According to the CDC there were 4,226 cases of illness in the USA due to COVID-19 on Monday, March 16th. Yesterday, the 26th, there were 85,356 cases. That’s a lot of growth in ten days!

I like to round things off and make estimates. It helps me get a handle on the size of the problem. For example I look at the above numbers and round them off to 4,000 and 80,000 because I can see right away that is a twenty-fold increase. There were twenty times more COVID-19 cases yesterday than there were last Monday. (4000 x 20 = 80000). That’s an easy idea to grasp: 20x. (If I do the actual math, subtracting 4226 from 85356 and dividing by 4226 I get approximately 19.2, so 20 is a good estimate.) But it doesn’t really tell us the growth rate, that is, how fast these cases are accumulating.

Growth is continuous, not discrete. Fortunately we have math for that. Don’t run away, I’ll keep it simple. You may remember from high school algebra—fondly, I’m sure—the lessons on logarithms. Many a math student has been crushed by logarithms. This is too bad because they are slick and have many applications.

We can estimate the continuous growth rate by taking the natural logarithm of both 85356 (approx. 11.35) and 4226 (approx. 8.35) and subtracting them. That’s an easy one. We get three (11.35 – 8.35 = 3.00).

For you mathy-types (non-mathies can skip this), the inverse of the natural logarithm, the base e, raised to the third power (e^3) is just about 20! 

We divide 3.00 by the ten-day period and get 0.3 and that tells us our continuous daily growth rate. Another way to say 0.3 is thirty percent (0.3 x 100 = 30). Percents are usually easier to grasp than decimals, and in this case they are a little more revealing. Imagine getting 30% on your investments! And we are talking continuous growth, like compound interest. I’d love to get 30% interest, wouldn’t you?

But the way to really grasp the speed of continuous growth is by calculating the doubling time. How long does it take for something to double? In this case, how quickly did the number of COVID-19 cases double in size? That is, how many days did it take?

If you take the natural logarithm of two (since we are doubling) and divide by the 0.3 we got earlier then you get that answer. The natural logarithm of two (written ln 2) is approx. 0.693 and that division yields 2.31, and that’s in days, so 2.31 days. My rough approximation of the rate of new corona virus cases is that they double every 2.31 days.

That’s fast. Now this trajectory is just a small snapshot of a big data set and there are far more sophisticated ways to analyze that stuff. I just wanted to play with simple math and see what it told me. I wouldn’t take my result too seriously. There are many smart professionals out there doing the real thing, and their numbers will be accurate. What I’ve got here is just an old blackboard lesson on logarithms, updated with some contemporary numbers.

According to the data on this site, the current USA doubling rate is FOUR days. Canada is currently experiencing a two-day doubling time, for example, and both New Zealand and South Africa are at three days. Other countries like Israel and Ireland are also at four days. According to the data* both China and South Korea have “flattened the curve” and pushed their doubling times to 46 and 25 days respectively. Japan is at 14 days.

That’s good news and I hope that we can do the same here at home.

Speaking of home, be sure to stay home! Be safe, my friends.

*The source for the data is called Our World in Data and the link is: https://ourworldindata.org/

I was an HIV/AIDS educator for a time. I remember the phrase “it ain’t love without a glove” running around. It was a reference to condom use. Our trainers told us that if person A had unprotected sex with person B it would be like person A having sex with everyone person B ever had sex with! Unprotected sex was not just sex with someone but with someone’s entire sexual history.

It was a graphic depiction of the nature of disease transmission.

COVID-19 is of course quite a bit different than HIV. But what’s being asked of us is the same. With HIV education we asked young people to protect themselves but we also made it clear they needed to protect others! Taking precautions, communicating honestly, and abstaining from certain behaviors takes effort. But if you care about yourself and the other people in your life you will put forth the effort.

If we want to reduce the threat of this virus we have to stop interacting with people. It is the best and most effective thing we can do.

This is hard. We need each other. We need close contact with friends and family. We need a healthy society that we can work and play in. We need goods and services. But we have to delay gratification. We have to inhibit our natural spontaneity. We have to isolate ourselves, as best we can.

We used to tell our students that you had to assume your partner had a sexually transmitted disease, that way you’d certainly protect yourself. And we reminded them that they could be carrying a disease and unwittingly infect someone if they were unprotected. They didn’t want to be that person, did they?

If you assume you are infected with COVID-19 you will take precautions not to spread the virus, like proper social distancing and self-isolation. This protects other people. And guess what? It protects you, to.

Isolation and social distancing are acts of respect. You are saying to your neighbors “I want you to be safe.” And at the same time you are looking out for your own health and well-being. Who can argue with that?

Remember:

“It ain’t love without a glove.”

If you didn’t already think you were living in a sci-fi world now you have no choice but to succumb to its inevitability.

A research team from several East Coast institutions (University of Vermont, Tufts University, and Harvard University) recently demonstrated “living” robots made from biological materials.

Their paper has a rather modest title: A scalable pipeline for designing reconfigurable organisms.

These folks aren’t as excited about what they created so much as they are about the process and what it suggests for future creations.

Stem cells were harvested from Xenopus laevis (African clawed frogs) as well as progenitor cardiac cells which were then manipulated mechanically and shaped into designs, creating “creatures” of about 1 mm in size. (The heart tissues are contractile and provide a crude locomotion.) The designs were done in silico and subjected to an evolutionary algorithm that winnowed out un-workable architectures and provided models for assembling the living-tissue robots.

The computational requirements to model the designs and test them in virtual environments were immense and done on the so-called “DeepGreen” supercomputer at the University of Vermont. The actual biological assembly was the least complicated part of the process. The “surviving” designs were further analyzed and improved in succeeding trials. The goal was to create novel organisms capable of four things: locomotion, object manipulation, object transport, and collective behavior. From the study:

Here, we demonstrate a scalable approach for designing living
systems in silico using an evolutionary algorithm, and we show
how the evolved designs can be rapidly manufactured using a
cell-based construction toolkit. The approach is organized as a
linear pipeline that takes as input a description of the biological
building blocks to be used and the desired behavior the manufactured
system should exhibit (Fig. 1). The pipeline continuously
outputs performant living systems that embody that behavior in
different ways. The resulting living systems are novel aggregates of
cells that yield novel functions: above the cellular level, they bear
little resemblance to existing organs or organisms.

“They bear little resemblance to existing organs or organisms.”

This is not Jurassic Park! This is something else entirely and the focus is on reproducibility, that is, industrial-scale applications.

What might such things be good for? Again, from the authors:

Given their nontoxicity and selflimiting
lifespan, they could serve as a novel vehicle for intelligent
drug delivery (28) or internal surgery (29). If equipped to express
signaling circuits and proteins for enzymatic, sensory (receptor),
and mechanical deformation functions, they could seek out and
digest toxic or waste products, or identify molecules of interest in
environments physically inaccessible to robots. If equipped with
reproductive systems (by exploiting endogenous regenerative
mechanisms such as occurs in planarian fissioning), they may be
capable of doing so at scale. In biomedical settings, one could envision
such biobots (made from the patient’s own cells) removing
plaque from artery walls, identifying cancer, or settling down to
differentiate or control events in locations of disease. A beneficial
safety feature of such constructions is that in the absence of specific
metabolic engineering, they have a naturally limited lifespan.

In the future—which is closer all the time—medicines will be customized to the patient. Extraction of materials from the earth, whether for remediation (waste cleanup) or resource mining, will be done without risking human workers.

I’m surprised this story didn’t generate more interest. I think it is pretty damn amazing and I hope I live long enough to see such schemes become economically feasible.