$30k challenge to Interpreter’s “Team Bayes”

[Gadianton]

"why would a sharpshooter pick those spots to aim, in particular"

Lem mentioned counting misses. I think KR gave us a great demonstration of that. He's shopping for a final term for his disjunction that goes like this so far: "either the Book of Mormon is ancient given x , or written by Smith, given x".

KR mulls over three possibilities for x. Age isn't unusual, so he drops that. education isn't unusual, he drops that. ahah, length is unusual. (draws target around length). But his sharpshooting didn't stop there. His original criteria was document length, and he found that the Book of Mormon was 2-3 times longer than average. But now he needs the length of ancient books. He assumes the Bible is a good proxy. Problem. the KJV has 750k words, the Book of Mormon has 250k words. It's 3x longer. hmmmm....we can't count our misses...Aha! what about chapter length? he runs the numbers and it's tolerable; calculates what the final result will be if he takes it, looks good, and so the crayon creates the next target.

(I'm working on a more detailed understanding of PG's sharpshooter examples I just had to comment on that one thing)

[Dr Moore]

Isn’t it strange to see senior Dale and KR dance around and even joke about the idea of statistical independence, but won’t go the essential distance to make a cool $30k for Interpreter? (or KR for 10k himself???!!!)

[Philo Sofee]

No, it's not strange because they cannot be seen to be associating with people who do not think and believe like them. And if they lose, then they eat crow forever. Now Granted, the Dale's are eating crow forever, but not because of some lost bet with an "anti." The good news for them is they are gonna be doin some fine testimony buildin! THAT is what it's all about, not validly using science and math. Do the work of the spirit, not the philosophies of men mingled with scripture...

[Dr Exiled]

I think they are using at least a subset of math and science called "religious math and science." It's just like regular math and science except shrouded in an overpowering desire to believe a certain conclusion. So, mathematical formulas and the scientific method are eternally skewed in favor of the religious claim. Then gaslighting, derision, and demands to read eternally long treatises about how the religious conclusion must be the ultimate conclusion are used to bolster the religious math and science. Also, make sure to demand lots of money for the enterprise without disclosure and take victimhood to its zenith, using it as a weapon.

[Dr Moore]

Junk science finds a way to reveal itself eventually.

[Philo Sofee]

Junk science finds a way to reveal itself eventually.

Yes, indeed, it does! Junk science has never been able to compete with the real thing. The problem with the real thing is it many times does not show us what we want to be real, but just what is real, at least on this size we find ourselves as humans. Were we the size of mosquitos, reality would be vastly different to us.
Somewhere I read or heard that humans are actually right in the middle of the size for living beings here on earth, not the smallest, not the largest, just right here in the middle...

[Gadianton]

Thinking about PG's sharpshooter, I'd first frame it with the simple Bayes expression without the alt hypothesis.

The apologist walks up with 6's on either hip and two friends in tow. It's 50-50 he could be a sharpshooter, as I have no other information. I make the mistake of saying, "oh yeah, show me what you got." The guns twirl from the holsters and 12 shots register. The barn door is left riddled with 11 spread-out bullet holes and the shooter collapsed in pain. One of those shots got his foot. The cheering of the apologists is as deafening as the gunfire had been, until the voices are washed out by the sirens of an approaching ambulance.

Later, the apologists maintain their guy hit everything he aimed at, including the deadly insect that was nearly to his bare leg, prompting a tough call for shot 4. Bonus points because he made shots 5-12 in pain.

I'm going to prove they are wrong with Bayes. I reckon it's .5 * .99 / .99. I give them the benefit of the doubt on .99 in the numerator, the probability a sharpshooter could have made those shot if he were really trying, if he really wanted to hit those spots. But it's a wash with the .99 I put in the denominator, which is the probability of the holes, not bounded by a specific condition. Basically, holes like that could be made by anybody.

The apologists say I've misunderstood. I've got to consider those particular holes could be hit, not just an arrangement similar to the untrained eye. They want a low number. But they can't go lower than a 50% probability p (holes), otherwise they'll go over 100%. Well, they'll take a .50 since it gives them a 99%. But, they aren't really happy admitting a 50% chance of just anyone making those shots. How can we say anybody would have vaporized that deadly bug alone with 50-50 odds? So they say, you're a critic, and there is no way you gave our guy a 50-50 chance from the outset. Can they interest me in telling the truth, that my prior was actually, say .001 instead? because if the prior is lowered, then they can substantially lower the probability that anybody could have made those shots, on a misunderstanding of what that variable means. That's my best guess as to what PG was talking about - in general.

