Transcript of Edgemont Stake Book of Mormon Classes by John W. Welch, 2007 to 2009

Transcript of Edgemont Stake Book of Mormon Classes by John W. Welch, 2007 to 2009

Alma 11-16 Weights and measures

(Class welcome and announcements)

Nephite System of Weights and Measures

Today we are going to talk about Alma chapter 12 and 13 mainly, but we will begin with 11 and,hopefully, get things wrapped up at the end with the end of Ammonihah in chapter 16.We have a couple of carry-over questions from last week at the top of the question list for tonight.The first one was, describe the Nephite system of weights and measures.Who instituted this system, by the way?King Mosiah, and it was a part of that big law reform that occurred at the beginning of the reign of judges.Why do you think they needed to have a system of weights and measures established at the same time they established this reign of judges and why would that would have been something that needed to happen?

(Student) It would help avoid conflict.

They had conflicts before when they had a kingship.

(Student) I mean they would all know, this is worth so much…

Do you think they had a monetary system or a weights and measure system before?Maybe the old Hebrew system was just to use a shekel, which was a weight of silver, but it did not have all of these different divisions, you know, names, for different amounts and weights, so what else might have been going on here?

(Student) You have a system of judges.You have amore finely detailed— I will call it constitution, so that they measure things in specific units

Yes. If they are becoming more of a legally organized society, the judges are going to have to award damages, and they are going to have to, for one thing, be paid themselves.It used to be that the king would administer the justice system.The king would appoint judges.It would be a position of honor and the elders of the city or of the country would take their turn serving as judges.It was kind of a universal responsibility of all adult men to participate in the legal process.You remember in the Book of Ruth where Boaz wants to buy the piece of property from Naomi, and you remember the story about how he cannot buy the property unless he isalso willing to take Ruth with the deal?He is concerned about getting clear title to that property and so he just shows up at the town gate and calls the first ten men he sees, and that is what it required under the old system.You had to have ten men because that is what they called a minyan or a quorum, but anybody who was hanging around the gate would be eligible to witness and judge.So the virtue of judging righteously was a kind of a universal virtue in the Old Testament in which all men were supposed to participate. They are supposed to know the law, supposed to judge according to the proper values and convictions of the morals and commandments of the Law of Moses.They are changing all of that with this change to the law of the reign of judges. Now they have a professional judiciary.People are paid. For one thing, they are going to have to know how much to pay them.I think that is why creating this legal system and this monetary arrangement comes part and parcel with the change to the reign of judges.

Now you do not have a Bureau of Weights and Measures, there is no way to— they are not even minting coins.I do not think that anybody in the Nephite world had ever thought of a coin other than some kind of a weight that was a standard weight. In other words, the value coin (if you want to call it a coin) was the value of the metal.You might have had some way of indicatingthat this is a senine, an onti, aseon, or whatever it was.Typically, however, in the marketplace, they would just have weights and measures, and they would then use a certain weight that was established such as a rock or a piece of metal that had been weighed out to be a certain size.They would weigh it in balance scales to decide whether you had the right amount of barley, or oil, or any other commodity.The king had to establish what the amounts were and the equivalents were.

It is interesting that way back in the beginning of legal history in Mesopotamia, a king named Eshnunna set forth a whole body of laws.He was before Hammurabi, and in his legal system he begins by giving a list of how much silver translates into how much barley, how much silver translates into how much sesame.All these weights and measures are established so that —we call this a kind of barter society, but it is not really a strict barter society because ratios and proportions have been established. That is exactly what we have King Mosiah doing.It is kind of price fixing, but it is also price regulation so that people cannot charge too much to people who do not have enough money.You cannotjust say corn happens to be really scarce in the marketplace today and so we are going to increase the price.It really was a step forward in creating an economic environment, but it was also subject to abuse.For example, once they had established what a day’s worth of work was, being a judge, I do not think King Mosiah had the faintest idea that people would say,“Wow!This is our ticket to wealth.All we have to do is cause a lot of law suits and get a lot of judges and everybody is going to get paid.”I wonder who paid that fee?We do not know whether it came out of the municipal coffers or whether the losing litigant had to pay the court costs. We do not know how that worked.

