The Mass of Money

By The Metric Maven

The metric system has always had an odd relationship with money it appears. I’ve had a confused relationship with trying to understand what money actually is as a noun. I’ve read a lot of books that tried their best to provide a definition. I found them all wanting. Finally after a couple of decades I finally arrived at a definition when I was watching Humphrey Bogart in The Maltese Falcon. Money is “the stuff that dreams are made of.” There seem to be a lot of dreams in that bird. The prop used in the movie sold for over 4 million dollars recently.

Below is a page that defines metric quantities, including the US dollar:

We see that money is included in the grouping, and provides a relationship between said dreams. I still recall my grandfather calling a twenty dollar denomination a double eagle. He also called a quarter two bits, which comes from the original Spanish dollar. My grandfather called a ten dollar bill a “ten spot”; it was also known as a “sawbuck.” The mill is the origin of the mill-levy.  One hundred dollars has been called a yard.

I decided that money is a concept that is essentially an attempt to put a number on emotional feelings about objects and services, which makes it susceptible to the vicissitudes of the human experience. I could not see writing an essay about money and the metric system at all. A longtime email interlocutor, with whom I shared some of the information to follow, enthusiastically encouraged me to write something.

Recently, I began to read Adam Smith’s The Wealth of Nations. I was a bit surprised when I read Adam Smith’s view of how money originated:

…we are told by Pliny…that till the times of Servius Tullis [575-537 BC], the Romans had no coined money, but made use of unstamped bars of copper, to purchase whatever they had occasion for. These rude bars, therefore, performed at this time the function of money.

The use of metals in this rude state was attended with two very considerable inconveniences; first, with the trouble of weighing, and secondly, with that of assaying them. In the precious metals, where a small difference in the quantity makes a great difference in the value, even the business of weighing, with proper exactness, requires at least very accurate weights and scales. The weighing of gold, in particular, is an operation of some nicety. In the coarser metals, indeed, where a small error would be of little consequence, less accuracy would, no doubt, be necessary. Yet we should find it excessively troublesome if every time a poor man had occasion either to buy or sell a farthing’s worth of goods, he was obliged to weigh the farthing. The operation of assaying is still more difficult, still more tedious, and unless a part of the metal is fairly melted in the crucible, with proper dissolvents, any conclusion that can be drawn from it is extremely uncertain. Before the institution of coined money, however, unless they went through this tedious and difficult operation, people must always have been liable to the grossest frauds and impositions; and instead of a pound weight of pure silver, or pure copper, might receive in exchange for their goods, an adulterated composition of the coarsest and cheapest materials, which had, however, in their outward appearance, been made to resemble those metals. To prevent such abuses, to facilitate exchanges, and thereby to encourage all sorts of industry and commerce, it has been found necessary, in all countries that have made any considerable advances toward improvement, to affix a public stamp upon certain quantities of such particular metals, as were in those countries commonly made use of to purchase goods. Hence the origin of coined money, and of those public offices called mints; institutions exactly of the same nature with those of aulnagers and stamp-masters of woolen and linen cloth. All of them are equally meant to ascertain, by means of
public stamp, the quantity and uniform goodness of those different commodities when brought to market.

Smith goes on to explain that the early metal pieces were stamped only on one side. This only guarantees the purity, but not the weight of the metal. “They are said to be the current money of the merchant, and are yet received by weight, and not by tale, in the same manner as ingots of gold and bars of silver are at present.” The word tale probably meant the amount of weight stamped on the pieces. This seems clear when he goes on:

The inconveniency and difficulty of weighing those metals with exactness, gave occasion to the institution of coins, of which the stamp, covering both sides of the piece, and sometimes the edges too, was supposed to ascertain not only the fineness, but the weight of the metal. Such coins, therefore were received by tale, as as present, without the trouble of weighing.

The public had confidence that the metal was pure and the weight stamped on the coin was accurate and could exchange it for goods and services without concern.

I found what Adam Smith said next of great interest:

The denominations of those coins seem originally to have expressed the weight or quantity of metal contained in them. In the time of Servius Tullius, who first coined money at Rome, the Roman as or pondo contained a Roman pound of good copper. It was divided, in the same manner as our Troyes pound, into twelve ounces, each of which contained a real ounce of good copper. The English pound sterling, in the time of Edward I. contained a pound, Tower weight, of silver of a known fineness. The Tower pound seems to have been something more than a Roman pound and something less than the Troyes pound. …

Smith points out that the Troy weight was used at the “fair of Troyes” in France and the weights and measures used at that market were well known and “esteemed.” This measuring unit has come down to us in the US to this day for determining the weight of precious metals.

