now, it was good enough to solve the problem. Somebody made little plastic pocket-shaped bags that wouldn't leak from the bottom and called them "pocket protectors".

People who wanted to carry a pen would put a pocket protector in their pocket and then carry the pen in the pocket protector. When the pen leaked, the ink would collect in the bottom of the pocket protector, and they could just pour it back into the inkwell built into the pen, and the shirt wouldn't be ruined.

That's a lot of trouble. If the pens leaked, why didn't they just use pencils? Well you see, back then pencils were made out of wood, and the point could not be retracted. If the tip broke off, you couldn't just click the eraser end a couple of times and extend the "lead". You had to actually sharpen the pencil using a device that cut away some of the wood to reveal more of the graphite "lead". Every time you did this, the pencil got shorter. Also, because the tip could not be retracted, and because the graphite "lead" was much thicker than on modern pencils, carrying a pencil in your pocket would often result in unsightly graphite stains, especially if you were wearing a thin or light-colored shirt. Then there's the possibility of poking yourself if the pencil was at all sharp. In short, the pencils were just as much of a pain as the pens.

So anybody who used pens and pencils on a regular basis (mathematicians, scientists, businessmen, teachers, students, doctors, nurses, ...) would wear a pocket protector all the time. People who didn't know how to write, or didn't have a job that required them to write, didn't need one.

So when old people ask you about your "pocket protector", all they're really implying is that you're not too dumb to write.