, ,

Probabilities and Biblical Studies

Stephen C

•

I’m no biblical studies expert, but I’d like to think I’m an informed amateur, and in my readings and podcasts I’ve run across a few reasoning habits and approaches from biblical studies folks that tweak me a bit in terms of the proper use of probabilities. 

  • Unknown unknowns, not rhetorically taking into account the probability space, and statistically overfitting the data 

Maybe Moses had a pet named Joshua. Maybe Mary had a bad relationship with her second cousin who defrauded her out of a lamb. Any one of these has a very small chance of happening, but if we take the vast space of all the very small possibilities added up altogether it’s clear that what we have is an infinitesimal fraction of the lived experiences of biblical figures. Of course, it’s not biblical scholars’ jobs to speculate about all the unknown unknowns, but rhetorically at least scholars sometimes tend to speak about biblical events and figures as if they exclusively consist of the strung together sequences of paltry evidence and theories derived from those shards of evidence, instead of a big mass of unknowns of which the rare in-the-ground or on-the-text evidence describes a small part. Again, this isn’t a criticism of their actual processes, but rather a matter of rhetorical emphasis and framing. The evidence is so sparse that they tend to overfit the data they do have, when in reality much of reality probably has nothing to do with any data that we have and will never have. 

I’m not trying to subtly flip the onus of justification, as if they have to prove that Mary didn’t have a bad relationship with her cousin, Russell’s teapot on all that, but rather making the point that when speaking about biblical figures and events we tend to speak less in terms of a vast unknown and more as if the entire event or person was triangulated within our theory. This leads to more confidence about things like personality and such than is warranted. 

And of course, people have to sell books when a more honest appraisal of the situation would list the “second best bed,” and a handful of confirmed details and leave it mostly at that, but instead some people have a tendency to layer conjecture on top of conjecture to fill out a word count.  To talk about Jesus the revolutionary or Jesus the rabbi, or this or that take on Jesus, when by any secular historiographic standards we really have very little idea outside of revealed religious truths. To paraphrase Joseph Smith, while there are consensuses, for big-picture issues so many scholars interpret the same piece of evidence in such drastically different ways so as to destroy all confidence by an appeal to the data. 

  • Assuming probability of .8= probability of 1. 

Cognitively we don’t handle probabilities very well and we tend to round up or down. We saw this during the first Trump election when people assumed that Nate Silver’s probability of 20% or so for a Trump victory was essentially zero. I also a recall an anecdote from a book (can’t remember which one) where an economic adviser quoted President Obama a 40% chance of something happening, and Obama said, “so a coin flip…,” and the adviser had to specify no, 40% isn’t a coin clip, it’s 40%. (Not to disparage Obama on this, it’s a common thing most of us do.) 

In much the same way consensus biblical positions are often rhetorically treated as givens. For example, the Markan priority, the idea that the book of Mark was written first, has some strong evidence for it last time I did a deep dive, so let’s place its probability at, say, a 90% chance of being valid. That’s pretty high; it is probably true. However, not believing in the Markan priority is not the equivalent of, say, thinking the earth is flat, and believing that the woman taken into adultery actually represents an older, more authentic tradition is not the same thing probabilistically as 9/11 being an inside job, but sometimes everything on the other side of a strong consensus is lumped together as a fringe theory when they really don’t belong in the same categories. 

  • Chained Probabilities 

Some theories take the position that given X (say the Markan priority), we can infer Y. There’s no problem with that, but we essentially have two different probabilities, the probability of X, and then the probability of Y given X. If we chain these probabilities together the overall chance of it being wrong increases. Is it a reasonable estimate given the evidence? Yes. But if we have more interconnected hypotheses, no matter how reasonable any given one is, then the chained probabilities decrease the chance that the whole web is accurate. If we have three linearly interrelated, contingent facts that each have an 80% chance of being true, that is only slightly more than a 50% chance that the entire system is true. Again, nothing wrong with that, but chained probabilities add up and that 10% chance that there is no Q source or that the documentary hypothesis is wrong should not be completely ignored when building theoretical edifices on them. 

  • Confidence Intervals 

Given all of the above and the sheer paucity of clear evidence for most biblical episodes, If you look at the evidence you have there’s a tendency to zoom in on that and to ignore the size of your confidence intervals on either side of your peripheral vision. This is an old back-and-forth among academic disciplines. Physicists demanded a p-value (the chance that they got those results by chance) of 0.00000059 before declaring the Higgs boson discovered. To them social scientists’ threshold of p=.05 it has the rigor of mud. Most disciplines can criticize other disciplines about how their thresholds are looser, but biblical studies and ancient history is near the bottom of that pile. People try to draw conclusions about prehistoric monuments from some ochre, burial sites, and neolithic monuments, when a paper about modern-day Presbyterians or whatever drawn from the same amount and quality of evidence would get laughed out of the room. 

Again, that is not to bag on ancient historians. While I am sure they would love to unearth a large-N survey on clay tablets in a Babylonian library, they have to deal with the data they have, not the data they want, and they’re probably doing an excellent job with the data they have. 

However, every once in a while it’s nice to take a step back and realize how broad the confidence intervals are when you’re basing your judgments on a very small amount of evidence. And yes, the physicists would say the same thing about survey-based social science; there’s always a bigger bully in the room, and that’s not to say that every discipline that can’t possibly get to five-sigma confidence should just wrap up and go home, but just because they’re dealing with inherent limitations does not mean that those limitations should be ignored when talking about the bigger picture. 

Comments

6 responses to “Probabilities and Biblical Studies”

  1. Mark Ashurst-McGee

    This is why I majored in mathematics first. It was the only thing I could trust (then I took Set Theory and my world was blasted). Now o am somehow comfortable studying Joseph Smith in the 1820s (which can sometimes feel like Bible Studies).

