The growth in ‘exponential’
COVID-19 HELPS PEOPLE TO UNDERSTAND TERM’S PROPER, TERRIFYING MEANING
Barely a few days ago, the word “exponentially” was one of those words, like “literally,” that has been misused so much there is no point in objecting anymore. It is usually best understood to just mean “fast.”
But now it is on the lips of politicians around the world, as they try to accurately convey the potential of a pandemic viral disease, and they are using it correctly as its literal meaning becomes horrifyingly clear. “Exponential” growth does not mean “fast,” it means “ever faster.”
“Everyone will understand at this stage that there will be an exponential increase in the number of cases in the coming days and weeks, increases of roughly 30 per cent in the number of cases every day.
That is inevitable. That cannot be stopped. We’re at the very start of that curve that people are starting to become familiar with,” said Irish Taoiseach Leo Varadkar.
“You’re going to see an exponential increase in the number of people who test positive on a daily basis,” said Texas Governor Greg Abbott. “So people just need to be prepared and not shocked by the mathematical reality.”
It is hard not to be shocked. Humans are accustomed to thinking in a linear fashion. Many familiar dynamics work like this: Save two dollars a week and in a year you have $104. That is addition, taking place over time: 2 plus 2 is 4, then 6, 8, 10, 12 …
Multiplication is a wilder magic. It will run away on you. 2 times 2 is also 4, but then 8, 16, 32, 64, 128 …
A measure that is growing exponentially is growing by multiplication with itself, so it just keeps getting bigger, faster.
That is the mathematical nature of infection, so if you start with two sick people who are each likely to infect an average of two others, then you have four, who will infect eight, who will infect 16, and so on unto disaster.
Plotting that out on a chart shows a curve with accelerating steepness, the newly familiar illustration of how this COVID-19 pandemic is threatening to infect ever more people every day.
As it does, it quickly passes the level at which hospitals are overwhelmed by the number of critical patients, which is why “exponential” is the great fear, and the new buzzword.
Even if just the merest fraction of those infected need hospital care, that can still become an impossible situation in a virtual instant, if the numbers increase exponentially. It is not long, theoretically, before literally everyone is either infected, recovered and immune, or dead.
But math is abstracted from reality, and pandemics are not billiard-ball simulations. Even the numbers that are known for certain have to be understood in the context of how many tests are being conducted.
A survey of national numbers from the World Health Organization shows patterns emerging, with hopeful signs that exponentially growing pandemics can burn themselves out in the real world.
Most people do not roam randomly throughout the world, for example, but follow familiar routes and patterns.
People can also move the numbers themselves, by modifying their behaviour, as in the newly rousing call to action: “Flatten the curve!”
China’s numbers illustrate this flattening. A dramatic spike in the middle of February of 15,000 new cases a day fell off drastically over the following days. So while the total cases remain incredibly high at 82,000, the rate of increase has fallen off to near nothing.
In Italy, where nearly 30,000 cases have devastated the country, the daily growth is still in the multiple thousands, but it is now lower than it was a couple of days ago, suggesting a peak in the number of new cases each day. However, there was a similar trough a week ago that was soon reversed.
Canada’s overall total number of cases remains low at 424, but the daily increase is itself increasing — the mark of exponential growth — and has recently jumped over 100.
That is a rough national picture, however, and contrasts with the numbers in Ontario, for example, the province with the most number of cases at 177, where there was a lower daily increase on Tuesday with 8 new cases, compared to nearly 40 new cases a couple of days before.
South Korea offers perhaps the clearest picture of a flattened curve. Its slow growth through February started to kick up into the hundreds of new cases per day, and a few days later peaked at more than 800 per day, before declining to where it is today, below 100.
Plotting that on a graph, measuring total cases against time, shows the familiar exponential rise being flattened, and hopefully finding a peak.
The numbers slow down, not as they would do if left to their own devices, but as pandemics do in the real world of humans who push back.