The Book of Mormon vs. The Laws of Chance

            While writing A Friendly Discussion I happened to read Duwayne Anderson’s Farewell to Eden: Coming to Terms with Mormonism and Science, a book that is a “must” read for anyone interested in the relationship between scientific knowledge and  the doctrines of Mormonism.   The Appendix of that book contains an analysis of certain events in the Book of Mormon and the laws of chance.  I found it fascinating, and wrote a chapter about it, but later decided to omit it from the book because I thought it would  be of limited interest to the general reader.  But for those who are interested in such things, here it is.

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           Aside from all the other problems with the Book of Mormon, there is one that hasn’t received much attention but is worth thinking about.  It involves the principle of random distribution.

            Random distribution?  How could that be connected to the Book of Mormon?

            I’ll demonstrate that in just a moment.  The idea is that the laws of chance tell us the probability of unrelated events occurring in various patterns.

            You’ve lost me already.  Give me an example of what you are talking about.

            Suppose you have six dice, which you throw on the table.  It is possible to figure, mathematically, the likelihood of all of them turning up with a 6. For example, with only one die the chance is 1 out of 6.  With two, the likelihood of them both being a 6 is  6 times 6, or one out of 36.   With three, the chance is 36 times 6, or 216.  With four it is 216 times 6, or 1,296, and with five it is 6 times 1,296, which is 7,776.  If you throw six dice the chance of getting a 6 on every one of them is 7,776 multiplied by 6, or in other words one chance out of 46,656.

            So?

            There’s an interesting application of this principle to the Book of Mormon, which I first became aware of when reading Farewell to Eden, Coming to Terms with Mormonism and Science, by Duwayne Anderson.   As Anderson points out, there are eight references in the Book of Mormon to specific days of the month, dates on which certain events took place.

            For example:

            • Amalickiah was killed  on the first day of the month (Alma 52:3);

            • Helaman wrote to Moroni on the second day of a month (Alma 56:1);

            • Cities were destroyed  on the fourth day of a month (3 Nephi 8:5);

            • A war began on the fifth day of a month (Alma 16:1);

            • Another war began on the third day of a month (Alma 56:42);

            • Alma’s son converted on the fourth day of a month (Alma 10:6);

            • Alma was left prison the twelfth day of a month (Alma 14:23);

            • Lamanites attacked  on the tenth day of a month (Alma 49:1);

            You will notice that none of the dates occur in the third or fourth week of a month, and the first six events  all occurred during the first  week.

            I don’t see any problem with that.  It’s not unusual -- that’s just the way it happened to be.

            That’s like saying there’s nothing unusual about having all six of those dice come up with a 6 -- even though the chance of it happening is 46,655 to 1!

            Let’s do the math:   The chance of any random event happening in the first five days of a month are 5 out of 30, or in other words, 1 in 6.  By coincidence, that is exactly the same as the chances with the dice.

            The first date on the list occurs during that five-day period.  The chance of that happening was 1 in 6.  No problem with that.  The second occurrence is also in one of the first five days of the month.  The chance of that happening twice in a row is 6 times 6, or 1 out of 36.   Still, no big problem.  But when the third unrelated event in a row also occurs during the first five days there is only one chance in 216 of that happening, and it’s beginning to look a little suspicious.  The fourth date once again occurs during that same five-day window, which the laws of chance predict would happen only once in 1,296 times.  But we’re not through.  The fifth occurrence is also during the first five days, which would happen once in 7,776 times.  And with the sixth occurrence we again must multiply by 6, raising the odds to one out of 46,656, the same as with the dice.

            Now, if the list had stopped at that point, those would have been the odds against those six random events being distributed as listed.  However, there are two more events, which are outside that five-day “window.”   This diminishes the odds, but they are still formidable.  Using all eight dates, Anderson applies standard statistical techniques to the likelihood of the dates being as listed.  I won’t go into the mathematics –– t;his isn’t the place to discuss standard deviations, Gaussian distribution, the Central Limit theorem and the Monte Carlo simulation procedure  –– but if you’re interested you can check the math on page 336 of Anderson’s book. Using all eight dates, he says, “The probability that the distribution of month-days in the Book of Mormon is random (i.e., representative of real history) is about 1 out of 2,000.”

            In other words, those numbers apparently are not actual random dates.   The law of averages would have distributed them more generally throughout the months, whereas an individual making them up could have had a habit of selecting dates early in the month.  If Joseph Smith was just making up dates out of thin air there would be nothing unusual about this distribution, because the law of averages doesn’t apply to fiction. He wouldn’t even have been aware of his subconscious tendency to pick early dates! 

            I’ll admit this is very puzzling.  There must be some error.  Perhaps there are other month-dates in the Book of Mormon, in which case the dates might be more randomly distributed.

            No, the dates resulted from a computer search of the Book of Mormon.  The list is complete.

            Well, maybe the Nephites used a different calendar which would define a month differently.

            No, in every culture a month is  period from one full moon to the next. And in every part of the world that occurs every  29 days, 12 hours, and 44 minutes, to be precise.  If we had used the lunar month, or if we had rounded off to 29 days instead of 30, we would have to adjust the figures slightly, but it wouldn’t make any substantial difference.  No matter how you figure it the numbers are absolutely incredible.

            Well, this is all very interesting, but you can’t deny that all of those events could have occurred just as the Book of Mormon states.  I will concede, however, that the odds against that are pretty high.

            Indeed they are –– about 2,000 to 1, to be precise.