(Student) It reduces the idea that how much gold a person has determines how much they can pay.

That is right. So the system regulates to eliminate haggling and price gouging.

(Student) You wonder why he chose just silver and gold.Was that the only metals of value?

They are the only metals we know of in that part of the world.I mean I do not know of any lead.They could have used other things like obsidianbut you can chip obsidian like an arrowhead, but you cannot melt it down and get the weights to be accurate.Maybe that was part of the reason.

(Student) Occurred to me; I wondered why just the two were chosen.

It is kind of universal symbol of wealth.

(Student) They have always been the standard, haven’t they, of monetary value.

I think partly because it is rare.It is also useful for jewelry and things like that.

If we describe the system, Lynn do you want to describe the system?How would you describe it?

(Student) Binary.

It is a binary system.What do you mean by that?

(Student) For any amount less than four, you only need one coin of a kind to make up the amount. Not only one coin, butonly one coin of the various kinds.Instead of having two of the smallest ones, you have one of the next one.You never need two of a particular coin until you get up to the highest value, then if you repeat that, you just repeat the highest value coin, although coin is not the right word.

You get all the way up to ten before you need three.Seven, two, and one makes ten,but for anything under ten, two of these measures will add up to any integer.Theyeven have the one-and-a-half.

(Student) Yes, they have an extra one thrown in here.

That was useful creating halves for in the market place under certain circumstances.That was one-and-a-half and two of those would make three. It adds another efficiency factor.

(Student) If you count only in binary, it tells you which coins you need for which amount.

Yes.In addition, if you have a sack of these weights, this kind of efficiency is useful because if you want to be able to quickly weigh out six, all you need is a four and a two and you have that.If you want to do nine under our system, youmust have a nickel and four pennies,that is five coins.If you want to do nine for them, you take a seven and a two and you are there.So it is very efficient and mathematically elegant.What about on the other side?

(Student) If you areusing the weight to measure things out.

Yes. It is not just geometry we are doing here.

(Student) If you are measuring things out, then it is most efficient but it requires you to put weights on both pans along with the products, but it is most efficient if you can use the smallest number of weights.

How much arithmetic do you think someone would need to know to create the most efficient possible weights and measure system?

(Student) Going back to the Egyptians, they knew how to add and subtract fairly well, but multiplication was more difficult.They could double and they could halve.So it turns out that their system of multiplication, their algorithm for multiplying involved a doubling one factor and dividing the other factor by two repeatedly, until you got down to the bottom on the dividing part and then you tally the remainder portions and add those up and you get the product.

Yes.They did not have Arabic numerals.Even the Romans did not and could not do a lot of some of the very simple mathematical operations that we think of, like creating fractions.

(Student) The Egyptians created fractions but their fractions always had denominators of certain sorts.

That is right and the numerator at the top was always 1.

(Student) It could not handle every fraction.

If you wanted to say three-quarters, you had to say one-quarter and one-half.They could not put a three up on thetop and divide it by four; they had not thought of that and their symbols were not conducive to making that happen.If you are a Roman, and you put a V over an X what on earth does that mean?We can do five over ten; that isfifty percent,but they did not do that.What is interesting to me here too, is this word percent.I mean a percent is, you know, Y over one hundred.If you cannot do three over four, you certainly cannot do fifty-six over one hundred.

(Student) They did not have the zero.Zero was unknown.

Yes. “The zero is unknown, soI probably ought to doL over D,” or whatever it is. How do they do the engineering?That is fifty percent.

(Student) Apparently not mathematically!

They figured out the Pythagorean theorem, and they knew how to do a lot of manipulation of drawings.Pythagoras was pretty smart, but they had some limitations.If you wonder if there is a concept of perfection in the scriptures, meaning being hundred-percenters, they do not have that concept.You could not report your home teaching and say, “Well, we got eighty-seven percent.”You either did it or you did not.And throughout the Book of Mormon we see things that are a little more black and white than we usually think of. The gray area was not in their gray-matter yet, and maybe it is a good thing it was not, because they are looking more at the essence of what is happening rather than the quantity of what is happening.

(Student) How do you think they mastered the acoustical?Because if you did not have the right numbers —I have been to places where we do not have buildings like they did and 4,000 years later their acoustics still works.

