According to Dominic Cummings recent revelations, a lot of people in charge of the pandemic failed to grasp the idea of exponential growth. As Mike Bird says, we often ask kids what pocket money they would prefer: a pound every week or a penny that doubles every week. It should be a simple thing for people to understand but I would argue it isn’t.
If you are reading this you will probably have a good grasp of exponential growth. But I think for a lot of people it isn’t so obvious. This is what I would call “surely” knowledge. As in, you will say to me: “surely, people know this, it’s easy”.*
I think the reason for this is that there are not many things in life where we directly observe exponential growth, in real-time. The only thing I can think of is fire. You wouldn’t just leave a smouldering fire in the corner of the room, as you know it could burn down your home. But what is less intuitive is exactly how this occurs. I would highly recommend watching a video of it, just to see how it happens.
At the start, the fire takes ages for it to do anything. It takes a minute for it to double in size. At this point, you think you can easily deal with it. And then, suddenly, it really starts to take off. Three minutes in and the room is completely on fire. This, to me, is what makes exponential growth so dangerous. It can lull you into a false sense of security that the situation is manageable before getting completely out of hand.
Let's look at the first 5 days of the virus.
We can see that the case where R=1.5 is obviously bigger than 1.1, it is not quite double the number of cases but it is certainly not very large. However, at this stage in growth, things are still moving pretty slowly. This is the false sense of security phase where you think things are manageable. You may even think it's just a linear relationship and so anyone saying the sky is going to fall pretty soon are just Chicken Little. Now let’s look at the next 5 days.
On day 10, with an R number of 1.1, we have barely seen a doubling over the original value of cases. With an R of 1.3, it is only 5 times more than we originally started with. R=1.5, however, has really started to take off. This is the moment we would say a loud swear word. It is nearly 40 times its original size.