The Interpreter; Bayes Theorem; Nephites and Mayans

[_Physics Guy]

I don't know how common it is to have multiple strong pieces of evidence pointing in opposite directions, blasting away at each other through clouds of gunsmoke like the Battle of Trafalgar. I do think it must be common in medicine to have no really strong evidence one way or another, because no set of numbers however decisive-looking can be stronger than the wobbly methods of measurement that produced them. In physics one can usually run experiments millions of times if one wants; the ultimate reason why CERN gave birth to the World Wide Web is that CERN was pushing a lot of computing envelopes generally just to handle all its vast amounts of data. The sad news is that Bayesian inference is seldom used in physics. With that much well-controlled data everything just looks Gaussian and you can use blue-collar statistics. Much as I admire the Bayesian approach, I suspect that the gap between being overpowered and being underpowered may be narrow for Bayesian inference. As soon as you have clear enough data for Bayes to be practically reliable, you no longer need Bayes.

The basic issue of whether you should multiply likelihood ratios is a tip of an iceberg, I think. If the ratios are really independent then multiplication is just logic, but how many issues are really independent? Things can be non-independent in surprising ways, and one quickly slips from the simple logical framework of conditional probabilities into the general problem of combining information, which crops up in a lot of fields. In political science and jurisprudence it's known as judgement aggregation, and the topic focuses on things like voting paradoxes. My favorite among these is one called the Discursive Dilemma.

The defining example of the Discursive Dilemma is a judicial panel of three judges who separately rule on three issues: 1) Did the accused technically commit the alleged act? 2) Was the alleged act illegal under the circumstances? 3) Is the accused guilty? Each judge is honest and rational, and therefore agrees that the accused is guilty if, and only if, the act was both committed and illegal. The three judges all answer the three questions differently, however. Judge A rules Yes, Yes, Yes; Judge B rules Yes, No, No; and Judge C rules No, Yes, No. The Dilemma is how to combine these three rulings into one final judgement.

If we just let the panel vote on the final issue of guilt, then by a 2:1 majority the defendant is innocent. But it would seem that it should also make sense to let the expert panel vote separately on the crucial legal questions 1) and 2), and then apply the logic about which everyone agrees in order to settle 3). In this case the panel votes by 2:1 majorities that the accused did commit the act and it was illegal, leading to the conclusion that the defendant is guilty. So what should we do with the defendant? Guilty or innocent? It's really not clear.

I formulated a somewhat similar epistemological problem in combining information that I call the Crow Paradox; it may well be better known under some other title. In a world where all crows are black birds and all black birds are crows, a nature photographer and an ornithologist both see an animal in a tree, and both agree that it is probably not a crow. Based on those two concurring expert opinions we should agree that this is probably not a crow, one might think. If we question the experts more closely, however, we learn that the photographer is absolutely sure that the creature is black, but not so sure it's a bird, while the ornithologist is completely sure it's a bird, but not convinced that it's black. Suddenly the chance that this is a crow seems much higher. And the general problem is that practically every piece of information we could ever obtain is itself some kind of aggregate judgement, like the two experts' conclusions about the crow. So it's hard to rule out that our aggregate judgement would change if we just dug into our information more deeply. Combination is tricky.

[_Res Ipsa]

I don't know how common it is to have multiple strong pieces of evidence pointing in opposite directions, blasting away at each other through clouds of gunsmoke like the Battle of Trafalgar.

I think it’s pretty rare. In the real world, the stronger the evidence for A, the weaker the evidence for ~A. The value I see in Bayes is that it can help one understand the relative strength of different pieces of evidence.

[_Physics Guy]

In the real world, the stronger the evidence for A, the weaker the evidence for ~A.

Yeah, I think that must normally be true. It's common to have no strong evidence one way or another but it must be pretty rare to have strong evidence on both sides of a question.

One exception that occurs to me, though, is deliberate fraud. Strong evidence that the fraud is a fraud may well be available, because even the best con artist can't usually cover up everything. But there may well also be strong evidence that the fraud is true, because good con artists are in the business of arranging such evidence.

