3 ms·

It's easy to be misled by the nature of exponential growth. In most people's vocabularies these days, the term seems to mean just "very fast", but correctly un

It's easy to be misled by the nature of exponential growth. In most people's vocabularies these days, the term seems to mean just "very fast", but correctly understood, it's more specific and more complex than that. Exponential growth, in this context, means that the rate of new infections is proportional to the number of existing infections. This cuts both ways: when the number of existing infections is large, the rate of growth is also large -- which is why exponential growth is so dangerous -- but when the existing number is small, the growth rate is also small. If you look at a graph of an exponential curve, there's a long relatively flat region to the left, before the knee in the curve is hit and the thing takes off. The point is, even though we here in CA started the lockdown relatively early, we've never gotten the case numbers down to a manageable level. I'm not sure why not. Although a lot of us have taken the virus seriously from the beginning, maybe there are still too many who don't. The sad truth is that a lot of people won't believe it until it affects someone they know -- and while it's well under control, that tends not to happen. So it looks like a bad outbreak in a region creates "mental herd immunity", where almost everyone cooperates with the lockdown; places that haven't had such an outbreak don't take it as seriously.

dragonwriter 6y ago
> The point is, even though we here in CA started the lockdown relatively early, we've never gotten the case numbers down to a manageable level. I'm not sure why not. Because we started reopening just as the curve was flattening, without bending the numbers down much.
trevyn 6y ago
The visual “knee” is purely a result of your chosen scale; there is no scale-independent mathematical definition. Put it on a log/log chart, and it’s a straight line; no part of the growth is qualitatively different than any other.
- ScottBurson 6y ago
  I'm well aware of that -- except that an exponential is a straight line on a semi-log chart. But to people hearing the numbers, who aren't familiar with the phenomenon of exponential growth, a linear scale, despite being somewhat arbitrary, better captures the psychological impact. Consider an idealized example: we start with one case, and a doubling time of three days. It takes the whole first month to get to about 1000 cases. Even though you and I know that that's an extremely aggressive growth rate, 1000 cases still doesn't sound like a lot to many people, when they compare it to the population of the US (or annual numbers of deaths from various other causes, like swimming pool accidents -- a comparison I've actually heard made). In the next month, though, it would get to 1M cases, which is a much larger fraction of the population and is correspondingly likelier to get people's attention.

dragonwriter 6y ago

> The point is, even though we here in CA started the lockdown relatively early, we've never gotten the case numbers down to a manageable level. I'm not sure why not. Because we started reopening just as the curve was flattening, without bending the numbers down much.

trevyn 6y ago

The visual “knee” is purely a result of your chosen scale; there is no scale-independent mathematical definition. Put it on a log/log chart, and it’s a straight line; no part of the growth is qualitatively different than any other.

ScottBurson 6y ago
I'm well aware of that -- except that an exponential is a straight line on a semi-log chart. But to people hearing the numbers, who aren't familiar with the phenomenon of exponential growth, a linear scale, despite being somewhat arbitrary, better captures the psychological impact. Consider an idealized example: we start with one case, and a doubling time of three days. It takes the whole first month to get to about 1000 cases. Even though you and I know that that's an extremely aggressive growth rate, 1000 cases still doesn't sound like a lot to many people, when they compare it to the population of the US (or annual numbers of deaths from various other causes, like swimming pool accidents -- a comparison I've actually heard made). In the next month, though, it would get to 1M cases, which is a much larger fraction of the population and is correspondingly likelier to get people's attention.