**Mathematical grounds for optimism concerning the coronavirus, but not governments.**

This is a companion article to “The Last Gasp.”

One of the things this coronavirus outbreak has revealed is widespread mathematical illiteracy. Early on, the number of cases was said to be growing exponentially, which was true, but only for a short while. As an equation, exponential growth is of the form f(x)=ax (x is an exponent, I cannot type a superscript), where a and x are both greater than one. With exponential growth, assuming days are the time period, the daily change is greater each day, but the percentage change remains constant. The sequence 2, 4, 8, 16, 32 … is exponential, f(x)=a2 (the exponent is 2) where a at time 0 (I cannot type a subscript) = 1. The change between numbers grows, but the percentage change remains 100 percent. As a graph, exponential growth is a curve bending upwards. Viruses typically show exponential growth early on, but that cannot continue or eventually the virus would take over the entire planet and then the entire universe.

When the percentage change starts decreasing, there is no longer exponential growth. What has happened with the coronavirus is that the curves have tended to shift from exponential progressions to linear. Linear progressions are straight lines, described by the equation f(x)=ax, where x is a multiplier. 2, 4, 6, 8, 10 is an arithmetic sequence, where a at time 0 = 1 and x = 2. With linear progressions, the daily absolute change remains constant, and the daily percentage change shrinks. Most countries’ coronavirus graphs have already shifted from exponential to linear. The US’s is no longer exponential, but it’s not yet linear.

The next stage is when the daily absolute changes start decreasing. The progression is no longer linear, it bends down. This is what happened in China, even if one incorporates a fudge factor for allegedly fake statistics, and South Korea, which nobody suggests has fudged statistics. South Korea’s graph and widely acclaimed success in stopping the coranavirus are due to its widespread testing early on and its isolation only of people who had tested positive. That should serve as a model for the rest of the world, not lockdowns for the healthy and infected alike. Such lockdowns keep everyone inside, where they are often breathing recirculated air and exposing themselves to the coronavirus from people who are infected but have not tested so and consequently, have not been isolated. Lockdowns also keep people from sunshine, fresh air, and exercise, all of which boost the immune system. I’m grateful to Bill Sardi for the insight on the lockdowns.

The good news is that over the last few days, many countries linear graphs have started to bend down, even where the restrictions are most draconian. Italy’s daily confirmed cases have started to decline. This may only be statistical noise, but it is happening in many different countries with different medical protocols and statistical procedures, which suggests it’s not. The global graph is linear, but as more countries’ daily change numbers decline, the global daily change number will also start to decline and the graph will begin to bend down.

When, not if, the US joins the declining group will depend on how widely effective tests are performed, how many jurisdictions enact lockdowns, and how stringently those lockdowns are enforced. If testing increases from current numbers, it may show more confirmed cases. However, the daily increase in confirmed cases will attenuate as total actual cases do. Lockdowns will increase actual cases, and the more they are enforced, the more they will increase them. Regardless of testing and lockdowns, the US’s actual cases will first go linear (on current, admittedly imperfect numbers we’re already close) and then the curve will bend downward. The curve is certainly not exponential.

Which means that many of the projections both globally and for the US, based as they are on exponential growth that no longer exists, will be off the mark by orders of magnitude. As this becomes clearer, the dictatorial types will panic and try to enact still more dictatorial measures. The time to oppose them is now, with everything you’ve got. Please circulate this article and yesterday’s article, The Last Gasp, from either SLL or TBP as widely as possible. Sunlight, the wonder drug, is the best cure for ignorance.