I found it very interesting that the value of money was originally in terms of a weight (or because they used scales, the mass) of the known metal in a coin. In other words, the numerical value of worth assigned to a metal was exactly equal to the measurement unit used to define the mass of the volume of metal. If you measure a metal in grams, then it’s financial value is expressed numerically in grams. This implies that mass is identical to  monetary value. This means that a universally accepted standard for mass is of paramount importance to determine the monetary value of a metal. This illustrates why people in the past might have the audacity to include money with defined metric system quantities. The current price of gold is about $41 per gram, but if we used gold directly, we could have US money in terms of grams. We could go with a milligram of gold which would be about 41 cents as our base unit for money, as could the entire world. Rather than use dollars, you could purchase items with 2, 5, and 10 mg coins. The value of the money would now be in milligrams. I think it is probably obvious to my readers, and it was to Adam Smith, that if the use of a value other than an accepted and standardized mass unit was used, nothing would prevent this from occurring:

I believe the avarice and injustice of princes and sovereign states, abusing the confidence of their subjects, have by degrees diminished the real quantity of metal, which had been originally contained in their coins. The Roman as, as in the later ages of the republic, was reduced to the twenty-fourth part of its original value, and, instead of weighing a pound, came to weigh only half an ounce.

…By means of those operations, the princes and sovereign states which performed them were enabled, in appearance, to pay their debts and fulfill their engagements with a smaller quantity of silver than would otherwise have been requisite. It was indeed in appearance only; for their creditors were really defrauded of a part of what was due to them.

When I was a boy, I recall watching a television program for children that explained how money had been invented. It is rational, reasonable, and I suspect apocryphal, and probably wrong. The person explained that when everyone came to the market at a big city from the small surrounding bergs, they would leave the items they wanted to sell, say a pair of oxen, at a place outside of town. The oxen would be kept by the people running this “hat check” for merchandise, and the owner given a slip of paper, a receipt, which listed what they had left for save keeping. When they were at the market they might decide to sell the oxen for a horse and some grain. The person could give his piece of paper to the person, and she would give him a piece of paper for a horse and the grain. The two would not have to go back to the “hat check” area make the transaction in person.

I suspect the truth is probably less local, and more at a governmental level. One of the amazing abstract notions created by humans was the idea that one could survey land, and once this was done, that plot of land would have a paper that allowed for a person to possess it when they had paper with a government certification. The Charter Oak is a tale of how important a certified paper document had become. The problem with physical gold is that it is tied by physics to retain the same mass and atoms, and therefore remain finite in quantity. If you want more gold, then tough luck. Go look in the mountains for ore. But, if you had a piece of paper that represented the gold, you could pass them out rather than issue coins. The new piece of paper can have a denomination that is defined with respect to the physical amount of gold, but not tied to any annoying reality based value like a gram of gold physically in your possession. Of course the values of these different currency denominations could be manipulated, and vary with respect to one another.  One could also control the amount of gold in circulation and manipulate the value of currency that way. This lead to the demand that silver be used as an alternative, which also had its problems. When one has a land deed, one does not expect the legal area defined square meters by the document to change, but that is how quantifying dreams with metal works.

To combat the monetary denomination versus mass of metal problem, some nations would place a quantity of gold or silver on the paper currency, not in terms of grams, but in terms of dollars. When I was a boy, I recall the recall of silver certificates. I still have one in my possession. Everyone was to surrender them to the bank. Most did, but one fellow my father knew went to the bank and demanded physical silver, as it said on the note it was his right to demand. The note states “This certifies that there is on deposit in the treasury of The United States of America Five Dollars in silver payable to the bearer on demand.” See the example below:

Silver Certificate — Wikimedia Commons – click to enlarge

But how much silver in grams is in a dollar? That is not defined on the bill, and so produces an uncertainty for dreams and schemes.

