Orders of Magnitude

As a full disclaimer, I’m terrible at arithmetic. Particularly if I think someone is analyzing my speed at manipulating numbers in my head. I think part of it is because I’ve had more than the average training in mathematics, and I think this is somehow supposed to make me a computer in the original sense of the word. I don’t have the attention span to have thrived in that particular profession.

As another disclaimer, even though I’m going to talk about COVID-19, I’m not claiming to be anything other than your typical armchair numbers person inspired by a global pandemic to ponder infectious disease. Except I guess it’s more like “standing desk” or “floor-sitting” numbers person, because I don’t own much furniture. But that’s another story.

All that to say, this article is inspiring a digression on orders of magnitude and the importance of context in interpreting numbers. The highlight is that the Governor of Oregon erroneously claimed a deal with Quest to buy 20,000 test kits (turns out the deal was for “just” 10,000):

Brown hastily announced a deal that wasn’t finalized and trumpeted an eye-popping number of tests that didn’t prove to be accurate.

Oregon, like much of the country, has a testing and tracing problem that it does not appear to be solving, which I think is what the author of the article really wanted to say. I’m not going to try for a precise definition of “eye-popping” here, but I do imagine the term would satisfy the following:

  • If x is an “eye-popping” number, than x/2 is also an eye-popping number.
  • If x is an “eye-popping” number, then x is probably at least an order of magnitude larger than 20,000.

For context, 20,000 is approximately the number of tests Oregon had already completed at the time of the article’s writing (April 8). This is not a particularly large number relative to Oregon’s population (~4.2 million) or relative to its geographic location in the context of this pandemic (sandwiched between our dear neighbors Washington and California, two of the first “hot spots” in the nation). Or relative to the length of time the disease has probably been spreading locally.

Which is to say, if Oregon had conducted 40,000 targeted tests as part of an early and ongoing test and trace program, I guess we wouldn’t be in bad shape here. Provided we had combined that with giving resources (e.g., food, basic sanitation supplies, housing) to those under quarantine.

But, together with the rest of the US, we didn’t. Are we even in catch up mode? I don’t have a beef with the gist of the above article, which goes on to point out that Oregon, at least, doesn’t seem to actually be ramping up its test and trace capabilities. Despite what the governor had claimed.

As the news devotes more and more time to antibody tests and visions of the recovered “reopening the economy”, it’s worth pointing out that even in the areas that are hardest hit, the group of people who have been infected with and recovered from COVID-19 is really quite small and we don’t yet know if the immune response is robust or lasting.

Put another away, most people are still susceptible to infection, and those who have already been infected and recovered may be susceptible to reinfection far sooner than we’d like. (And here I don’t mean a measly ‘most’, but more like oh, I don’t know, well over 99% of humanity.)

Oh, and let’s not forget that viruses mutate.

This Vox article is worth a read.