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.
Good analysis. One trend we need to demand and see more of is the advent of real-time healing (caring for health and the receding of a pure science (disease care mislabeled as health care). Pure science is what the FDA and CDC are geared for…they failed us badly in this contagion when real world demands suddenly hit. They oversold themselves and are terminally infected with Agency Capture and Public Choice disease….deal with that lame horse later. Now progress only comes in two ways: Test, treat, test,treat. Masks, ventilators, beds, quarantines, etc. are all secondary. If we can test fast and ubiquitious and then treat safely and effectively Covid-19 is just a nasty flu which is super contagious. Life is a contact sport.
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I’m no good with the math so thank you. Is it a coincidence theory that the two states led by true believer ideologues with open borders are having the most trouble?
Kaiser Hospitals say nurses do not need masks when dealing with Covid-19 patients
You can indicate an exponent (x) with a^x or a**x.
The curve you are trying to describe is a sigmoid curve or logistic function. The function described by the curve is, among other things, bounded. Nature has limitations or boundaries, regardless of anyone’s wishes or fantasies. This includes everything from film’s response to light to populations of viruses to economies.
The entire civilized world is essentially locked down at the moment (democratic hoax, I heard) and you’re copying some equation out of your undergrad math text book to prove essentially nothing and solve exactly 0% of the current problem at hand. Bravo and thanks for the advice to go outside.
I’m here because I have greatly enjoyed your writing in the past but these last two articles have left me shaking my head. Have you ever been intubated Robert? I have and it was so terrifying that it radically altered the course of my whole life. Do you know anyone currently working in healthcare? I think many healthcare workers would find the suggestions you have made in these last two articles to be unhelpful. We are close friends with the GM of a hospital in a medium size town in the Midwest (who was set to retire next month and has been working in hospitals most of his adult life) and a week ago he implored us to stay at home giving us details of what he described as the worst week of his life as the hospital that he manages has become overwhelmed with critically ill patients and has run out of supplies, run out of ICU beds and run out of ventilators and has a staff that is exhausted and afraid.
And for anyone thinking I’m not a fan of liberty or that our family generally lives in fear, one visit to our farm would be enough to suggest otherwise. I believe the larger philosophical question that should be answered by all of us is why we have allowed a system to takeover that can’t survive even a couple of weeks of individuals and corporations taking a break from their hamster wheels of wanton consumption and debt creation. I would suggest that bravery and embracing liberty in the face of this crisis has little to do with ignoring short term social isolation routines and everything to do with developing long term self reliance and removing our participation as much as possible from an economic system that is an abomination relative to the ideas of community, common sense, sustainability and decency.
I have no doubt that those in charge will do what they always do in a crisis – attempt to steal everything that is not locked down and further centralize and grow their power. That’s already happened. But it happens because people are helpless dependents on the system and have almost zero options other than compliance. IMO the wisdom of the ages relative to fighting corrupt human made systems is that “trying creates impossibilities – letting go creates what is desired”.
Wishing you the best and sending a lot of gratitude for all of the times in the past your writing has been an inspiration.
I have never been intubated. My sister is a doctor and my sister-in-law is a nurse. From the perspective of the medical profession and the afflicted, I understand their stress, dismay, and overwork stemming from the coronavirus outbreak. That was not the perspective I was writing from. As emotionally draining, distressing, and debilitating as this has undoubtedly been, from the perspective of someone who cherishes what’s left of my and my fellow citizens freedoms and livelihoods, I don’t think what we are doing now will in the long run be justified by whatever medical benefits are obtained. I also believe that much of the fear being peddled is founded on flawed reasoning, science and mathematics.
I’m sure, as you assert, that “many healthcare workers would find the suggestions you [I] have made in these last two articles to be unhelpful.” That is not the end of the argument. There are many ordinary citizens who are losing their livelihoods and freedoms because of the measures enacted. They are certainly being subject to significant financial and emotional hardship. Unemployment and poverty cause disease, illness, and suicides, all of which will place an additional toll on the medical industry. Politicians and bureaucrats are granting themselves extraordinary powers, many of them clearly unconstitutional and many of which, like the Patriot Act–enacted in response to a previous “national emergency”–we will live with and rue far into the future. Precedents once enacted are not often rescinded, especially precedents that give governments more power. Healthcare workers are not the only people in this country, and I don’t think you can look at this outbreak solely from their perspective. As they say of the military, they know what they’re signing up for.
These two articles stem from the same philosophy that in the past you have found inspirational, and I’m glad that you have enjoyed my earlier work.
Thank you for the thoughtful response.
My readers deserve no less. Thank you for your thoughtful comment.
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