In the 1922 US Metric Hearings, there was a proposal to create a standard-ounce silver dollar divided into dimes, cents, and mills, just like the decimal divisions of the current version. Then they finally decided to get back to using  gold as a universal metallic standard, and try to undo the decoupling of a currency unit, such as dollars, yen, rubles, drachmas and so on, from the mass value of a metal, which is not fungible. A table that does its best to equate currencies was offered at the hearing:

click to enlarge

In the end, it is still a kludge at best, as the closest equivalent mass values in gold are only approximate, and because currency values are political definitions, they cannot be expected to be exactly equivalent. It is suggested that the 23.22 Troy grain dollar be replaced by a 24 grain dollar. I don’t see how this makes sense for international trading, but to someone in 1922 it did. The last line in this documentation is a bit surprising: “Standard gold weights for coins are only second in importance to standard uniform weights and measures.” In the end, did they realize that an accurate measure of the mass of the physical metal was more important than the arbitrarily assigned values put on the coins?—which can be manipulated. I have no idea, but if weights and measures were that important, and the need for accuracy so acute, then why would they not push for the metric system to be adopted?

John Bemelmans Marciano in his book Whatever Happened To The Metric System, seems to assume the reader understands what I just explained, that originally the unit of mass of a metal was equal to its numerical monetary value. He discusses the idea of creating a universal coin on page 137:

Chevalier and those of like mind wanted weight to equal value; ideally, names like “franc” would be redundant, and coins would simply be stamped ONE GRAM GOLD.

Few thought such a coin possible.

Marciano argues that “pragmatists” tried to equate and consolidate currencies of and in different countries. The same attempt to use the value that dreams are made of, to equate grams of gold, like that later proposed in 1922 with Troy grains as detailed above. One problem was that other countries used silver, and the US effectively was “bimetallic” using both gold and silver. So how does one equate the value of a dollar in gold and in silver? Perhaps by using atomic  number? It was no less than an attempt to equate dreams and metals. Blowing right by this question JBM argues that:

The first [gold] was only slightly more logical than the second [silver], but one indisputable fact was that gold was a lot more convenient.

A silver dollar was a fair-sized disc of metal—-four times the size of our quarter—whereas a gold dollar was a good bit smaller than our current dime.
If you bought a horse for $180 from someone insisting on payment in coin, you could either lug a ten-plus-pound sack (avoirdupois) of 180 silver dollars
to the stable, or slip into your vest pocket a ten–ounce purse of nine double eagles.”

Then JBM states:

With the war, the Union had suspended payment in specie and gone on the paper greenback, a major reason why some Americans were so anxious for a universal
coin—at the moment they had no real currency at all.

Think about the reality of that statement, when contrasted with the dream values that have been assigned to gold and silver. What is their everyday utility?  Can one eat gold or silver? What makes them “real” as a currency? He goes on:

To have that universal coin be gold was an extra bonus, considering that the United States held vast deposits of it

The simple choice of what metal was used for currency determined the financial value of a country?—-and not its actual creation of goods and services?

The origin of the nickel is discussed, and the fact it was exactly 20 mm (yes, JBM says 2 cm) in diameter and “weighed five grams,” or for those who use and understand the metric system, had a mass of five grams. How is a copper-nickel alloy related back to gold or silver? JBM goes on:

The new five-cent piece has achieved the holy grail of coinage, where value equals weight—a cent for every gram.

And the question is never addressed, but clearly JBM sees this as the imposition of metric dimension and mass on the American public. JBM spends a lot of ink artificially conflating metric system concerns of the late 1860s with the lack of a universal coin. He then argues that the death blow to a universal coin was Germany issuing its own gold-backed currency, the mark.

He finishes the chapter seemingly arguing that currencies are very unified with a somewhat unstated assumption that gold is the unifying factor. He
argues:

There was now, indisputably, one standard of value, which meant that exchange rates could be permanently fixed. Traveler’s checks, a concept
just about to find wide use, could be printed with their value in multiple currencies……

JBM has only a couple of pages that even mention the euro, and only see it in the context the dream of a universal currency. What is strange is that  the US dollar has not been on the “gold standard” since the 1970s, and so what is the basis for his idea that international currencies have become interchangeable and fixed? I’m not even sure why JBM addressed the issue of currency, unless it is to show that it is stable and fixed without the metric system?