Bonus:

One argument is that any sequence of coin flip 120 times in a row is just as unlikely as heads. All heads is just easier to remember. We can put a grid on the side of the barn, and the probability of any sequence of grid squares is just as unlikely as any other. So it's only our preconceived notions of simplicity that we prefer certain squares. Only an expert could hit any sequence of squares at their bidding. It's just as hard or harder to hit 12 different squares in random places than the same square 12 times in a row.

That's true.

But it's all about counting the misses, as Lem put it. Even if you're making your target up ad hoc, the whole power of Bayes is to keep you in check by the probability of chance accounting for your pattern.

the analogy between grid squares and the coin flips is false. Flipping a coin is a stochastic process that produces either heads or tails. A human shooting a pistol at a barn door is a stochastic process that produces patterns with holes that are spread apart from each other by relatively large amounts. So our real question is, how does your pattern account for the inability of amateurs to put holes close together from a distance?

[drumdude]

I have constructed a mirror argument to show that Kyler's logic cuts both ways. He starts with an extreme skeptic and multiplies probabilities to move the skeptic's belief towards the authenticity of the Book of Mormon. One can just as easily start with an extreme believer and multiply probabilities to move the believer's belief towards that Book of Mormon being a fraud.

For every single arbitrary possibility that Kyler comes up with as a "hit" for the Book of Mormon, it is just as easy to come up with a "miss" for the Book of Mormon. The needle can be arbitrarily moved in any direction you want to make the claims for and against the Book of Mormon.

I've easily re-written his introduction to his project from this mirror viewpoint. If Kyler thinks his argument stands for the truth of Mormonism, then it simultaneously stands as a tool for proving the Book of Mormon false.

The TLDR
Belief can’t be equated with knowledge or understanding. True belief is the need to thoroughly assume all claims, regardless of their unlikeliness. Our belief of the Book of Mormon embraces this type of belief, allowing us to evaluate the strength of the evidence both for and against.

The Narrative

Imagine the typical Mormon, born into the covenant somewhere in the middle of Utah. This Mormon has been raised LDS, and never been exposed to any of the issues of Mormonism. This Mormon has a firm testimony, and an incredibly strong belief in the truth of Mormonism. Like many Mormons, they have experienced undeniable events in their life that could not possibly have been explained by anything else except that Joseph Smith was a prophet and the Book of Mormon is true. He spent 2 years of his life on a mission for the church and he is the stereotypical “true believing Mormon.”

The Commentary
An Experience of Belief

You’ve now been introduced to our believer, the person whose testimony should theoretically NOT be changed by anti-Mormon literature regarding the Book of Mormon. He has a strong testimony which should remain strong in the face of critics. His belief should be familiar to any Mormon who has been raised in Mormonism. The supernatural experiences we’ve experienced may not be as deep as his, and the specific testimonies we’ve gained are obviously different, but I don’t think anyone has gotten into Mormonism without feeling at least a sliver of the testimony expressed by our believer.

For me, it was seeing the happiness of the Mormons in my life and feeling the spirit every Sunday with them. The feelings of belief were strongest when singing along with them and having them bear their testimony to me of all that they have experienced. That they *know* the Book of Mormon is true, and they see all the blessings in their life that being a member has brought them.

That’s not what this episode is about, though. I’ve experienced belief, and I’ve had my share of faith, but my question here is, when our believer says that he “knows the church is true”, is he actually expressing belief?

Faith as belief

Judging by the behavior of some of the church’s leaders and apologists, you might think so. I often hear them offer evidence of the church’s truth claims, but I also hear almost all of them say, in no uncertain terms, that they know the church is true. They leave little to any room in their own minds for skepticism or doubt. “Doubt your doubts” comes directly from general conference.
Now, this does seem to align with how the word belief is commonly used. It’s usually defined as embracing the truth of something, and is treated as synonymous with knowledge and understanding. However, that kind of perspective doesn’t jive with how philosophers and academics treat belief. According to those philosophers, belief is the theory that knowledge is possible—that some amount of apparent evidence is necessary to make a truth claim; there is always room more evidence to make the believer more certain in the truth. We may use the term colloquially to “know” something is true, and our believer is certainly expressing knowledge, but true knowledge is an affirmation that all beliefs require evidence, no matter how likely they may seem.

The apologists I’ve encountered spend quite a bit of time worrying about Latter-day-Saint use of the term “know,” and for good reason. We hear the phrase “I know the church is true” a dozen times every first Sunday, because this is the level of belief and faith in their testimonies that Mormons are expected to obtain. Now, there are definitely some doubters who have studied the history of Mormonism and had their faith shaken. But every believer I know would shut down immediately when confronted with anything that make them question their testimony. They have been conditioned over decades of general conference talks not to let doubt creep into their minds.

