Most theologians, I suspect, do not do math well. But it appears that one of the biggest challenges to the many religious explanations of theodicy (Why do bad things happen? Why do good things happen?) may the basic normal probability distribution. I’m not trying to be sacrilegeous here. However, if I must describe this in theological terms, I prefer a favorite dictum: “If God is real, then the more we learn about reality, the more we learn about God.” Let’s look at some reality.
I cringe every time I hear someone say, after some tragic event such as the murder of Black shoppers in a Buffalo grocery store a few months ago, or the murder of schoolchildren in Uvalde, Texas, “Everything happens for a reason.” I understand the sentiment, since most of us are not very articulate with our theologies and, frankly, even the most treasured scriptural words of comfort times feel inadequate and lame in times like these. Unfortunately, my explanation likely provides little comfort either.
We don’t want to “curse God and die,” as Job was counseled by his wife, but the cognitive dissonance of a loving God causing such suffering often makes my head hurt. This is a very old problem, given the name of theodicy (the “justice of God”) by German polymath Gottfried Leibniz near the turn of the 18th century. It is a subset of theology that most priests/ministers/rabbis/imams have to confront on a regular basis, but likely prefer not to.
I am personally feeling a bit like old Job these days. What should have been a routine gallbladder removal has turned into six weeks of pain and three hospitalizations in addition to the initial outpatient laproscopy operation, plus lots of pokes for tests, interrupted by a major hurricane turning the hospitals into chaos zones. Then again, I did lose that stubborn twenty-five pounds…
But finally, I think I am on the mend. A few years ago, I had a medical scare with a troublesome kidney, which turned out to be a more transient problem, but during its worst I went (as one does) to the data published by the Centers for Disease Control to see “what my odds were” regarding cancers of the kidney. Based on age-adjusted statistics over the last reported ten years in the state of Florida, 3.3 people per 100,000 die of renal (kidney) cancer every year. And over those ten years, that fatality number was never lower than 3 and never higher than 3.5. There are some good statistical reasons for that narrow range, and if you cut it finer demographically you get different numbers for different groups, but even a CDC statistician who looks at data all day would likely say, “That’s a narrow range for 10 years of data.”
Over that same period, another quite-narrow range of between 13.9 and 15.4 per 100,000 people are first diagnosed with this type of cancer, although that event likely occurs in a different year from the aforementioned deaths. Basically, fourteen Floridians per 100,000 people (and there are now over 20 million people in Florida) are diagnosed and three die. If you believe in some kind of God with “divine purpose,” the question may nag at you: “Why three?” I’m taking a stab here and guessing that a majority of those fourteen were religious to some degree and likely prayed at some point for a healing from their cancer. Eleven of those people perhaps even testified in church that they “were healed,” while three did not.
All the classic reasons stink here. Did these three “deserve it” more than the others? Were they more sinful, perhaps, or “had less faith” or didn’t seek out the “correct” healing religious denomination? This conundrum is why the best we can often do is to mutter, “Everything happens for a reason…”
In my more irreverent moments, I imagine God saying in this particular case, “I would heal you, but the quota this year is 3!”
The curse of the normal curve
A disclaimer for the math nerds: My explanation of some complex probability math has been greatly simplified here. Bear with me.
From the moment of our conception, numerous natural events (and many human-caused events as well) buffet our fertilized ovum as it develops into a human (or, also probabilistically, not), and for the remaining years of life as well. Multiple genetic, epigenetic and external factors go into determining adult height, for instance.
When that happens, the many forces stretching one’s height are offset by forces limiting one’s height. As a result, two normal curves form, one for those with XX and one for those with XY chromosomes. That is the Central Limit Theorem – multiple contributing probabilistic events of widely-varying types in nature often average out into the familiar “bell” or “normal” curve, which has definable mathematical properties. (Skipping here a fascinating discussion about how there are more alternatives here than just these two, and how “maleness” vs. “femaleness” is itself a probabilistic variable biologically, if not theologically.)
The “overlap” between the normal XX curve and the normal XY curve on various human traits is often larger even than that of height, which is shown below, and dominance swings between the two sexes depending on the trait.
Narrowing the demographics
But what about those disease correlations where we “know” a cause? Even if narrow our demographic boundaries considerably, say to male two-pack smokers over 50, a normal curve will start to emerge over time. It turns out that most heavy smokers do not die of lung cancer. Some are “lucky” (statistically on the low extreme of the curve) but there are multiple “comorbidities” such high blood pressure or COPB that are just as likely to get them first.
Living on the extremes
The statistical measure of the “spread” of each normal curve is called it’s “standard deviation,” which could be large (a wide and broad curve), or small (a tall, skinny curve) like the kidney cancer death statistic noted earlier. There are human beings on each tail of these distributions. For instance, I am about two standard deviations out on the high end of that height curve, which covers less than 2.5% of the population.
(The Greek letter sigma represents standard deviations.)
As a result, even though the laproscopic removal of a gallbladder “normally” goes well with few complications other than an intolerance of fatty foods, it can, on the edge of that curve, screw up your digestive process completely, either in the short term (I hope) or for longer. And I have been at that bad far end of the curve.
The “squashed” normal curve
Sometimes “Acts of God” seem to occur in clumps, like the classic “bad things come in threes” theory (mostly an illusion). It turns out that when you take events that “normally” plot to that normal curve over the long term and put them on a short time scale measuring infrequent events, that curve gets “squashed” against a “hard stop” of zero, but with long “tail” hanging out on the high end. This is called a Poisson distribution (pronounced Pwah-sohn), named after the French mathematician who discovered it, Siméon Denis Poisson (1781–1840).
During my recent hospital stays, the PA system would ring out with Brahms’ Lullaby (“Lullaby and goodnight…”) every time a baby was born (aggravatingly, 24 hours a day). If we are measuring, say, the number of babies born each day in a large hospital where the average is four deliveries per day, the curve likely looks like the one above. On about seven days each year (about 2%), there will be, just by chance alone, zero babies born. There will be about an equal number of “three days” and “four days” (about 70 each) but on about nine days a year you might have a run of eight babies. And ou need to be prepared for the good probability of eight.
This is all “normal.” Or, in theological terms, “God’s will” in action in the “real world.” We have just squeezed the measurement timeframe.
Living in the middle ground
It may seem odd, but humans live in the “middle ground” of objects in the universe — if you rank them on logarithmic size. Nature usually counts logarithmically. The chart below shows the size of some objects on a logarithmic scale of meters.
At the biggest end of the universe, determinism rules, so Albert Einstein claimed. The effects of the Big Bang continue to unfold, using the rules of classical physics at the level of the Cosmos. There is likely at least one more massive asteroid that has Earth’s name already programmed as its ultimate destination, but that event may be millions of years into the future. At the smallest end of the universe, however, as quantum physicists have demonstrated, a strict world of probability determines the orbital shells of electrons, for instance.
Humans seem to be stuck somewhere in the middle. In the end, we all die, the ultimate deterministic fate for us all. But between birth and death, our lives at least appear to follow some path made up of a combination of probability, coincidence, volition, and human intention. You might even throw in some Fate, Karma, or Grace into that list. God or no God, life remains an indeterminate mystery.
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