Today, currencies are moving much closer to my definition of “the stuff that dreams are made of” with cryptocurrencies like Bitcoin, and after the fork, Bitcoin Cash, Ethereum, Ehereum Classic, and numerous others. They are but a set of bits, represented by voltage values and magnetic fields. They are at best made of imagination, and at worst made of nightmares. It is possible to see them as but an information theory representation of “the stuff that dreams are made of.” In the case of Bitcoin, recent estimates indicate the annual electrical energy consumption to maintain its blockchain is 83 Petajoules. This is about the amount of electrical energy used by Ecuador each year.

There have been other attempts at creating currencies outside of governments. In the 1970s a group attempted to create a currency denominated in “barter points” which as I recall did not end well. Money, even when we define it in terms of the mass of a pure metal, it still is nothing but a number tied only to our imagination.

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I would like to thank Amy Young for her inquiries, and persistently suggesting I write this essay.

A Bridge Too Far?

By The Metric Maven

Mini-Bulldog Edition

The view that “diversity in measures” is a good idea is absurd whether it is stated by George Orwell, or former NIST Director Gallagher.  The metric system was developed because all that “measurement diversity” offers society is at worst an opportunity for fraud, and at best an opportunity for conversion error.

A very important benchmark used to determine the vertical height of a position on Earth is sea level. One would think that in the age of GPS, and the metric system, that a universally agreed upon sea level  value would exist. Alas, it does not. The UK’s mapping agency measures altitude on the Earth with respect to mean sea level using a value determined during World War I at Newlyn in Cornwall.[1] Today this figure has increased by 200 millimeters.

GPS has a spherical “Earth model,” but alas the Earth is not a sphere. It is a lumpy and in-homogeneous solid that looks much like a sphere. Satellites were launched and have provided enough data to create an accurate geometric model of the Earth–warts and all. The model will be accurate within a few tens of millimeters. Combined with ground based measurements, the new model should provide millimeter accuracy. The value of altitude on Earth will not be in terms of sea level, but with respect to the Earth’s center. Currently, European countries each use their own definition of sea level. The new data shows how much sea level variation there is across European countries. Amsterdam’s vertical benchmark will be about 10 mm above the proposed European Vertical Reference System, Helsinki is 210 mm higher and Ostend is 2320 mm lower than the new benchmark. Tregde happens to be very close to zero offset from the new standard.

This farrago of vertical measurement references can have engineering consequences.[2]  In 2003 a bridge was constructed to span the Rhine River, and connect Laufenburg, Germany and Laufenburg Switzerland. Each country began construction on its respective side and were to meet in the middle. The German reference for sea level used the North Sea. The Swiss reference for sea level used the Mediterranean Sea. The two reference values differ by 270 millimeters. The two cities have always seen themselves as a single metropolis, and so they communicated this difference to one another so that it could be taken into account. A problem occurred when the simple conversion had a sign error, and the German side of the bridge was 540 millimeters higher than that constructed by the Swiss. The German side was lowered, and eventually the two sides connected.

With a costly error like that, it would seem obvious that the world should embrace the new single model of our Earth developed using the latest satellite data. The US, Canada and Mexico have all agreed to use a unified geoid-based height system in 2022. The International Union of Geodesy and Geophysics passed a resolution in 2015 to support the adoption of a single global model.

Mount Everest

This sounds all well and good, but often anatomical measurement contests interfere with rational ones. The development of an international standard for elevation could precipitate a “Pluto Controversy” here on Earth. We all know that Mount Everest is the tallest mountain on planet Earth. It is generally accepted to be 8848 meters above sea level. China and Nepal argue over whether the height of Everest should be measured in terms of its rock height, or snow height. The National Geographic Society has its own ideas of how to measure the peak and in 1999 argued it is 8850 meters high.

Chimborazo

When one starts to use the Earth’s center as a reference, considerable change can occur. The peak of  Ecuador’s Chimborazo is a mere 6310 meters above the local sea level, but because of the Earth’s deviation from a sphere, this peak is much farther from the Earth’s center. When using the Earth’s center as a reference point, Chimborazo is over 2 Kilometers taller than Mount Everest. One can only hope the political creatures that inhabit our planet can look past “who’s is bigger” and all agree on a single standard for elevation, but in the past, one country in particular has been incorrigible when it comes to international standardization of measures. We can hope this obstinate attitude is not contagious when it comes to altitude.

[1] New Scientist 2017-02-11 “Vertically Challenged” pp 38-41

[2] Heather A. Lewis (2015) Math Mistakes That Make the News,
PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 25:2,181-192

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