Posted by:
baura
(
)
Date: August 02, 2015 03:55PM
Without getting mathematical, I want to show how Mormons and non-Mormons disagree on things and why a lot of the differences can be illustrated by applying a result of probability theory known as Bayes Theorem.
First a couple of examples of Bayes Theorem in action:
(A) Suppose you have two coins in your pocket, a fair coin and a two-headed coin. You reach in your pocket and grab a coin and flip it. It lands heads. Now, what is the probability that it is the two-headed coin? Well there are FOUR possibile outcomes to the experiment: 1. fair coin heads, 2. fair coin tails, 3. two-headed coin heads and 4. two-headed coin the OTHER heads. If it lands heads we've ruled out option 2. So of the remaining equally likely options two of them are with the two-headed coin and one of them is with the fair coin. So the probability that you've chosen the two-headed coin is 2/3.
OK. you flip it again and it, again comes up heads. Now what is the probability it's the two-headed coin? Now there are FOUR ways to get two heads in a row with the two-headed coin (two choices for the first flip times two choices for the second flip) and only one way to get two heads in a row for the fair coin. So now the probablity it is the two-headed coin has risen to 4/5.
You flip it again and it comes up heads again. By this time you are becoming sure it's the two-headed coin, and the probability is 8/9. A fourth heads would make the probability 16/17 and a fifth heads in a row would make it 32/33.
We'll come back to the coins in a while. Here's a second applilcation of Bayes Theorem which is more practical
(B) There is a test for a certain disease which, if it says you have the disease is correct 95% of the time but gives a "false positive" 5% of the time. You take the test and it says you have the disease. Now, what is the probability you have the disease?
Answer: You have no idea. Not enough information has been given to answer the question (shockingly even many doctors do not get this one right)
Think of this. What if the disease is VERY rare, What if only one in a million people actually have the disease. That means that if the test gives a false positive 5% of the time then it will test positive on 50,000 of the million people who do not have the disease. So the question is, which is more likely, are you the one-in-a million who has the disease or one of the 50,000 who doesn't have the disease but tested positive anyway?
Going back to the coins, I started the problem with two coins. What if I change it to 1001 coins: 1000 fair coins and one two-headed coin? Now you reach in your pocket and randomly grab a coin. Three flips in a row give heads. There are 1000 ways this can be done with a fair coin (1000 coins to choose from each showing heads on 3 successive flips) and 8 ways it can be done with the two-headed coin. Now the probability it is the two-headed coin is 8/1008--MUCH less.
The difference between skeptics and apologists has to do with the initial "estimate" of how many "coins" are in the pocket or what percent of people "have the disease."
Let's apply this reasoning to the famous "NHM" found in Yemen. Mormon apologists are saying "we've found Nahom!" It's called the best evidence yet for the Book of Mormon.
If you start by ASSUMING the Book of Mormon is probably true, then the NHM would be a good choice for the BOM Nahom. If you give a 50% likelyhood to the Book of Mormon being true then finding NHM would up the chances, much like when there were only two coins and one flip came up heads. Or the likelyhood of actually having the disease when the test says you do, if the disease is a very common disease.
But if you start with the assumption that books given by angels are VERY rare, then your situation is more like the scenario with 1001 coins or when only one in a million have the disease. What is more likely? That the book was given by and angel and you've found NHM on a stone in Yemen, or that the book was not given by and angel and you've found NHM on a stone in Yemen? Clearly, if it is assumed that books given by angels are very rare then the second interpretation is more likely.
This is why Mormon apologists shake their heads at critics when they say "coincidence." "Oh," they say, "you're just saying that because you don't like the result." No, this is not why we're just saying that. We're saying that because coincidence in such investigations is the null hypothesis. It's ALWAYS possible to find coincidences. They crop up all the time. It is the duty of the person making the claim to prove that their find is NOT a coincidence, not the duty of the rest of the world to prove it is. As we saw with the 1001 coins, the "coincidence" of 8 heads in a row would be MUCH more likely than having grabbed the two-headed coin.
Let's extend this idea to two other aspects of "evidence." First, let's look at the idea that EXTRAORDINARY CLAIMS REQUIRE EXTRAORDINARY EVIDENCE. Two-headed coins are Very rare. If you have a coin which you've flipped four times in a row and has come up heads each of the four times, how justified would you be in concluding it's a two-headed coin? Given that fair coins outnumber two-headed coins by millions-to-one, you'd not be justified at all. It's MUCH more likely that it's an ordinary coin defying the odds (even though that's a one-in-sixteen chance with a fair coin) than it's a two-headed coin. To conclude it's a two-headed coin you'd have to get more like 25 heads in a row (or, more simply, look at both sides).
Another claim that we can look at is the idea that "ABSENCE OF EVIDENCE IS NOT EVIDENCE OF ABSENCE." This can be valid in some situations and invalid in others. Let's consider the question of life in the universe. Are we the only planet with life? The fact that we've found no life on any other planets would be an "absence of evidence." But we've looked at only a few planets. And we've not searched those exhaustively. Results in astronomy in the past quarter century have shown that planetary systems around stars are not at all uncommon. There could easily be trillions of planets in the universe. The absence of evidence after looking at a handful is not evidence that none of the others have life. We have to ask the following question: What is the probablity that if there is life out there, on, say, a million different planets that our efforts so far could have missed it? Even with a million life-supporting planets we can expect to not have found one yet so the absence of evidence so far doesn't mean much.
However let's look at a different situation: the absence of archaeological evidence for the Book of Mormon. What is the probability that IF there were this advanced civilization which spoke and wrote a hybrid of Hebrew and Egyptian, used horses and chariots, cultivated wheat and barley, smelted iron and steel, had a Judeo-Christian religion and "filled the land," growing into the millions etc. that it wouldn't have been discovered?
If you were to have asked this question in 1830 there could be a good case such a civilization could had not yet been detected. However in 2015 after teams of archaeologists have combed every square mile of the Americas, using infra-red and ground-penetrating radar, and other modern technologies, and having searched for every bit of archaeological information they could find, then it stretches credulity to the breaking point to claim that they just haven't looked in the right place yet. In such a situation it is proper to say that the absence of evidence is strong evidence of absence.
Edited 2 time(s). Last edit at 08/02/2015 04:05PM by baura.