An active LDS reader sent me this, as he was frustrated in not being allowed to respond over on Millennial Star. As I’ve mentioned, I have a very open comments policy: I don’t block anything that isn’t spam, obscene, or grossly insulting to other commenters (obviously, people are quite free to insult me at any time, and they do.)

I’m continually impressed with the education, wisdom, and intellect of people who read this blog. I think Millennial Star missed out in not posting this. But, I need to make clear that I did not write this post, I don’t take any credit for it, and the opinions expressed are its author’s.

## An Invitation to Meg Stout

On her blog, Meg recently posted an essay, “Joseph’s Wives – an Algorithm,” which was in response to something I said to her first in a private email discussion, and then again publicly in the comments on John’s blog.

*TDLR:* Sexless marriage arguments based on lack of DNA-proven children are weak and need a probabilistic model to become persuasive. Meg’s algorithm/model isn’t; it’s junk science, a table of made-up numbers that mean nothing. If she would like assistance with the math, formulating a real model, happy to help.

### Context

First I should set the context for all this. By email Meg said to me:

Yeah, Hales and the Prices aren’t known as the most objective historians. As for me, I went into my journey presuming that Joseph had been a full-blooded sexual partner to many of his wives. But it was the scientific data that persuaded me that he likely wasn’t.

Quick aside: For those unfamiliar, she is referring to Ugo Perego, an LDS biologist, who has tried to find children fathered by Joseph Smith through DNA analysis. So far, no conclusive DNA proof has been found which links Joseph to any of the children born to his polygamous wives.

My response to this was:

As I understand it the DNA evidence hasn’t ruled out Joseph having fathered any children, it simply hasn’t been able to prove that he conclusively did. A notable data point but I don’t really find this very persuasive. It’s not evidence of absence. We could speculate quite a large number of good reasons why there aren’t any children. Actually, I think in terms of probability it’s unlikely Joseph would have gotten many, if any, of his plural wives pregnant.

Meg then said to me:

The instances that can be tested have all yielded proof that Joseph could not have been the father except for the case of Josephine Lyons, where the data makes Joseph’s paternity unlikely but not conclusively disproved (Josephine’s descendants have common ancestry with Lucy Mack and Joseph Smith Sr.). There is a reason Sylvia Lyons would have told Josephine Joseph was her father, which I have laid out. Ugo Perego is attempting to definitize that answer one way or the other.

It isn’t just Joseph. None of the polygamists in Nauvoo produced children with plural wives prior to Joseph’s death except:

Joseph Bates Noble (child born in Feb 1844)

William Clayton (child born in Feb 1844)

Things are starting to get interesting at this point. She’s arguing that not only did Joseph not father any children, but neither did any of the other polygamists. This is something I had never heard before. What’s interesting about this to me is that, if true, I think this would undermine her scientific evidence and underlying argument that the relationships didn’t involve sexual relations based on the lack of children.

I responded to this argument by saying:

I’m not sure some of your claims can be made. You say, “It isn’t just Joseph. None of the polygamists in Nauvoo produced children with plural wives prior to Joseph’s death except:” What you really mean is, “Other than this guy and that guy, we don’t have hard evidence to conclusively prove that any of the other polygamist unions produced children.” These are two very different statements.

For the lack of children, or more correctly the lack of proof of children, to be a persuasive argument, one would have to prove that children should be expected in the first place. Which hasn’t been done.

For instance, women have a relatively narrow window during which they can conceive. And even with consistent and regular tries, most women take months to get pregnant, and that’s by modern health standards. The environment during early polygamy was such that Joseph didn’t likely have many opportunities to engage in intercourse with his wives. With all the secrecy and such, keeping things hidden from Emma, liaisons would have been very infrequent.

Moreover, in general, polygamous wives were not in the best of spirits, sacred loneliness and all that. It’s a well established fact for instance that polygamous unions resulted in fewer children per woman than monogamous unions. That being the case, even when opportunities existed, it’s a fair bet the women might not have been “in the mood.”

