Facts are Stubborn Things: Two Numerical Facts and a Very Short Course in Statistics– Blog Post Number 9- July 12, 2015

John Adams, the second President of the United States, once said: “Facts are stubborn things; and whatever may be our wishes, our inclinations, or the dictates of our passions, they cannot alter the state of facts and evidence.”


That should also be our attitude toward facts.

The Book of Mormon, and the other revelations given to Joseph Smith, are full of statements that claim to be facts:  not vague generalities or “spiritual” statements, but concrete, real statements that are put forth as facts. We can test Joseph’s prophetic credentials with these factual statements.

I have often worked as an expert witness.  It is really important when testifying to not say more than you really know-especially not to commit yourself to specific testimony that might be proven wrong later on.  If Joseph were a fraud, he would have avoided going out on a limb, making such specific, testable statements.  Instead he committed himself to all sorts of specifics.

I have already written about a number of his testable assertions including stone boxes, steel bows, chiasmus, plates made of a gold and copper alloy, the number of plates needed to write the text of the Book of Mormon, the existence of matter that we cannot see, and others.  As I continue with this blog I will continue to offer such pieces of evidence.  In this post, I want to mention two specific numbers related to the Book of Mormon that propose to be facts and can be tested. One number is a bit hidden, the other is out there quite plainly.  I also want to give a very short course in statistics. Statistics deals with how probable or likely certain events are to happen.

Here is the first number—out in plain sight.

Number One: the standard military unit in Old Testament times was fifty men

In the Book of Mormon, Laban was apparently acting as the military governor of Jerusalem in about 600 BC.  He was a man of influence and power.  Laban had robbed and attempted to murder Nephi and his brothers.  As these sons of Lehi discuss what to do about Laban they make these statements in 1 Nephi 3:31 and 1 Nephi 4:1.

“And after the angel had departed, Laman and Lemuel again began to murmur, saying: How is it possible that the Lord will deliver Laban into our hands? Behold, he is a mighty man, and he can command fifty, yea, even he can slay fifty, then why not us?  And it came to pass that I spake unto my brethren, saying: Let us go up again unto Jerusalem, and let us be faithful in keeping the commandments of the Lord; for behold he is mightier than all the earth, then why not mightier than Laban and his fifty, yea, or even than his tens of thousands?”  (Italics added.)

So, Laban commanded a “platoon” of fifty men in the city and probably a division of 10,000 men in a time of war.  (The military is a conservative institution– 10,000 men still constitute a division in many armies.)

About 250 years earlier, around 850 BC, the prophet Elijah was ministering to the Israelites and got in trouble with king Ahaziah, who sent his soldiers to arrest Elijah. The story is told briefly in Second Kings, Chapter 1.  Here it is:

“Then the king sent unto him a captain of fifty with his fifty. And he went up to him: and, behold, he sat on the top of an hill. And he spake unto him, Thou man of God, the king hath said, Come down.  And Elijah answered and said to the captain of fifty, If I be a man of God, then let fire come down from heaven, and consume thee and thy fifty. And there came down fire from heaven, and consumed him and his fifty.  Again also he sent unto him another captain of fifty with his fifty. And he answered and said unto him, O man of God, thus hath the king said, Come down quickly.  And Elijah answered and said unto them, If I be a man of God, let fire come down from heaven, and consume thee and thy fifty. And the fire of God came down from heaven, and consumed him and his fifty.  And he sent again a captain of the third fifty with his fifty. And the third captain of fifty went up, and came and fell on his knees before Elijah, and besought him, and said unto him, O man of God, I pray thee, let my life, and the life of these fifty thy servants, be precious in thy sight.  (Italics added.)

Each of these three captains of soldiers commanded fifty men.

So, Joseph Smith said that Laban commanded fifty men, not forty men or a hundred men, or no specific number of men at all, which Joseph would probably have done if he were making up the Book of Mormon and wanted to avoid being specific so he could not be pinned down.  No, Joseph made a specific statement implying that in 600 BC the standard military unit was fifty men.  A couple of hundred years earlier, in the Israelite military of that time, that was indeed the size of the basic military unit.

(By the way, “platoon” strength in modern armies typically varies between about 25 and 60 men. https://answers.yahoo.com/question/index?qid=20080424225740AAV9Euu)

But how did Joseph know that fifty men was the standard “platoon” size in Old Testament times? Did you know that?  Would you have put a specific number in a book you were making up and which you knew would be ridiculed and examined for every possible flaw?  How probable do you think it was that Joseph guessed that one right?

