Part One of this series of posts introduced the idea that natural probabilities for life events like a cancer diagnosis or a traffic accident are counter-intuitively very predictable in the aggregate, although usually not individually. Part Two demonstrated how a low-probability and very skewed random event begins, after a lot of time and repetitions, to look very “normal” because of the Central Limit Theorem.
In this third part, I want to “smooth out” the normal curve even further by looking at what happens when an event has not one, but perhaps many causes, each with a different probability pattern of occurring.
If you were to plot the heights of a large sample of the adult males in the United States (or any other single country), you would quickly form a close approximation of the classic bell-shaped “normal” curve. The statistical mean (commonly called the “average”) and the statistical mode (the “most likely”) of your sample would get closer to one another the larger the sample size gets, and this mean is currently close to 176 centimeters, or just over 69 inches (five feet, nine inches) for the U.S., as measured in a recent year,  looking something like this:
A comparable plot of American adult females would look similar, with a mean just under 64 inches but a nearly identical standard deviation (the “spread” of the curve). Importantly, the two curves overlap greatly. 
The normal distribution and its classic curve are so ingrained in us that we assume this is “nature’s probability.” In reality, this curve is more often the result of over-determined causation, as well as the Central Limit Theorem described in the prior post of this series. “Over-determined” means just one cause might be sufficient to see an effect, say one particular gene affecting adult height in this case, but more often there are multiple contributing factors. What we are often seeing in the normal distribution is the net result of all of these factors interacting with each other.
The standard deviation of this height curve is just under three inches, so my personal spot on this curve would be somewhere a bit over two standard deviations above the mean height, getting into the “tail” of the curve. I arrived at my height, as you did yours, through two primary biological processes. The first is the interaction of perhaps dozens of genes in the DNA “thread” you inherited from your parents, some of which are sex-related and some not. This makes up about 80% of your height.  I call this your Clotho effect height, after the Greek Fate who, legend says, randomly grants you the initial “thread” to start your life.
The other 20% of your height is the result of what I call Lachesis effects, after the Greek Fate who randomly “measures out your thread.” In biological terms, thousands of life events, either apparently random in nature or part of “God’s plan,” depending on your perspective (see Part Four of this series), may affect how your height genes are “expressed.”  Childhood illness, nutrition, and the environment in which you grew up have the greatest effects here. Some of these effects are called “epigenetic,” in that we also inherit different ways in which our bodies will respond to these environmental conditions. Because of epigenetics, the same condition does not necessarily result in the same effect on different people. 
And most of these independent variables affecting your height are likely not themselves “normal,” rather they may be gene-based “on-off” (“binomial”) probabilities skewed any number of ways besides 50-50. Many of the “ons” are tiny “lottery level” probabilities in themselves, but since there are thousands of variables, something becomes much more likely to happen because the Law of Large Numbers and the Central Limit Theorem.
So, my height is random, but probabilistically related to the height of my parents, my socioeconomic upbringing, my home neighborhood, and perhaps hundreds of other yet-unknown factors, multiplied by thousands of events through my life that acted as “traffic lights” to slow down or speed up my growth over its course. My height, like yours, is over-determined.
Most of the time, “normal” is just a statistic, but humans have historically placed a lot of societal acceptance, and even moral judgement, on “normality,” and likewise either curiosity or rejection based on “deviation.”
And back to our original topic of cancer probabilities, you often find the same “over-determined” character in trying to find the causes of cancer. There are likely numerous genetic, epigenetic and environmental factors coming into play, some with higher probabilities than others, but in the end, “smoothing out” and normalizing the reported cancer statistics in each demographic grouping (age, sex, income, location, etc.) you choose to select. Some of these probability distributions have very narrow spreads, and some wide, but the means, the top points on the normal curve, are usually remarkably consistent from year to year.
Important to later posts in this thread, deaths from cancer, though still adhering to a quite-normal curve in most demographics, have been on a steady decline since 1991, with the average death rate for all cancer types going down about 1.5% per year.  This demonstrates both the amazing ability for effective human intervention, but also the stubbornness of the remaining randomness. We typically don’t “cure” cancer in some absolute sense. We just change the average death rates and the average life expectancy of the survivors, one individual success or failure at a time, added together, which is a humbling thought.
What is also stubbornly missing from these normal curves of disease is a statistical trail of divine or supernatural intervention affecting some demographic groups (say, my faith tradition) but not others. That thought will bring us to Part Four, where theodicy makes its return.
Part Four of this series is now posted.
- Centers for Disease Control and Prevention. “Anthropometric Reference Data for Children and Adults: United States, 2011-2014.” Vital and Health Statistics. Centers for Disease Control, Aug. 2016
- Note, by the way, that it is statistically and factually incorrect to say that “men are taller than women,” even though they have different mean heights. The curves overlap greatly, so that there are millions of women around the world taller than the average height of U. S. males, and likewise millions of men shorter than the mean female height. This overlap also applies to other XY and XX chromosome-affected qualities like physical strength and even breast size. The large overlap of most sex-related characteristic curves makes differences in mean values much less relevant than most assume in many circumstances.
- Lai, Chao-Qiang. “How Much of Human Height Is Genetic and How Much Is Due to Nutrition?” Scientific American.
- Francis, Richard C. Epigenetics: the Ultimate Mystery of Inheritance. W.W. Norton, 2011.
- Bakalar, Nicholas. “Cancer Deaths Continue a Steep Decline.” The New York Times, 5 Jan. 2018.