All this makes for a situation where frankly I wouldn’t expect many children to be conceived, if any at all. And then of course we can also toss in miscarriages and infant mortality which would eliminate testable evidence of a child. A fun exercise might be to try and develop a probabilistic model to predict how many children we would expect Joseph to produce if unions had been sexual. Something like this would be necessary to persuasively argue that children should be expected in the first place.

Meg didn’t have a response to this. Until now.

### Meg’s Algorithm

Taking me up on my suggestion to “develop a probabilistic model,” Meg created what she calls “an algorithm” to assess the importance of Joseph’s wives. She says:

I think we should establish guidelines for the importance we attribute to different women as wives…I’d like to start, then, with each such woman having a score of 100% (or 1.0). Then as we consider various factors, that score may be decreased. If there are mitigating factors, a “penalty” may be reduced. Thus, as I go forward to talk about the various women, we can focus on those individuals whose “score” gives us greatest confidence that she is of import. This scoring matter can also give structure to the discussion of each woman.

Here’s a proposed structure:…By this scoring system, Emma would score 100%.

Meg then treats us to a table of values that weight different things with a score, for instance “DNA negative” is given a score of -0.25, “Motive to lie” is given a score -0.06, and so on.

It’s important to note here that her “algorithm” is not meant to directly answer my question, “How many children should we reasonably expect if the unions were sexual?” Instead this “algorithm” is meant to give Joseph’s wives a kind of relevance score, from which I assume the history related to these women is then going to be ranked and weighted.

In other words, this is meant to be a mathematical justification for ignoring historical evidence, or something. This is how I’m interpreting what she’s doing here. *Yikes*.

### My Motivation

Let me start by saying my motivation here is not to belittle Meg. I want that to be clear. I fear this may come across that way, though, because I am pointing out what should be obvious. Perhaps let the ramifications of that speak for itself. I am taking Meg at her word that she is, per her claim, a scientist and engineer. And maybe I misread her; perhaps she only meant that she has worked in the “science/engineering” industry, in which case I wouldn’t expect her to understand any of this. Either way, I do not presume to give her remedial math lessons. I don’t believe she needs such instruction.

I have two objectives.

One, I fear that lay readers (who don’t understand math) won’t understand what’s bad about her arguments. I assume that Meg knows her arguments are bad, but all this is fun for her. That’s my impression. In general I find Meg’s arguments (double-standard, logical fallacies) and behavior (censorship) to be dishonest.

Giving her the benefit of the doubt (no pun intended) I don’t think she’s being intentionally deceptive. I think she’s mostly just having fun, like a nerdy fan at a science fiction conference (see *Galaxy Quest*) engaging in wild speculation that isn’t meant to be taken too seriously. The debate is fun, and I sincerely appreciate that mindset.

At the same time, I think she’s a hypocrite. And I don’t mean that in a mean-spirited, name-calling kind of way, but a very calm observation that in my opinion she is not thinking critically or being introspective. However noble her intentions, she’s leading people astray, in my opinion. People are reading her material and taking her seriously. In its current form, her “algorithm” is pretty silly, and I have to believe Meg knows this, but I see this going in a bad direction.

Two, I’m genuinely interested in an answer to my question, a real and unbiased answer. A serious and credible answer. I’d like to see a legitimate model developed that can reasonably answer the question, “How many children should we expect Joseph to produce if the unions had been sexual?” Such a model might be completely inconclusive and results entirely flip based on assumptions that nobody can agree on. It could be, though, that even if we’re using the most faith-promoting of assumptions, children either weren’t likely to begin with, or they are unlikely enough that it amounts to the same, and the “no children = no sex” arguments immediately become irrelevant. My hunch is those arguments are (unfortunately) irrelevant.