It is amazing isn’t it?

(Student) So I do not know if I will agree that they did not have a better concept than ours when it comes to the numbers.

They certainly used numbers and, Euclid was brilliant.They had other ways of doing it than we do.I think part of it too was trial and error.At least when you build a theater, you learn that hillsides work the way they do.

(Student) They copied those hillsides right?Some of the pyramids are replicas of hills.

Exactly, and down in Oaxaca and Teotihuacan even the configuration, the angles, of the pyramids are exactly the same as mountains off in the distance that were holy mountains.They are bringing the holy mountain down to the city and that is why they will build things the way they do.They had their reasons and they were pretty good ones.Glen, another point on that?

(Student) Most of the mathematics that were done anciently was approximate. For example, “We are going to make something, thenwe describe it to the workman, and the workman figures out how to make it fit.”They did not have the precise measurements.

Yes, that is a good point, and they never calculated π to a million significant decibels, did they?

(Student) In fact the Egyptian value for π wassixteen ninths which is off quite a bit.The Greek value was no better.

Right.They knew it was out there, they just could not get any closer.

(Student) The Old Testament value for π, of course, was three.

Yes, which is even worse.You all recognize what is here on the board?If you look at this side of the handout, what is going on here?This is an Egyptian hieroglyph called the Horus eye or the Wadjet eye. There is a myth that the God Horus had his eye pecked out and it was broken up into little pieces and it was finally brought back together again.He was brought back to life and resurrected and Osiris and a lot of Egyptian mythology comes into play here.When his eye was pecked out, Horus was the god of grain. The full hieroglyph stands for one full measure of grain, but each one of the parts of the eye became a hieroglyph so this part here becomes a half and the pupil becomes a fourth, and so on, and this is a thirty-second the eyelash, the tear duct is a sixty fourth.The other part of the iris here is a sixteenth, the eyebrow is an eighth.

Now what is interesting, is if you add these up, if you add a half, a fourth, an eighth, a sixteenth, a thirty-second and a sixty-fourth, Lynn what do you get?You get sixty-three sixty-fourths.The whole is greater than the sum of the parts. The sum of the parts are a little less.In fact, it isone sixty-fourth off.This is your point about approximation.It was good enough, and if people asked,“If you take all these parts and add them up,”so you put all these pieces on the scale and then somebody says, “Here is your full measure of grain,” and you think to yourself, “Hey wait a minute, I’m getting shorted here one sixty-fourth,” if they were smart enough to figure that out— they did not—but if they had figured it out, there was a little answer, and that was that God just made up the difference.Anyway, God is in the details, right?And so it is here.

So what else is interesting about this?I listed these out for you on here so that you can see what is going on here with the sixty-three sixty-fourths.How many symbols are there in this?I mean you count them up,1, 2, 4, 8,16, 32 and the sum of them all is seven, right?If you look at the Nephite measuring system ithas seven; the onti, seven, is the sum of them all.Very close don’t you think?

(Student) If you identify one-eighthas the senine,then the ones going up are the greater measures.Then you take the smaller measures, and they are the ones going down and they are all halves.

Yes.So we have a binary system here. We know this from a papyrus calledthe Egyptian mathematical papyrus. I think it was first translated in the 20th Century, 1900s.Anyway, I think that iskind of neat.Now it also raises an interesting question.How did Mosiah know this?Is this a part of the Egyptian hieroglyphs?I mean they do know reformed Egyptian.Was this something that they learned in how to count?

(Student) Joseph knew of it.

We know how Joseph knew it, right?

(Student) It is just another one of those things that mean you add another pearl.

Yes.So there you have a little bit on how it works mathematically.

One last question on this is, “why do you think this information was included in the Book of Mormon?I mean, Mormon left this in.Any ideas?”

(Student) So the Savior could use the word senine and know what it meant.

You know, that is not a bad suggestion.Where does he use that?Remember?Yes, and where he says, “You will not come out until you have paid the uttermost senine.”So if the Lord had used that word, maybe Mormon, who knows that text, thought,“Maybe I had better tell people how our system worked.”This is the place to do it because King Mosiah was the one who created it.