Milliards and Milliards


By The Metric Maven

Bulldog Edition

A seminal advance that allowed for the development of the modern world seems never to be consciously noted by most persons. That advance was when people began to identify groups of objects with the abstract idea of numbers. The concept that 1, 2, 3, 4 and so on could be mapped with a one-to-one correspondence to a group of skins or fruit or whatever, took a considerable amount of abstraction, and can be counted as one of the great conceptualizations humans embraced.

Francis Galton (1822-1911) is reported to have made this observation about a tribe in Southwest Africa:

When inquiries are made about how many days’ journey off a place may be, their ignorance of all numerical ideas is very annoying. In practice, whatever they may possess in their language, they certainly use no numeral greater than three. When they wish to express four, they take to their fingers, which are to them as formidable instruments of calculation as a sliderule to an English schoolboy. They puzzle much after five, because no spare hand remains to grasp and secure the fingers that are required for units. Yet they seldom lose oxen; the way in which they discover the loss of one is not by the number of the herd being diminished, but by the absence of a face they knew.

I don’t know if Galton felt sanctimonious about this lack of numeracy, but if he was, it was not particularly justified. Isaac Asimov (1920-1992) was the person who led me to this realization. In his book Fact and Fancy he states:

It was 1300 A.D. before the word “million” was invented. Until then, the largest number word was “myriad,” which was Greek for 10,000. Even Archimedes, in calculating the number of poppy seeds in the entire Universe as he knew it, used expressions meaning “myriads of myriads of myriads. …

It was only seven centuries ago that a word to describe 1 000 000 was created, which is equivalent to the modern metric prefix Mega—and adopted only in 1960.

In 1871, Fredrick A.P. Barnard (1809-1889) gave a speech which was expanded into a book called The Metric System of Weights and Measures. Barnard had done his best to make the metric system the exclusive system of measure in the US, but Charles Davies managed to derail this initiative. In his book Barnard presents this table:


The largest metric prefix used with a meter is a myriametre. The myriad apparently continued to remain an upper value limit for the everyday person. This is true even though the word million existed at that time, and Friedrich Bessel (1784-1846) determined in 1831 that the star 61 Cygni was about 98 Petameters from Earth, or 9 800 000 000 000 myriametres. The early metric system was provincial and still mired with numerical magnitudes from the time of Archimedes. It would not be until 1960 when a prefix larger than myria would be adopted, which is of course Mega. The prefixes Giga and Tera were also adopted that year. The use of myria as a prefix, despite its ancient origin, seems to have been eschewed without much difficulty, and the better by 1000 approach began. The seldom used prefix cluster around unity has proven much more difficult to eradicate.

While the numerical value for the word million was agreed upon after 1300 A.D., a fork occurred when English words were chosen for larger numbers. The word billion is used for Giga in the short scale; in the long scale, the word milliard is used. The word billion is used for Tera in the long scale, but it is called trillion in the short scale. The history of the changing values of words used to describe large numbers is considerable and meanders. This prefix table provides succinct documentation of the differences between short and long scale words:

Metric-Prefixes-Long and Short Scale
Cover of New Scientist November 8-14 2014 which describes the Rosetta Probe
Cover of New Scientist November 8-14 2014 which describes the Rosetta Probe as travelling 6 billion Kilometers and not 6000 Gigameters . The distance to Pluto is about 5419 Gigameters. (click on image to enlarge)

Douglas Adams’ The Hitchicker’s Guide to The Galaxy has a computer called the Milliard Gargantubrain, which shows that long scale usage is still with us. The use of the short and long scales has allowed for very poor literary numerical expression, which was long ago forbidden in the metric system, but is ignored when long and short scale words are combined with metric prefixes. The statement that a celestial object is one million Kilometers from Earth does not meet with objection, but if it is a KiloMegameter away, that would be laughable. The proper term Gigameters would probably also cause heartburn for the provincial literary crowd who are proudly literate and willfully innumerate, but it is the most succinct prose expression, and does not contain any numerical ambiguity. If we have a billion meters, it could be a Gigameter or Terameter. Carl Sagan (1934-1996) used the term billions and billions. But which billion? Alternatively he could have said milliards and milliards, which would have been unambiguous by comparison—even if it is a metaphor.

The long or short scale words are not prefixes, they are improper prefixes which at worst have dyadic values (i.e. two different values for billion and billionth) and at best are redundant. Long and short scale words should not be combined with metric prefixes to present a numerical value. They only promote innumeracy. Does a milliardth of a nanometer improve one’s understanding of magnitude? Attometer is shorter and clearly and unambiguously defined and has a metric context. When I see a headline like: 35 years and 18 billion kilometers later, NASA’s Voyager approaches exit from solar system, I can only do a face-palm. Is this 18 Terameters or 18 Petameters? 18 000 Gigameters is probably more meaningful.  Until we are able to reform our prose, and make them all metric, we have little justification to believe that we are clearly more numerically advanced than the Southwest African tribe described by Dalton in the 19th Century.

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Evanescent Measurement Policy

By The Metric Maven

Bulldog Edition

One day I was visiting a production plant which creates and molds materials for electronic components. I noted they were measuring the length of the component in barleycorn inches with a few zeros at the front of the decimal. The data was being entered by hand onto a paper table held with a clipboard. I indicated that it would be wiser to measure in millimeters so the data didn’t contain so many leading zeros and provide such an easy opportunity for error—and there would be less redundant digits to write down. They next measured the mass of the object in grams with a scale that went way way down into the microgram range. It also had a large number of leading zeros to the right of the decimal point.

