Why I wear a Mask

A lily pad grows so that each day it doubles its size (area). On the 30th day of its life, it completely covers the pond. How long does it take for the pond to be half covered?

Most of us have seen a variant of this problem and know the answer is 29 days. But most of us can also remember knowing someone who got it wrong or getting it wrong ourselves. 

Exponential growth (and our generally poor intuitive understanding of it) is why, when an area sees a rapid upsurge in Covid-19 cases, we need to resort to heavy-handed measures like partial shutdown of normal services. Parts of the US are currently seeing new cases double every 10 days. Without preventative measures they will quadruple in 20 days.

Market capitalism does a good job of ensuring that we do not keep excess medical capacity available "just in case." So much of that demand, absent regulating elective procedures, would need to be met by increasing capacity. Can you imagine doubling our medical capacity in 10 days? If in Boston we have about 10 major hospitals, it would mean building 10 more in 10 days. And then staffing them with trained professionals. But then it would mean adding 30 more in the 10 days after that. And to meet the demands of 30 days of exponential growth, Boston would need to build and staff 120 new hospitals in the 3rd period of 10 days.

Even allowing that I've made a number of simplifying assumptions, this is clearly ridiculous. We know intuitively that our capacity to build critical infrastructure is more or less linear and can never keep up with exponential growth. 

But it is worse than that. To start with, we cannot train medical staff in 10 days, even if every new facility is a tent hospital. Further, while it might take only 10 days to double the number of new cases, it typically takes 20 or more for a hospitalized patient to be discharged from what I understand. So we cannot even clear our facilities as fast as we fill them.

In our modern, connected and social world, once the virus takes hold in a community this 10-day doubling period seems about typical. Or roughly speaking, we are sure it is not doubling every day and we are sure it doubles much more quickly than every 100 days, again excluding community-wide preventive measures. And because of our connected and social modern world, most communities will eventually see this impact. To respond before the virus takes hold, we would need readily available testing that gives us results in one or two days. And we'd need very good contact tracing. We just do not have either of those capabilities at this point.

Given all that, to prevent spread, we really have two choices if we want to prevent tens or even hundreds of thousands of preventable deaths in the US: masks with social distancing, or quarantine. The first choice allows our economy to reopen, the second does not. I would prefer to see our economy restart; I will wear my mask.