The US now has over one million confirmed cases of COVID-19. Over 60,000 people have died. Those are shocking numbers, but it does appear that the spread may be slowing down. The doubling time for new cases is now 19 days and for deaths it is 15 days. Let’s hope the first two numbers don’t grow much more and that the last two numbers keep increasing!

So how big is a million? A thousand times a thousand! Does that help? Probably not. If you go to the beach and pour a handful of sand on to your open palm you will have about a million grains in that small heap.

A million seconds is just short of 12 days (60 x 60 x 24 x 12 = 1,036,800).

If you take the thickness of a dollar bill to be 0.0043 inches, then a stack of one million one-dollar bills would be 358 feet high. Sather Tower, aka The Campanile, on the UC Berkeley campus is just over 300 feet tall. The tallest tree in Redwood National Park is about 380 feet tall.

A baseball is between 9 and 9-1/4 inches in diameter. If you laid out one million baseballs end-to-end (I’ll use the larger number) they would stretch 1,752 miles! That’s the distance from San Francisco to Lincoln, Nebraska.

A trip to the moon and back is only about half a million miles. You’d have to make two trips to get your spaceship odometer to cross 1,000,000.

If you lined up a million people shoulder-to-shoulder (let’s say 24 inches apiece) you’d need nearly 400 miles of space.

A million people is 1/340th or about 0.3% of the US population. That doesn’t seem like a lot unless you think about the fact that you easily know 340 people. There’s a good chance you know someone infected by the corona-virus or at least you know someone who knows someone. Two degrees of separation is what they call that. That’s pretty damn close. Certainly if you lived in NYC or LA you’d have a better chance of being personally impacted by this disease. Those of us fortunate to live in a rural area have been somewhat isolated from the pandemic compared to our urban brethren, but we’ve experienced, like them, the economic fallout.

It bears repeating: we are all in this together. My good luck—i.e., my reduced risk compared to family and friends in the metro regions—is not immunity! Much is still unknown and uncertain about COVID-19. It will be hard to make good decisions without good numbers. But good numbers have been really hard to pin down! There seems to be a lack of coordination among the various epidemiological studies. Ideally, each data set would be added to a global repository that everyone could access. That way each new model of the disease can be better than the previous one because it can be updated with the latest information.

Scientists and other “experts” have taken a bit of a beating with this pandemic. That’s because all models are wrong. And you have to be wrong a bunch of times before you can get closer to being right. But you have to remember that all models are wrong, so you have to keep adjusting and that means letting go of a lot of previous work and previous assumptions. That’s hard to do. People get invested in their ideas and they are reluctant to part with them. Solving a problem like COVID-19 requires a tremendous amount of intellectual flexibility. You have to be able to see where you were wrong in order to improve your work. The public doesn’t like it when experts are wrong and experts don’t like to be wrong, so people fight over who is “right” because they don’t have the patience to stick with the process. It’s not about who is right or who is wrong. It is about how to work together and build the best knowledge base.

Public policy decisions are political, not scientific, but getting the best information into the hands of the decision-makers still needs to be done. What are the odds of that?

Oh, I can’t resist: a million-to-one!

Over half a million infected. That’s one American in seven hundred. Do you know 700 people? There’s a good chance you do.

More than twenty thousand dead. That’s four percent of the half million. That’s a lot, 4%. Four out of every hundred. How many times have you been in a group of 100 people?

We saw an Easter gathering on our walk this morning. The service was in the church parking lot with people in their cars. The preacher was up on a platform with a microphone. That’s a tough racket—being a preacher. You have to sell stuff that isn’t there! You have to convince people they’ve received what you’re sending them. I was a schoolteacher and I know that’s no mean feat.

It made me happy that folks figured out a way to celebrate. This pandemic has us imagining new ways to do things, and I like to see solutions to problems.

