“At the first glance, the only ‘law’ … seems to be that of Caprice — caprice in inheriting, caprice in transmitting, caprice everywhere, in turn.” — Philosopher William James (1842– 1910)
One of the classic examples in an introductory statistics class is the drawing of billiard balls from an opaque sack containing an unknown mix of various colored balls, and then trying to estimate the makeup of the entire sack. How many balls do I need to draw out in order to get a prediction that is accurate to within some confidence window?
I support the Centers for Disease Control and Dr. Anthony Fauci’s National Institute of Allergy and Infectious Diseases. But let me assert that a lot of the public’s unease with recent pronouncements from the CDC and NIAID stem from some statistical “sticking points” that make the public less than confident in some recommendations:
- Their life-or-death decisions are necessarily made based on a relatively small number of samples from a massively large and very opaque bag, and
- Those virus billiard balls in the bag keep changing colors and propagating at a ferocious rate, and
- If you had a statistics class at all, you likely slept through it.
A recent example of this confusion is the reporting of “breakthrough” Covid infections after mass gatherings in Provincetown, Massachusetts. In the end the outcome was extremely reassuring; hospitalization or death from a breakthrough infection in a vaccinated person is far more unlikely than for an unvaccinated one. But the net result of this report clearly undermined public confidence in mitigation measures, giving ammunition to the antivaxxers. Especially to those of a religious bent, the CDC and NIAID advice begins to appear “capricious,” or uncertain and unpredictable.
In April of 2020, early in this pandemic, I wrote about the theodicies (literally “God’s justice”) expressed by various religious traditions in response to the faith challenges posed by the virus, in a post entitled Avenging angels and the Coronavirus. You can consider this post to be a vaccine-inspired update, since many religious groups have been as vocal in their opposition to this life-saving vaccination as they were to the various available mitigations all the while “God decided” to remove 600,000 Americans and over four million people worldwide from the Earth via Covid-19.
As a number of internet memes have pointed out, we have embarked on a grand scientific effectiveness experiment with these new vaccines, and many of these religious vaccine deniers have self-selected to be part of the “placebo-receiving control group” (I got a vaccine; you get “thoughts and prayers”). How will this vaccine denial play out in the churches over the next years?
The quote at the start of this post was the response of noted philosopher William James to Charles Darwin’s 1868 book The Variation of Animals and Plants Under Domestication. In that follow-up to On the Origin of Species (1859) Darwin proposed a process he called pangenesis, with inherited gemmules to account for variation in visible characteristics of descendants.  James was objecting to the seeming lack of controlling purpose in Darwin’s inheritance process. On the surface, and without our subsequent understanding of DNA, pangenesis looks awfully random and, James says, capricious, subject to change on a whim by some controlling divinity.
Augustinian friar Gregor Mendel (1822–1884) had figured out with his pea plants that this process of inherited variation was instead “probabilistically random” as opposed to “capriciously” random. However, Mendel’s work went largely unnoticed during Darwin’s time (and well beyond), and he died in obscurity.
Natural “stochastic” processes, which demonstrate randomness in some sort of probabilistic manner, have a statistical “shape” in the long term, even if they often look capricious in the short run. You can play a seemingly random game of Monopoly by rolling two six-sided dice, but over the long term, players will land on certain streets more than others (hint: build your hotels on Illinois Avenue and not Mediterranean Avenue). 
A probabilistic or a capricious God?
“Divine fatalism” is the notion that “God’s will” determines whether you live or die today. The version of this idea expressed by Swiss theologian John Calvin (1509–1564), which is at the root of most of the denomination-correlated anti-vax movements in the U.S., is religious predestination. A “contemporary Christian” song first recorded by the Archers in 1977 expressed this theodicy well:
You know the future and you plan all my days;
You know each season and you know all my ways;
You own every hour and there’s nothing hid from you;
You own tomorrow, so I won’t fear today.
Several biblical scriptures appear to support this theodicy, for instance words ascribed to Jesus in Matthew 6:26-28 (NRSV):
“Look at the birds of the air; they neither sow nor reap nor gather into barns, and yet your heavenly Father feeds them. Are you not of more value than they? And can any of you by worrying add a single hour to your span of life?“
However, the very next line says, “And why do you worry about clothing? Consider the lilies of the field, how they grow; they neither toil nor spin.” My observation is that most of these anti-vax folks are well dressed on any given Sunday, and most adults return to “toil” on Monday. The Bible is always selectively read.
The theodicy of “probabilistic randomness” just does not go down well in these religious circles. I noted in a very early post on this blog that some cancer occurrence probabilities are remarkably consistent from year to year, regardless of religious persuasion or prayerful intervention. But a “cancer lottery” is a hard theodicy to digest for most religious people.
Even though most believers likely own multiple insurance policies actuarially based on probability, the trade-off of a very-low-risk vaccine reaction versus a relatively-low-risk of dying from Covid seems somehow to deny “God’s will.”
Add to this a propensity of literalist Christians to follow messianic “naturopathic” medical practitioners like Floridian Joseph Mercola, who has made a fortune selling vaccine misinformation. And then add in politics. As religious journalist Garry Wills has noted, the American “religious right” is sometimes more ideology than theology. I wrote recently about the persistent split in vaccination rates between “blue states” and “red states” where anti-vaccination Christian groups are more prevalent.
Math-aware Christian pastors, especially in evangelical congregations, have walked a difficult tightrope with vocal dissent to Covid vaccination in their flocks. Increasingly, faith leaders such as Franklin Graham have urged vaccination, but especially in Graham’s case, a long tradition of his questioning of science has stomped on that toothpaste tube too many times, and it is not going back into the tube anytime soon.
I don’t “know the future” of unvaccinated Americans, but their health and life insurers had better raise their rates. 
- The William James quote is from Carl Zimmer’s very readable account of the science of heredity called She Has Her Mother’s Laugh (Dutton, 2018). Darwin’s vision pointed in the right direction, but it was flawed. Coincidentally, the better alternative of DNA was first isolated by the Swiss physician Friedrich Miescher the very next year, 1869. However, it took until the 1950s for Francis Crick and James Watson to figure out the basics of how the “double helix” DNA structure worked to pass genetic information from parent to child.
- Between the “Go” and “Jail” squares, players are more likely to start from some squares than others, and the higher likelihood of, say, rolling a seven over rolling a two tends to land players on some squares more than others. And when you also factor in the differential rents among the streets, Pennsylvania Avenue actually beats out Illinois Avenue for hotel profitability.
- Note that the Affordable Care Act limits the ability of insurers to vary rates based on vaccine status, so the rest of us will pay.
- Avenging angels and the Coronavirus
- When public health gets political
- Cancer, probability, normality and theodicy
For additional posts on probability, volition and ethics, follow the Dice icon back or forward where it appears.