If the opposite is true though and there’s a truly high probability of children, then that’s worth noting, and I would find it personally persuasive that Joseph didn’t have sex with these women. I am not biased towards a particular answer. I want the actual truth, whatever that may be. But, as a member of the LDS church who’s trying to be faithful, I would be very happy to learn that Joseph wasn’t as bad a guy with respect to polygamy as it’s currently reasonable to conclude. At a superficial level, I truly love Meg’s argument that the sexual dynamic of polygamy was a perversion mistakenly created by the ignorance of Brigham Young. If such a conclusion could be reasonably arrived at, I’d love it. Think of all the problems that could be solved by plucking section 132 out of the D&C and setting it on fire.

All that said, Meg’s “algorithm” is horrible.

### Math Lesson

First, I would like to point out that Meg’s “algorithm” isn’t an algorithm at all. What Meg gives us is a table full of probabilities literally pulled out of thin air. That’s not an algorithm. I’m not sure what it is, nonsense mostly. An algorithm would be a step-by-step process for deriving the probabilities listed in her table. I would in fact love to see the algorithm she used to come up with those numbers. It could come in the form of a math equation, a description in English, or a programming language.

Wikipedia defines an algorithm as “a self-contained step-by-step set of operations to be performed. Algorithms exist that perform calculation, data processing, and automated reasoning.” Pulling one of my engineering textbooks off the shelf, it describes the word “algorithm” as a “term used to in computer science to describe a finite, deterministic, and effective problem-solving method suitable for implementation as a computer program.” and then goes on to use Euclid’s algorithm, which computes the greatest common divisor or two numbers, as an example.

For example, an English-language description of Euclid’s algorithm is:

Compute the greatest common divisor of two non-negative integers *p* and *q* as follows: If *q* is 0, the answer is *p*. If not, divide *p* by *q* and take the remainder *r*. The answer is the greatest common divisor of *q* and *r*.

A Java-language description is then:

public static int gcd(int p, int q)

{

if(q == 0) return p;

int r == p % q;

return gcd(q, r);

}

That’s an algorithm. What Meg created is not an algorithm by any reasonable definition of the word. She has given us the output of some unknown algorithm that I assume exists only in her mind. It probably goes something like this: *Make Joseph Look Good ==> Make Up Numbers*.

Next I’d like to give a very simple example of what an actual probability problem looks like. This seems appropriate, as her table is listing probability values, and my original suggestion was that a probabilistic model should be developed in order to answer the question. This may seem off-topic, but just bear with me for this simple problem.

OK, so here’s my simple example:

Suppose 1% of a population has cancer. A new test for cancer shows positive 90% of the time when a person actually has cancer, and correctly indicates “negative” 95% of the time when run on someone who do not have cancer. This test is conducted on a person at a doctor’s office and the results come out positive. What is the probability that this person actually has cancer?

Baye’s rule is:

The theorem is also sometimes referred to as the theorem on the probability of causes because it allows us to find the probabilities of various events A1, A2, …., A*n* that cause event A to occur.

From the problem we are given the following:

*P(cancer|population) = 0.01*

*P(positive|cancer) = 0.9*

*P(negative|notcanter) = 0.95*

From which we can then derive:

*P(notcancer|population) = 1- P(cancer|population) = 0.99*

*P(positive|notcancer) = 1- P(positive|cancer) = 0.1*

*P(negative|cancer) = 1- P(negative|notcancer) = 0.05*

So, if you go to the doctor and test positive for cancer, what is the probability that you actually have cancer? The answer might surprise you.

[+] = positive test result

8.33%!! No, that’s not a typo. So, for this particular population, if you get tested positive, your chances of actually having cancer are 8.33%. In other words, don’t freak out just yet. This may seem strange, but it’s not, if you think about it. In the case of this cancer test, even though our test is highly accurate (90%), there will still be a lot of false positives. So the probability of a false positive also has to be weighted, which makes the likelihood of a true positive quite low.

My point with this exercise is to demonstrate what an actual probability problem looks like and also to show how probabilities can be counterintuitive, especially for those who don’t understand mathematics and probability theory. Most people who get a positive cancer test are likely to freak out. Even understanding probability theory, I’d probably feel my stomach hit the floor upon hearing such a result. Calming down, however, and taking a moment to think about things critically, we shouldn’t be freaking out just yet. The result tells us we should do more testing, that is all.