Could you imagine a general conference talk given where the Prophet asks: “How many of you have ever doubted whether you’re right about there being or not being a God?” Among the crowd of Mormons, there wouldn’t possibly be a hand to be seen. Skepticism is not allowed in the religion and is actively preached against.

Testimony meetings are meant to be a place to express to others that your faith is so strong it has become synonymous with knowledge. Many testify to the supernatural personal witnesses they have been given which have elevated mere faith to the position of absolute knowledge. When someone says, “I know the church is true”, they are signaling to others that they have special access to the metaphysical veracity of the truth claims of the church. They have had dreams, visions, events in their lives that couldn’t possibly have happened if Mormonism wasn’t true. They spent hours praying to God and the spirit returned the answer “true.”

Even if they didn’t express this testimony, they would be quickly asked to sit down. If they began to express doubts from the pulpit, they would never be asked to talk again. When that phrase gets said in testimony, what I hear is something like, “I have eliminated every doubt in my mind to the point that I no longer merely believe, I know without any doubts that the church is true.” Given that I generally know these people and their experiences (or they’ve just finished relating a bunch of them), that statement gives me a pretty good sense of how the church, or church leaders, or God, have not proven reliable. In that context, they’re lying. They’re pretending. They are expressing false confidence. They’re testifying of the knowledge they have available to them, which is mere belief. It means I must buy into what they’re saying, and unless they’re specifically spouting known falsehoods, I’m in no real position to question their experience or their interpretation of it. My testimony needs to line up with their level of belief or I am not a true Mormon.

Belief as Knowledge

So, back to belief. Say that our believer was expressing supreme confidence that God did exist; say he was expressing knowledge. Is that more than what is required to be a faithful Mormon? Based on the gospel topics teachings, you would certainly think not:
“A testimony is a spiritual witness given by the Holy Ghost. The foundation of a testimony is the knowledge that Heavenly Father lives and loves His children; that Jesus Christ lives, that He is the Son of God, and that He carried out the infinite Atonement; that Joseph Smith is the prophet of God who was called to restore the gospel; that The Church of Jesus Christ of Latter-day Saints is the Savior’s true Church on the earth; and that the Church is led by a living prophet today. With this foundation, a testimony grows to include all principles of the gospel.”— Gospel Topics, “Testimony”
Given how it’s used there you would think that knowledge was required to be a true believing Mormon. But that sort of approach doesn’t automatically apply to how Mormon belief exists in the wild. Belief hardly ever exists in a vacuum; it always exists in relation to some proposed truth. Yes, it’s a move towards certainty in that proposition. And, most of the time, it’s also a move to exclude some other, competing proposition. As my belief in Mormonism increases, so too does my disbelief that there can exist any credible evidence against Mormonism. Belief can imply disbelief as much as it implies belief.

This is particularly the case when it comes to belief in the teachings of the church. The way I usually see it employed; belief does just mean that a person is certain about particular truth claims. For whatever reason, they’ve become persuaded that the church is capital T “True”, along with a number of related propositions—such as that “there are no homosexual members of the church”, that women shouldn’t hold the priesthood, or that the Book of Mormon is historically accurate. And here’s the kicker—that kind of belief does a pretty good job of discouraging sincere investigation. Given its unknown origin, the warm fuzzy feeling of the spirit doesn’t need a fair hearing—it needs to be embraced without question. So, too, given belief in the truth claims of the church, church leaders would generally be happy to see those disbeliefs go away. As is true of everybody, if they do pray, they do so in service of supporting their currently held beliefs.

When we use the term belief, it usually only points one way—belief is something that true Mormons have, and doubt is something that anti-Mormons have. But belief is only truth when it serves as a double-edged sword—when individuals are believing of any and all truth claims including ones that conflict with their religious faith like evolution and the lack of archeological evidence for the Book of Mormon.

Pure Belief, Undefiled

So, what is belief? By what characteristics can we recognize it and distinguish it from knowledge? The way I see it, belief is itself the tendency to NOT investigate— to be satisfied with how things appear at first glance. Pure believers of this variety likely don’t exist. Everyone has limitations on their piety and willingness to believe without evidence or in the face of contrary evidence. All of us have a threshold of “that is too unlikely.” Some part of church history, or theology, that leads down a road towards “if this isn’t true, what else that I believe isn’t true?” These limitations mean that our belief is necessarily lopsided. We tend to believe the claims we agree with and to deny uncritically the ones that undermine our own beliefs. We criticize evidence against Mormonism and let the old and familiar belief pass unscathed. And the fact that some people have less time and less patience for investigation means that some of us are more faithful than others.