I suspect we will come through this crisis in due time. It’s the length of time that I can’t get a handle on. The distancing measures and lockdown strategies seem to be working. I’ve no idea when the timing will be right to ease off on those. Let’s hope the epidemiologists get a good model of the disease progression and can make better estimates. That way any public policy decisions can at least have some decent numbers to work with instead of just a bunch of useless opinions.

As of yesterday, 4/8/20, this site reported 427,460 cases of COVID-19 in the US.

Let’s do some math. On 3/16 there were 4226 cases. That’s 23 days of growth and we see a 100-fold increase. When something grows by a factor of ten (that is, 10x) we say the increase is “one order of magnitude.” So a growth of 100x is “two orders of magnitude.”

The natural logarithm of 4226 (ln 4226) is roughly 8.35 and ln 427460 is roughly 12.97 and that difference (12.97 – 8.35) is 4.62.

Using the same math as before, I divide 4.62 by the 23 days of growth and get 0.20 which is 20% growth. We’d love 20% growth on our investments, right? That’s still a high rate. But it has come down from the 30% we got previously. Remember we had seen that figure drop to 27%.

We now take ln 2 and divide by 0.20 to get the doubling time. The result is 3.47 or about 3-1/2 days. That beats the 2.56 we got last time! Remember that I’m just running these numbers for fun, they are not meant to be a serious analysis.

According to this site the doubling time in the US is currently 8 days. That’s good news. We continue to see the rate of growth of new infections dropping.

One caveat: testing, as we know, is woefully inadequate. We won’t get a real handle on the numbers of infected people without widespread testing. There could be a lot of asymptomatic carriers and if we can’t test enough people then we can’t know for sure. But so far we have seen that aggressive social distancing measures appear to make a big difference. So, keep up the good work, people!

Manganese is an essential nutrient. You have to have it in your food in order for your body to function properly. That being said, instances of manganese deficiency are rare. This particular trace element is found in sufficient amounts in a wide variety of foodstuffs, everything from nuts to grains to vegetables and fruits. It would be hard not to get the 1-2 milligrams per day you need just from ordinary eating.

Manganese, like many metals, is toxic in larger quantities. People who are exposed to manganese in the workplace—mostly welders—have to take precautions. Manganese is a crucial ingredient in the production of stainless steel. In fact, there are few substitutes for manganese in its metallurgical applications.

So why should we care about manganese? Clearly it has enormous industrial importance. Without steel there is no modern world! The other reason we should care is that there is no domestic production of manganese in the United States.

We import ALL of the manganese we use in this country. It comes from places like South Africa, Brazil, Gabon, Ukraine, India, and China. There are probably billions of tons of manganese on the seafloor in the form of nodules, but no one has figured out how to mine that stuff. Known deposits here in the States are too low-grade and extraction costs too high to be an alternative.

That means we have to depend on other countries for a critical mineral.

It’s not the only one. Vanadium—another significant ingredient in steel—is entirely imported. So are tantalum, indium, gallium, cesium, fluorspar, asbestos, niobium, arsenic, rubidium, and several other important industrial materials.

We live on this great big rock. The spot we live has a lot of good stuff. But not all the stuff we need. That means we need other people.

There is no such thing as “self-sufficiency.” It is one of those nice notions that gets kicked around by romantics, back-to-the land types, politicos, and ill-informed pundits (are there other kinds?). Humans are a social species. We live in a web of inter-connections. Without each other, that is, without society, we cannot survive. Civilization may be a relatively recent thing in human history, but society is not. The first humans lived in groups and depended on each other, the last humans will as well.

It’s OK to re-watch Jeremiah Johnson and marvel at the independence and self-sufficiency of those old mountain men, but stop and think a little. All those guys had rifles and cartridges. It takes an industrial base to manufacture such things. All those guys had horses and pack animals. Those are the fruits of a well-developed agrarian economy. Jeremiah and his pals may have been tough and smart, but they couldn’t have done shit without steel and animal breeding. And those are just the first two things that come to mind.

If you want to “shop local” and “buy American” because you want to do right by your neighbors, I say good on you. I try to do that. Even if they are selling Japanese cars made in Mexico!