As I said, I do agree that the piece’s qualitative conclusion was correct. However, the gaussian assumption does make a large quantitative difference. Comparing it to the extreme: If we always have the maximum number of people in ICUs, continuously, the time until herd-immunity would be 4.9 years, which is a factor 3 less than what the normal assumption gives you. Although it is still clearly too much, it’s only one or two additional factors of 3 away from being reasonable. This extreme isn’t even that unrealistic; something like it could plausibly be achieved if the government continuously alternated between more or less lock-down, keeping the average R close to 1.
To be clear, I think that it’s good that the post was written, but I think it would have been substantially better if it had used a constant number of infected people. If you’re going to use unrealistic models (which, in many cases, you should!) it’s good practice to use the most conservative model possible, to ensure that your conclusion holds no matter what, and to let your reader see that it holds no matter what. In addition, it would have been simpler (you just have to multiply/divide 3 numbers), and it would have looked less like realistic-and-authoritative-math to the average reader, which would have better communicated its real epistemic status.
As I said, I do agree that the piece’s qualitative conclusion was correct. However, the gaussian assumption does make a large quantitative difference. Comparing it to the extreme: If we always have the maximum number of people in ICUs, continuously, the time until herd-immunity would be 4.9 years, which is a factor 3 less than what the normal assumption gives you. Although it is still clearly too much, it’s only one or two additional factors of 3 away from being reasonable. This extreme isn’t even that unrealistic; something like it could plausibly be achieved if the government continuously alternated between more or less lock-down, keeping the average R close to 1.
To be clear, I think that it’s good that the post was written, but I think it would have been substantially better if it had used a constant number of infected people. If you’re going to use unrealistic models (which, in many cases, you should!) it’s good practice to use the most conservative model possible, to ensure that your conclusion holds no matter what, and to let your reader see that it holds no matter what. In addition, it would have been simpler (you just have to multiply/divide 3 numbers), and it would have looked less like realistic-and-authoritative-math to the average reader, which would have better communicated its real epistemic status.