And this is where our “extreme believer” can actually deserve the term. It’s unrealistic to make our believer completely unbiased, but he can have an insatiable appetite for a testimony. We can show them as much evidence as we have available and his testimony will never crack. Our believer will just consider the evidence against Mormonism as some degree of probable. And since we’re only considering one claim (the authenticity of the Book of Mormon), it doesn’t really matter that this belief is one-sided. It can approximate the faith and belief of the Mormons without borrowing their implied (but certain) doubt of alternative claims, or their tendency to dismiss evidence against Mormonism.

Can we quantify this sort of extreme belief? How high of a wall does evidence against the Book of Mormon authenticity have to climb? Does it have a 1 in 100 chance of being true? 1 in 1000? I don’t think we need to be nearly as accommodating as that. We could take the advice of Dr. Richard Carrier (as discussed in the FAQ at the end of this episode) and give it a 1 in 1,000,000 chance of being false, but, as we’ll see, even that won’t be a particularly difficult bar to clear.

We could always go by the standard set by Wagenmakers, who conducted a Bayesian analysis of one particularly controversial claim that reared its head within psychology more than a decade ago. Dr. Daryl Bem, an experimental social psychologist with an otherwise sterling CV, put his lot in with parapsychology in his old age, claiming to have found evidence of extrasensory perception—of some people being able to detect the future. You may have caught his segment on Colbert called “Time-Travelling Porn” back in 2011. It may seem ridiculous on its face, but his methods were sound enough to merit publication in the field’s flagship journal, and his findings have since been replicated by researchers around the world. The probability that we’d observe those findings by chance currently stands at 1 in 1010—impressive enough that if it was any other topic we’d already be teaching it in textbooks.

But as we’ve heard many times before, extraordinary claims require extraordinary evidence, a statement with which I happen to agree. In their analysis of Bem’s study, Wagenmakers set the prior probability of paranormal events at 1 in 1020. (Wagenmakers apparently believes there’s a better chance of him being personally crushed by a meteor than of ESP being real.)
Which is fine; that kind of skepticism and doubt is his right. And whether it’s reasonable or not, we’ll do Wagenmakers one better and use an even higher ultra-skeptical bar—1 in 1040. In Bayesian terms, we’ll be using that as our starting prior probability—our initial guess at the likelihood of the Book of Mormon being a fraud.

Conclusion

In the episodes that follow, we’ll examine the most compelling evidence for and against the authenticity of the Book of Mormon. We’ll place it in front of our hypothetical believer, analyzing how likely we should be to observe that kind of evidence, and use Bayesian analysis to track how his beliefs change over time. What we’re looking for, ultimately, is whether the evidence we bring to bear can show that the Book of Mormon does not beat the odds—that the odds of it being produced by supernatural means (i.e., with angels and seer stones) are even less than 1 in 1040. If it does, even the most hardened believers should take notice, and somewhat more reasonable believers (e.g., those on the fence who give the Book of Mormon 50-50 odds), should be obliged to move their belief to the realm of firm doubt in the book’s authenticity.

We’ll also be interested in comparing different pieces of evidence, in the hopes of identifying the strongest (and weakest) evidence both for and against the Book of Mormon. To that end, we’ll be using our Bayesian analyses to give each piece of evidence a likelihood magnitude score (see the FAQ below for more details). In doing so, we’ll make use of the Wagenmakers standard of 1 in 1020. If a single piece of evidence is strong enough to clear that particular bar, that means it will have shifted the probability of the book’s authenticity by at least 20 orders of magnitude—representing a “critical strike” (think D&D) either for or against.

What these essays represent are essentially a series of mathematically grounded thought experiments, and it’s important to treat them as such. These aren’t intended to be the final answer proving the book true or false. Since no one else has really taken this sort of approach, I’m very much trodding on unbroken ground. This is an initial exploration, a first stab, and an invitation to others to improve on what I’m doing. I hope you’ll adopt the same spirit of skepticism I outline above, keeping in mind that all things are possible, that investigation is always worthwhile, and that such investigation won’t—and shouldn’t—end here.

[Philo Sofee]

Drumdude that is absolutely BRILLIANT!!!!! Very, very, VERY WELL DONE.

[Dr Moore]

I have constructed a mirror argument to show that Kyler's logic cuts both ways. He starts with an extreme skeptic and multiplies probabilities to move the skeptic's belief towards the authenticity of the Book of Mormon. One can just as easily start with an extreme believer and multiply probabilities to move the believer's belief towards that Book of Mormon being a fraud.

Hey, that’s cherry picking. No fair!