Number Two: How many is “a few?”

We are told in the Book of Mormon that three people will first see the actual plates, and then “a few” will see them. From 2 Nephi 27:12-13 we read:

“Wherefore, at that day when the book shall be delivered unto the man of whom I have spoken, the book shall be hid from the eyes of the world, that the eyes of none shall behold it save it be that three witnesses shall behold it, by the power of God, besides him to whom the book shall be delivered; and they shall testify to the truth of the book and the things therein.  And there is none other which shall view it, save it be a few according to the will of God, to bear testimony of his word unto the children of men; for the Lord God hath said that the words of the faithful should speak as if it were from the dead.”  Italics added.

It is certainly possible that “a few” just means an undetermined, relatively small number.  It is also possible that God was being specific in this case, just to see if we are reading carefully. 🙂  Because, from the New Testament, in 1 Peter 3:20 we read concerning Noah and his family:

“Which sometime were disobedient, when once the longsuffering of God waited in the days of Noah, while the ark was a preparing, wherein few, that is, eight souls were saved by water.”  Italics added.

In this scripture “few” is assigned a specific numerical value, that is, eight.  How many witnesses gave their testimony of having seen the Book of Mormon plates? Well, first there were three witnesses as promised in 2 Nephi Chapter 27


and then there were also eight more witnesses, also as promised in 2 Nephi 27 and specified in 1 Peter.


Again, this may be just a coincidence.  But I prefer to believe God has put small, specific statements in the Scriptures to see if we are paying attention and to reward us for paying attention. How likely do you think that the only time in Scripture that the quantity “a few” is defined, it is exactly equal to the “few” who were to witness the Book of Mormon?  How probable do you think that is?

OK, I have used the word “probable” twice now in this blog.  Let’s talk about probability and statistics.

A Little Bit of Statistics

Please remember the basic premise of this blog: Joseph was either making it all up, or he was a prophet.  He was either a fraud, or he was telling us the truth as he received it from God. I don’t think any other choice is available to us. We are being forced to choose between those two options.

Joseph made a lot of very specific, very concrete statements that invite us to test his prophetic credentials.  If he was guessing, then his guesses ought to be distributed among right and wrong guesses, and easy to spot using statistics.

What is statistics? In brief, statistics is the mathematical description of the probability (the liklihood) of certain events occurring within a particular population.  While statistics may sound complicated, at its heart, statistics is dead simple common sense applied to how likely certain events are.

One of the clearest illustrations of statistics is given by rolling dice.  The population here is the values (1 through 6) on the six sides of the die.  Since a die has six possible values, then there is a one in six chance (16.66% of the time) that the value “1” will turn up when the die is cast, ditto for each of the other values 2 through 6. If you have two dice, then each die is independent of each the other die and there is still only a one in six chance that any given value will turn up for that die when it is rolled.

Here is the key point: probabilities of individual events must be multiplied to estimate the probability of all the individual events occurring simultaneously While the probability of each individual die coming up with a “1” is 16.6%, the probability of rolling “snake eyes” or both dice coming up with a “1” on the same roll (simultaneously) is not 16.6% but 16.6% (0.0166) times 16.6% (0.0166) or about 0.02756 or 2.76% of the time. So roughly three times out of a hundred times that you roll two dice you will get snake eyes.  I invite you to perform that experiment.  You can test this assertion and verify it for yourself.

Going on further, if we want to roll three dice, what will be the probability of rolling three “1”?  It is 0.166 x 0.166 x 0.166 equals 0.00457 or about 5 times in a thousand.  (That’s a lot of dice rolling to test the assertion, or you can just take my word for it.  :)).  If we roll four dice together, what is the probability of rolling four “1”s simultaneously?  It is 0.000761, or about 8 times in ten thousand rolls of the four dice.