After they had obtained the mass (in grams) and volume (using inches) they computed the density or mass/volume. I was told it was expressed in grams per cubic centimeter. I did have an attack of the vapors realizing they were using pigfish measurement, and then converting to metric, and worst of all used cubic centimeters. The metric system has a nice unit for volume called the liter. A cubic centimeter may be a volume dimensionally, but it is a milliliter which is an appropriate volume unit in my view, and identical to a cubic centimeter.  The cc is a part of the cgs system, and has long been abandoned.

Along the way I was shown the dielectric material in granular form before it undergoes processing for later fabrication into electronic parts. The materials chemist was pleased to tell me that they were all created to be about 100 microns in diameter. I cringed slightly, and then said “you mean micrometers?  Micron is a term from the 19th century and is not expressive.” Little was said after my comment and we moved on.

During a discussion about part fabrication difficulties, mils (thousandths of an inch) were bandied about constantly. I finally asked about the surface roughness of the material. I had determined it could contribute to the problems they were having. I was given a value in microinches. A metric prefix with Ye Olde English?—sigh. I could only reply with “I have no idea what size that is.”  I was then quoted a value in microns. Again with the microns? I wanted to do a face-palm, but refrained.

I have been on many tours of engineering and production facilities. It was only when I was at this particular establishment that I realized, I’ve never toured ANY company that has a measurement policy or measurement coordinator. It is not discussed, contemplated, seen as a concern—nada. When I bring up metric measurements, it is as if my statements and questions vanish into a black hole of indifference.

A week or so later another engineering client sent me a drawing which has a part made from a similar ceramic material. The dimensions on the drawing were all in inches, but in the notes, the metalization thickness on the part was called out in micrometers. The second note described the density of the part in grams per cubic centimeter (g/cc). I just stared at the drawing, and thought about my recent visit. Inches, micrometers, and the cgs unit g/cc all on the same drawing? Three different measurement types on one drawing. Why does this strike only me as bad engineering practice?

Density is mass per unit of volume. The density value on the drawing was 3.73 g/cc +/- 0.1%. In SI the milliliter (mL) would be an appropriate volume which would be 3.73 g/mL +/- 0.1%.  The cgs/SI/Ye Olde English mixing of units has become so accepted in the US that it goes without notice apparently. As I said, thus far I’ve never seen a company that has a “Measurement Coordinator.”  This would be a person who would help create a measurement policy and apply Naughtin’s Laws as well as the rule of thousands. That person would examine, simplify and coordinate measurements to maximize the understanding of data presentation and reduce possible mistakes—and implement the metric system. It never occurs to business management that measurement coordination could be a cost or efficiency issue.

I’ve always been tasked with design work, and never anything which would involve setting measurement policy. Pat Naughtin was the first to discuss the fact that NASA’s measurement policy is “change to metric, if you want to, use centimeters and/or millimeters, if you want to.” In other words NASA simply didn’t see measurement policy as a problem which is in need of any coordination or effort. This means they don’t see it as a problem at all, and so they do not have a measurement policy. Unfortunately the current former head of NIST also has a “do your own thing” measurement policy.

In the back of my mind I wondered what the reaction of one of my clients might be if I brought up the possibility of a measurement coordinator. I had concerns about it, and the next time I was on the phone with Sven, I asked him what he thought the reaction might be from management and a group of engineers.

Sven: “They would not see any need for it, and they would look at you as if you were wearing a gunny-sack with a belt and sandals, had a long beard, and were holding a sign which read REPENT!”

MM: “I was afraid you would say that.”

Every engineer I know believes they understand measurement units and measurement. There is no need for a policy, we “learned” it all in college. Some co-workers have indicated to me that metrology is what people do who really don’t have any engineering talent. You can imagine how my psyche greeted that notion. I’ve met way too many “engineers” who embrace measurement methods which are ad hoc and unsound. They chase down blind alleys of impromptu measurement and waste time. But as long as a product “gets out the door” and appears to work—there is no problem here—move along.

Isaac Asimov in an essay called Forget it! pointed out that often measurement units that should have been abandoned long ago, continue to be used. The units are also only imperfectly forgotten, which leads to an even more chaotic usage. The cgs system was abandoned many years ago, but the inertia of unrestricted usage propels them into the future.

I spoke with a medical researcher at a block party last summer, and mentioned metric. He proudly stated he uses metric in his work and cited the cubic centimeter. I pointed out that the cc was part of centimeter-gram-second system, and the cgs system is not compatible with SI. He should be using milliliters. He looked at me as if I was daft, and going out of my way trying to be annoying.

The technical drawings I received with cc’s on them, show an incomplete ability to forget cgs, as do the density measurements performed by another client. Recall they first started in inches with a long number of zeros past the decimal point, then converted the inches to cc’s, and then finally computed grams/cc for a density. The inch is Ye Olde English, the gram is SI, and the cc is cgs. Both the inch and cc should be forgotten and eschewed; but the 10th, 14th and 19th  centuries live on in the US, never forgotten or allowed to be. They are the products of the “unexamined engineering life.”

I wholeheartedly agree with Pat Naughtin’s call for measurement coordinators and measurement policies in industry. As he himself pointed out, often questions of measurement are considered so minor, that scales and other measurement instruments are chosen and ordered by secretaries or interns. To show they are giving the company the most value, they order dual or multiple scale measurement devices. This perpetuates the farrago of units in use.

NASA demonstrated itself to be immune to the notion of measurement coordination even after the Mars Climate Orbiter disaster. The much less well-known DART “mishap” even appears to have been obfuscated with a mantle of junk prose. It was more important for NASA to deny there is a need for measurement coordination, than to address the problem. I really have no idea what it might take for the technical community, educators and the public to realize that measurements are the real currency upon which our modern technical society operates, and there is a need to coordinate and simplify them. I can only hope for the US metric coma to finally recede, the country to wake up, and then finally address the problem.

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