[Guest]

It's been about a week since Bruce Dale fired off the volley of comments, including accusing Billy, a poster named Jared and myself of avoiding the devastating evidence in his latest correspondence on the descriptions of fortresses in the Book of Mormon compared to, well, let's say the Maya for now. All three of us responded with different versions of essentially the same point: The Dales only stay within the lines demarcated by the Book of Mormon and The Maya when it suited them and this correspondence is a very good example of bad form when a) the approach doesn't represent a mutually exclusive set of hypotheses, b) one makes a report from Cortez the centerpiece of the correspondence and then complaining when others point out the mound builder myth is a better fit for explaining the Book of Mormon than the Maya, and c) there are many, many other examples from history around the world that also fit that same description so what makes the correspondence actually a "million to one"* hit for the Book of Mormon and the Maya?

* Bruce noted that if he hadn't been constrained by the LRs, he would have given this one a million to one odds it could have been a guess on Joseph's part because of how exactly Cortez's description matched the book of Alma's description. Never mind that Billy pointed out The Maya limits it's descriptions to a period which would be a time of universal peace according to the Book of Mormon (200-400CE), or that I provided both a poem from 1832 describing the "redskins" overrunning the fortresses of a civilized mound builder race as well as illustrative plans and cross-sections from a British fort in North Carolina from before the revolution that is essentially what the Book of Mormon describes as well. I've been curious how he'll respond to that but so far, silence.

That all said, it seems the real breakdown for the Dales occurred due to the way they attempted to translate the accumulated evidences Bruce has built up over the years for claiming the Book of Mormon is describing the Maya into something that could be shoehorned into a probability calculation of some kind.

The issues with interdependency, the scaling of the LRs, the general lack of supporting documentation for how the details in the Maya were defined and then compared to the Book of Mormon really seem to be due to the Dales not actually having set out to follow a statistically defensible process they defined and then worked towards. Rather, it seems like they came up with the idea of trying to turn a bunch of "plausible" correspondences at least Bruce Dale believed showed the Book of Mormon was historical and was describing the Mayan people into something statistically defensible and then cobbled the approach together from there. Had they actually done what they claimed they did, I think the results would be far different, but they would also probably look more like an actual, defensible process, too.

I've thought more about how the Dales have been wishy washy regarding the intent of the paper. Is it intended to just show Dr. Coe was incorrect in stating the Book of Mormon has nothing whatsoever to do with the Maya? Or to prove the Book of Mormon is historical? Dr. Bruce Dale seems to think these are one and the same thing which is probably a large part of the issue. I mean, if hypotheses a is "The Book of Mormon has nothing to do with the Maya", how does one appropriately frame the opposite hypothesis to make them exclusive AND exhaustive in a way that can be tested? "The Book of Mormon has something to do with the Maya" just seems like a grade school comeback. "The Book of Mormon has plausible correspondences with the Maya" isn't the opposite of the original hypothesis because it may have plausible correspondences but still in reality have nothing to do with the Maya. But you know what? I think that's what we're dealing with. Dr. Bruce wrote a paper over 100 pages in length to show that the multiple Book of Mormon "bulls eyes" he's been accumulating over the years as evidenced by his blog are plausible correspondences with the Maya if one defines plausible very, very loosely and dresses it up with maths.

[_Gadianton]

The fraud example is really interesting, especially in this context. I'm not sure exactly what you mean by evidence on both sides, my thought though was it shows just how little superhuman examples of mimicry mean when weighted against provenance. Those UFO photos that stumped the best studios to explain suddenly mean nothing when the photographer drops his suitcase one day in public and a hubcap rolls out.

I mean, really, unfortunately for the apologists, the manner in which the Book of Mormon was produced outweighs pretty much any conceivable textual evidence for it.

[_honorentheos]

My personal favorite post in the entire original thread about the Late War, and most memorable to me, was made by EA regarding the fairy photo hoaxes from the early 1900s. I went back and tracked it down to be quoted below. Of course it was towards the end of a 76 page thread:

Is everyone here familiar with the Cottingley Fairies photos? It was a series of 5 photos taken in 1917 in England.

This is the most famous one:



It has influenced depictions of fairies even to this day.

Quaint as it might seem now, there was a great deal of controversy over them with many people, including Sir Arthur Conan Doyle, taking them as evidence of spiritual beings. There were experts in photography who declared them as legitimate.