  2. Jonathan Green

    That’s been more or less my experience with doing philological work in my own field. You come up with the best model you can based on the evidence you have, but there’s never as much evidence as you really need, and sometimes weirdly unlikely things actually happen. The proposed solutions can be fascinating and even compelling, but the uncertainty is real. Humility about one’s own work and charity towards others’ work are needed.

    It’s a problem more broadly throughout the humanities. When I’m reading secondary literature, I’ll come across what are in effect statistical claims for which no thought has been given to statistically sound evidence. One way to avoid a replication crisis in your discipline is to ignore the idea of replication altogether.

  3. Hoosier

    Was the eponymous lamb in the Mary’s Lamb tale originally described as “little”? What was the coloration of its fleece? Why did the author choose to omit these details?

    Recent work on the apocryphal Mary’s Lamb tale has convincingly demonstrated its dependence on a children’s jingle popular in the twentieth century. This would, of course, provide a terminus post quem for the earliest version of the Mary’s Lamb tale. Critics of the hypothesis note that the parallels between the children’s jingle and the Mary’s Lamb tale comprise solely (a) the presence of a principal character named Mary, and (b) her ownership of a lamb. Notably, the received version of the Mary’s Lamb tale makes no reference to the diminutive size of the lamb nor the coloration of its coat, both of which figure prominently in the children’s jingle. More importantly, the Mary’s Lamb tale directly contradicts the children’s jingle regarding the proximity of the lamb to Mary. Compare the children’s jingle (“everywhere that Mary went, the lamb was sure to go”) with the clear alienation of the lamb from Mary which forms the central narrative element of the Mary’s Lamb tale. Furthermore, the children’s jingle makes no reference to any second cousin.

    In this essay, we argue that the parallels between the Mary’s Lamb tale and the children’s jingle are strong enough to convincingly indicate a direction of influence. The divergences are best explained by positing a significant revision of the tale (or perhaps even its original authorship) during the twenty-first century. This accounts for the divergences from the children’s jingle while retaining and explaining the convergences between the two writings. The authors’ omission of the lamb’s size and coloration in the Mary’s Lamb tale was, we propose, prompted by changing attitudes towards physical stature and skin coloration in the early twenty-first century. The lamb being “white as snow” was likely viewed as overly specific and too exclusionary in the divided racial environment of the early twenty-first century United States, thus limiting the rhetorical reach and force of the pericope. The addition of the treacherous second cousin, meanwhile, allowed the author to critique kinism, which was a growing fringe ideology during that same period. As we will demonstrate, this theory parsimoniously harmonizes…

    Just kidding, this is good stuff.

  4. Aragorn

    From Mark Shea:

    “Experts in source-criticism now know that The Lord of the Rings is a redaction of sources ranging from the Red Book of Westmarch (W) to Elvish Chronicles (E) to Gondorian records (G) to orally transmitted tales of the Rohirrim (R). The conflicting ethnic, social and religious groups which preserved these stories all had their own agendas, as did the “Tolkien” (T) and “Peter Jackson” (PJ) redactors, who are often in conflict with each other as well but whose conflicting accounts of the same events reveals a great deal about the political and religious situations which helped to form our popular notions about Middle Earth and the so-called “War of the Ring.”. Into this mix are also thrown a great deal of folk materials about a supposed magic “ring” and some obscure figures named “Frodo” and “Sam”. In all likelihood, these latter figures are totems meant to personify the popularity of Aragorn with the rural classes.

    Because The Lord of the Rings is a composite of sources, we may be quite certain that “Tolkien” (if he ever existed) did not “write” this work in the conventional sense, but that it was assembled over a long period of time by someone else of the same name. We know this because a work of the range, depth, and detail of The Lord of the Rings is far beyond the capacity of any modern expert in source-criticism to ever imagine creating themselves.
    ….
    Of course, the “Ring” motif appears in countless folk tales and is to be discounted altogether. Equally dubious are the “Gandalf” narratives, which appear to be legends of a shamanistic figure, introduced to the narrative by W out of deference to local Shire cultic practice.

    Finally, we can only guess at what the Sauron sources might have revealed, since they must have been destroyed by victors who give a wholly negative view of this doubtlessly complex, warm, human, and many-sided figure. Scholars now know, of course, that the identification of Sauron with “pure evil” is simply absurd. Indeed, many scholars have undertaken a “Quest for the Historical Sauron” and are searching the records with growing passion and urgency for any lore connected with the making of the One Ring. “It’s all legendary, of course,” says Dr. S. Aruman, “Especially the absurd tale of Frodo the Nine-Fingered. After all, the idea of anyone deliberately giving up Power is simply impossible . . .”

  5. thor

    Aragorn,

    Slow clap for this comment and for Mark Shea! Made me chuckle for sure.

  6. Stephen C

    @Mark Ashurst-McGee: I wouldn’t be surprised if Set Theory gets us closer to the realm of the Gods than almost any academic endeavor, and if Georg Cantor wasn’t a prophet in some way–even if he did go crazy.

    @Jonathan:

    One item on my ever-expanding get-to-it-before-I-die list is to run a survey of ancient historians/biblical scholars and have them give some kind of expert probabilistic estimate for the various theories in their field, and then hopefully have a large enough sample size that I can run interrater reliability statistics, etc. Not to make some kind of point, it would just be fun.

    And yes, while I think anti-evolutionist types sometimes abuse the “and then we found this one bone and it overthrew everything!” Sometimes we really do find a bone and it overthrows (nearly) everything (within limits).

    Aragon and Hoosier: I second the lol; that was beautiful.

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.