Exponential growth

A disease with a constant R-value > 1 exhibits exponential growth until something changes -- a substantial fraction of the population has immunity or a substantial fraction of the population stops interacting with one another, whether voluntarily or by getting sick or dying. Exponential growth is really fast, as demonstrated by the famous grains of wheat on the chessboard problem.

Every day for some weeks now the New York Times has published an info box with the number of confirmed new cases of COVID in the US yesterday, the number of confirmed COVID deaths yesterday, and the percentage changes in those numbers since two weeks before. Note that any positive number for the "percentage change" figure means we're in an exponential-growth situation, although the smaller the number the less-horrible the curve. A few weeks ago the percentage change in new cases was steady in the 20% range. Then one day it was 26%. Then, the next day, 32%. The next day, 37%. Then 42%. You get the idea. We were in super-exponential growth territory.

As I recall, on July 2 (reporting the numbers of July 1), this figure reached 92%: the number of new cases was not-quite doubling every two weeks, equivalent to compound interest of 4.77% PER DAY. At that rate, it would take 128 days to infect every person in the US (if I"m doing my arithmetic correctly, which is not guaranteed).

Then on July 3, the figure was 90%. Then 89%. Then 87%. Then 84%. It's not dropping rapidly, but it appears to be dropping. Note: this does not mean the number of new cases per day is dropping, but that it's growing only exponentially (or slightly less). If the 14-day growth number were to stay at 84% (compound interest of 4.45% per day), then starting from a point four days later, it would take 132 days to infect every person in the US, 8 days beyond what it would have taken at 92%.

I assume the drop in the past few days has been due to formerly-reopened states putting the brakes on their re-openings over the previous two weeks. Which means it's unlikely to keep dropping at that rate, because there are only so many states that have brakes left to slam. But it's a tiny glimmer of hope.

Meanwhile, the rate of change in deaths (as opposed to new cases) has been consistently negative, for which there are two likely explanations: (a) we're getting better at treating COVID, and (b) deaths lag new cases by days or weeks. Unfortunately, this number seems to be getting less negative each day, which suggests reason (b) more than reason (a). We can expect the number of daily deaths to start increasing again within a week or two.

Da Night Sky

There was a lunar eclipse the night of July 4. I didn't hear about it in advance, and didn't notice anything different about the moon that night except that it was remarkably full.

But last night the still-almost-full moon formed an almost equilateral triangle, maybe two degrees on a side, with Jupiter and Saturn, both of which (being in the same direction as the full moon) are near inferior opposition and thus as bright as they ever get. And the Earth happens to have been at aphelion, the farthest it ever gets from the Sun, on July 4, which means we're ever-so-slightly closer to Jupiter and Saturn than we would have otherwise been, making them (let's see...) 1.6% brighter than if this same conjunction had happened when we're at perihelion.