For anybody interested in a deeper treatment of probability theory, here’s a link to one of my undergraduate textbooks which is available for free in PDF format.

http://www.faculty.jacobs-university.de/poswald/teaching/ESM2B/handouts/ProbabilityRandomProcessesBook.pdf

Here’s a chapter from the textbook *Computer Analysis of Human Behavior*, which will give you an idea of what probability theory looks like when applied to human behavior. This is more about gesture interpretation, but similar principles would apply to historical observations.

http://www.springer.com/cda/content/document/cda_downloaddocument/9780857299932-c2.pdf?SGWID=0-0-45-1214740-p174133703

Now, back to the original problem and question. Meg has not given us an algorithm or anything that even remotely resembles a probabilistic model. She has a table of made-up numbers. Behind each of those numbers should be a mathematical proof justifying how the number was arrived at. Why is motive to lie -0.06 for Emma Smith? But, what she has might be a useful starting point to come up with a list of features that should be included in a proper model. I’m sure if we ask a psychologist, the observation of lies is indicative of something and we could factor that into our model. Counting lies within a period of time could be a method of determining a trustworthiness feature, maybe. Then, based on that, we could reasonably add less credibility to the testimony of untrustworthy individuals we’re relying on. Meg might not like how these results turn out, though.

### Invitation to Meg

If Meg is interested, I’d be happy to work with her (and/or any others) on developing a credible model that attempts to answer my question. I’m not used to applying probability theory to social science or history, but it should be an easy shift compared to what I’m used to, and I would find the prospect quite interesting. Frankly, I’m a bit surprised a model like this doesn’t already exist. I would have expected someone like Ugo Perego to have already created one, and maybe he has, if we ask him.

My starting approach would be to do some journal searches and see what kinds of models already exist with respect to fertility and what-not, and also seek out any relevant data I can use in my model. I think what I’d do is start out by just developing a model that determines the probability of a random male getting a random woman pregnant today from having intercourse once. P(child|sex) = ?

And then from there add relevant features which would alter the probability given the environment of polygamy, frequency, potential mindset of Joseph, etc. (such as, how well did people understand the calendar method back then?). What would result is a model that could be run based on varying assumptions. So the assumptions being fed into the model by someone like Meg or Brian Hales would likely be different than the assumptions of Richard Bushman or Dan Vogel or Grant Palmer.

One assumption might be that Joseph didn’t want the women to get pregnant and acted accordingly. Perhaps he was concerned about pregnancy for the single sisters, but not the already-married polyandrous ones. What is the probability that an average male in the 19th century could successfully employ the calendar method if he wanted it? What is the probability that Joseph would be the father of a child if a woman is having sex with two men at the same time? Even if Joseph didn’t care about getting anybody pregnant, what are chances he’d get them pregnant based on frequency of sex?

We could run the model based on different assumptions and see how the probability distribution changes. In the course of this, though, I’d want to consult with some bona fide experts on the history of polygamy so they can guide feature selection as well as tuning constants that we arrive at. For instance, how many opportunities for intercourse would Joseph have had per woman? I’m hoping the history buffs could come up with a calendar, and block out times when we know he’s not even in town, etc. I think we could come up with a model that could be applied individually to each plural wife and come up with a probability of children per wife, then sum those together to arrive at an overall likelihood of no children at all assuming that sex took place. How “impossible” is it that he fathered no children despite sex?

As I said earlier, it might be completely inconclusive, but it could tell us something. The results might be surprising, just as with the cancer test. Meg seems to think it’s intuitively obvious that if Joseph were having sex there should be children, but that has not been demonstrated to be true. It might also just be a useful exercise to see how reasonably we can employ mathematics as a tool for historical analysis. Putting together a proper model is something that will take time and a lot of consideration. I think starting out by developing a list of features is a good idea though.