A few months ago, I read parts of “Witchcraft, Oracles and Magic among the Azande” (E.E. Evans-Pritchard, 1937). I like cultural anthropology, and I much prefer descriptions of the creative ways that humans have constructed societies to the more “scientific” anthropology that now seems more prevalent, and so it’s not surprising that I found Evans-Pritchard’s book fascinating. What was surprising, however, was finding that it intersected two topics I think about a lot: intestines and statistics.
The book describes the Azande, a group in central Africa, for whom witches and witchcraft are (or were, in the early 20th century) an important reality, central to everyday life. As Evans-Pritchard notes: “Mangu, witchcraft, was one of the first words I heard in Zandeland, and I heard it uttered day by day throughout the months.” Witches can cause harm to others in their community, and preventing or detecting this is an important task.
Guts
Remarkably, witchcraft is an actual physical trait of witches. It is a substance, an “oval blackish swelling or bag” associated with the intestines. One can, therefore, confirm or refute allegations of witchcraft by autopsy, in which the intestines are drawn out from the belly and inspected by experienced old men for signs of the witchcraft substance. Obviously, this isn’t very useful for the suspected witch if it’s his or her entrails that must be examined, but thankfully genetic inheritance comes to the rescue: “The sons of a male witch are all witches but his daughters are not, while the daughters of a female witch are all witches but her sons are not” (p. 23). Therefore, if a man dies, it can provide the opportunity to clear the name of his father or son, if they had been accused of witchcraft; similarly, for women, mothers, and daughters.
I don’t know why the intestines were settled upon as the home of the witchcraft substance. Perhaps it’s just that they’re an important organ, or perhaps their messiness allows a lot of leeway in deciding whether the vague “substance” is present or not. In any case, since my lab spends a lot of time looking at zebrafish intestines [e.g. post1, post2], both in live fish and dissected ones, we should perhaps keep an eye out for magic! And, of course, one could study in humans at connections between the composition of the gut microbiome and supernatural powers. There’s a more interesting connection between the magic of the Azande and science, however.
Unfortunate Events
“Witchcraft is ubiquitous… there is no niche or corner of Zande culture into which it does not twist itself” [p. 63]. Any unfortunate event has witchcraft as its cause:
If blight seizes the groundnut crop it is witchcraft; if the bush is vainly scoured for game it is witchcraft; if women laboriously bail water out of a pool and are rewarded by but a few small fish it is witchcraft. [p. 63]
Evans-Pritchard notes that the Azande are rational and intelligent, and moreover do ascribe events to causes we would agree with. For example, if the supports of a hut’s roof break, and parts of the roof collapse and hurt people sitting under them, this may be due to poor woodworking on the part of whoever built the roof, or damage from termites gnawing the wood. But why did it collapse on this particular day and not another? Why did the pieces of roof fall on the side of the room with people in it, and not on the empty side? The answer: witchcraft. In another example (p. 67):
Likewise a potter will attribute the cracking of his pots during firing to witchcraft. An experienced potter need have no fear that his pots will crack as a result of error. He selects the proper clay, kneads it thoroughly till he has extracted all grit and pebbles, and builds it up slowly and carefully. On the night before digging out his clay he abstains from sexual intercourse. So he should have nothing to fear. Yet pots sometimes break, even when they are the handiwork of expert potters, and this can only be accounted for by witchcraft. ‘It is broken — there is witchcraft,’ says the potter simply.
Witchcraft, therefore, is the explanation for apparent randomness. This may seem odd, but discomfort with the idea that “noise” exists is universally human. Most people find it hard to accept that the outcomes of events are, to some extent, governed by complex interactions that are effectively random. (They may also be fundamentally random, but that isn’t relevant or necessary.) We look for causes and patterns, and most people, now and throughout history, try very hard to ascribe causes to random events. My external hard drive failed this morning, without provocation, and I realize that it’s taken quite a bit of training for me to believe that this was not due to black cats seen on today’s ride to work, or to the present positions of certain stars and planets. Rather, due to a million independent forces all adding up as random noise, there’s simply some nonzero probability of hard drive failure, and today is when that failure happened to occur.
Statistics
In the sciences, we try to train students to understand uncertainty. Moreover, we aim to quantify it: What’s the probability per unit time that a hard drive fails? Given some probability per unit time of random mutations in a genome, what’s the likelihood of finding 3 mutations in a 1 year period? Given some amount of random variation in life expectancy, how accurately can I estimate the mean life expectancy of a population, or how it’s affected by air pollution?
As mentioned, it’s not easy to think like this, and I encounter more scientists than I’d like who have trouble accepting randomness — who, at least at first thought, attribute every bump in a graph to some real, meaningful process that should be (fruitlessly) chased. More broadly, though, I think a lack of acceptance of uncertainty underlies many of the present problems with bad statistics in science, and the abundance of bad science.
Statistics, properly applied, quantifies uncertainty and guides the inferences we can make from data. It doesn’t eliminate uncertainty; that would be impossible. Misapplied, there is a perception that statistical tools can magically extract certainty from data, that if we just find the right statistical test, the spell that reveals a small p-value, we can draw conclusions from data no matter how noisy. It’s this implicit belief, I think, that contributes to nonsense like this graph, from a 2017 PNAS paper, of life expectancy in various cities in China on either side of a river North and South of which are different environmental policies:
(This graph, and the paper, have been discussed in Andrew Gelman’s blog.) If you ignore the grey curve and the vertical line at 0, you’d never conclude that the river boundary has a dramatic effect. There’s a lot of scatter in the points — a lot of variation. But if you fervently believe that a signal can always win out over noise, that a witch is always to blame, you’ll concont an appropriately convoluted analysis approach to reveal it.
The link from Azande witchcraft to air pollution analysis is, admittedly, a bit of a stretch. Still, they remind me of each other. In terms of elegance and honesty, however, the Azande text wins.
Today’s illustration
I drew something vaguely intestinal.
— Raghuveer Parthasarathy. August 30, 2018