Interestingly, I once saw a show on the Cottingley Fairies filmed in the 1970's that covered this as a controversy over the existence of spirit beings. Skeptics were brought on to offer a variety of theories for how the photographs were produced. All of them involved some relatively sophisticated photographic techniques for girls in 1917 to be using or remarkable coincidences. The show, being fundamentally interested in portraying this as a supernatural controversy, rightly cast doubt on accepting any of those theories as correct. No one explanation seemed in particular likely.

Then something marvelous happened. In the 1980's, the girls who produced the photos admitted it was a hoax. They also described how they did it. It turns out they cut out pictures of fairies from a book, stuck them to hatpins, and took pictures of them. That's it. That's what they did. So much for acid etched engravings and complicated exposures.

This story has long stuck with me for two reasons. First, whenever I see complicated and remote explanations for unusual phenomena and potential hoaxes, I'm always reminded that the reality can be devastatingly more simple. Second, while everyone was right to reject those complicated theories for how the photographs were produced, it's always fascinated me that people lost sight of the fact that even though those theories were unlikely, the explanation that entailed the photos were of actual fairies was vastly, vastly more unlikely than that. You can't prove extraordinary supernatural claims simply by attacking somewhat unlikely natural explanations.

This story does inform what I see in Book of Mormon debates. I personally am skeptical of theories of authorship that do not involve Smith. Elaborate plagiarism hypotheses have always struck me as strained. And while I find myself on the same side as believers when seeing this, I also see them as having a huge blind-spot for not appreciating just how much more implausible the supernatural tall-tale version of events is than the authorship theories they are finding without sufficient basis.

What I've highlighted in blue is one of those fundamental points that transcends the topic of any thread.

[_honorentheos]

In the real world, the stronger the evidence for A, the weaker the evidence for ~A.

Yeah, I think that must normally be true. It's common to have no strong evidence one way or another but it must be pretty rare to have strong evidence on both sides of a question.

One exception that occurs to me, though, is deliberate fraud. Strong evidence that the fraud is a fraud may well be available, because even the best con artist can't usually cover up everything. But there may well also be strong evidence that the fraud is true, because good con artists are in the business of arranging such evidence.

This got me thinking about if there is more to the issue in most instances than just weighing evidence that can be considered strong or weak equally? I can think of many examples of positions people hold to quite adamantly that are opposed where each side considers the evidence for their position to be quite strong. It seems to me that framing of issues is both incredibly important as well as more subjective in many cases than our own security in our position being right allows. Right now the abortion debate is front page, polemic, and certainly consequential. The question of how to frame the issue is fundamental, controversial, and defines the evidence. Yet when one looks at it from one's own position the so-called controversy seems to be due to the disingenuous approach of those who disagree. Ones own position seems practically self evident and irrefutable. So. Is it murdering babies or not? Or at what point does it become murdering babies? It comes down to a lot of definitions which are reflective of a position in many ways themselves.

[_aussieguy55]

This issue will be a major report of Scratch when he does a summary of events in Mopologetics.

[_Philo Sofee]

This is most definitely one of the singular MOST significant events in Mopologetics this year, without question!

[_Physics Guy]

I remember the Cottingley fairies revelations, after the story had already been a famous episode for decades largely because of Conan Doyle. It seems to me that the only real reason the fairy photos ever seemed impressive is that the fairy pictures in that book had been painted so well that the cut-outs looked surprisingly realistic. They looked too good for children to fake—and somehow no-one considered that children could cut pictures out of a book.

EAllusion's point bolded in blue above is a really good one. Shooting down the details of any particular skeptical theory does not establish that a paranormal phenomenon is genuine. Neither is it a solid objection to accuse skeptics of not being able to provide a convincing naturalistic explanation for weird events. On the contrary, history seems to suggest that "It was faked somehow" is a perfectly reasonable position.

The fakers always have the initiative. They were not set the task of figuring out how to achieve a particular effect. Instead they found a clever trick and once they got it working well, they performed it. The real reason why they had this particular effect to show is just that it was the thing they happened to have learned how to do, but after doing it, the fakers successfully framed it as being precisely the miracle that everyone should have been expecting. It's a form of Texas Sharpshooting.

Asking a skeptic to discover the specific trick that was actually used for a specific fraud is like the Sharpshooter asking a visitor to hit his barn-side bullseye. In principle it can be done, but it's hard. It wasn't nearly as hard for the Sharpshooter because they didn't do it that way. It wasn't as hard for the faker, either. They had the initiative. They didn't have to figure out a particular trick.