How about three different events, with different probabilities, each occurring simultaneously due to the same cause?  Let’s say that the first event has a probability of 1 in a hundred (0.01), the probability of the second event is one in a thousand (0.001) and the third is one in 10 (0.1). What is the probability of all three of these events occurring simultaneously if they are part of the same population? It is 0.01 x 0.001 x 0.1 = 0.000001 or 1 in a million.  Conversely, the probability that all of these events will NOT occur together is 1.0 minus the probability that they all will occur together.  In this example, it is 1.0 minus 0.000001 or 0.999999, or 99.9999%, or 999,999 to 1.  How do you like those odds? Would you bet against those odds? 🙂  (However, people do it all the time when they play the lottery–sigh…)

How about guessing steel bows, stone boxes, gold plates that were actually an alloy of gold and copper, the size of a standard military unit in Old Testament times, what “a few” is, chiasmus, the number of plates needed to write the Book of Mormon, matter too fine to see, and so on? What probability do you assign to getting each of these individual events correct in this statements of Joseph Smith? Pick any number you think is reasonable between 0 and 1.0.  Then multiply them together.  That is the probability of Joseph getting all of them right, all at once…if he were guessing.

The Best Theories Explain the Most Facts

I am not interested in arguing with anyone in this blog. I am not going to fight, contend or try to compel anyone to believe what I believe.  I intend to present evidence and let people decide for themselves.  But for those of my readers to whom actual facts matter, I would just point out that in science, and hopefully in common sense, the theory or explanation that explains the most facts is the best theory.  Here is a good explanation of this point of view taken from the following source.


Here is the key quote from this link, all in italics. Please note especially the underlined part of Step 4 below.

Below is a generalized sequence of steps taken to establish a scientific theory:

  1. Choose and define the natural phenomenon that you want to figure out and explain.
  2. Collect information (data) about this phenomena by going where the phenomena occur and making observations.  Or, try to replicate this phenomena by means of a test (experiment) under controlled conditions (usually in a laboratory) that eliminates interference’s from environmental conditions.
  3. After collecting a lot of data, look for patterns in the data.   Attempt to explain these patterns by making a provisional explanation, called a hypothesis.
  4. Test the hypothesis by collecting more data to see if the hypothesis continues to show the assumed pattern.  If the data does not support the hypothesis, it must be changed, or rejected in favor of a better one.  In collecting data, one must NOT ignore data that contradicts the hypothesis in favor of only supportive data.  (That is called “cherry-picking” and is commonly used by pseudo-scientists attempting to scam people unfamiliar with the scientific method.  A good example of this fraud is shown by the so-called “creationists,” who start out with a pre-conceived conclusion – a geologically young, 6,000 year old earth, and then cherry-pick only evidence that supports their views, while ignoring or rejecting overwhelming evidence of a much older earth.)
  5. If a refined hypothesis survives all attacks on it and is the best existing explanation for a particular phenomenon, it is then elevated to the status of a theory.
  6. A theory is subject to modification and even rejection if there is overwhelming evidence that disproves it and/or supports another, better theory.   Therefore, a theory is not an eternal or perpetual truth.

My theory or “hypothesis” is that Joseph Smith was the prophet he claimed to be. This blog presents a small fraction of the evidence I believe supports my hypothesis. Over time, I expect to deal with and address apparently contradictory evidence also, as I have already done with the forensic DNA and archaeological data.

However, if someone believes that Joseph was making all of this up, then in fairness, that person must also deal with all of the stubborn facts.  That person must also deal with statistics, the mathematical analysis of probabilities.  An honest person cannot “cherry pick” his data—considering only the data that support his point of view.

I think most critics of the Book of Mormon and of Joseph Smith are “cherry-picking” their data, either consciously or unconsciously.  They are ignoring the vast body of evidence that support Joseph’s claim to be a prophet while pointing to a few pieces of evidence that they believe undermine Joseph’s claim to be a prophet.

That approach is unfair and unscientific–and not very logical, actually.  To be honest and fair and “scientific” we must also consider evidence contrary to our point of view.   When that contrary evidence piles up, as I believe it does, then the honest investigator can apply statistical methods (and common sense) to the pile of accumulating data.

If a person wants to consider the things Joseph got right as lucky guesses, then he can pick a probability of getting that particular fact right, whatever number he thinks is fair, between 0 and 1.0 and multiply them by the individual probabilities of all of the other “lucky guesses” of Joseph Smith. The product of all of these individual probabilities is the probability that all of these guesses were lucky guesses.  Multiply that number by 100 to get the probability as a percent.

So all of us have to answer the question…to ourselves today and to God eventually; was Joseph Smith the luckiest guesser ever, or was he a prophet sent by God?