Context and Units

By The Metric Maven

Bulldog Edition

The late Isaac Asimov once pointed out that people often use units alone to imply the magnitude of a dimension. A certain store is only minutes from your house, or a car missed another by inches and so on. Of course if the two cars were separated by 63 360 inches, they then also missed each other “by a mile.” The statement that two cars were separated by only inches as they passed each other is true, but they were not in any danger of colliding.  Using a unit without any numerical magnitude leaves one to comfortably assume a magnitude,  and trust that the person offering said unit is using it appropriately.

Years ago my father sent away for a set of cookware. The price was too good to be true, and the items that arrived were all about 25% of their expected size. I watched a consumer  advocate expose this rip-off on television. The advocate showed that using the cookware was not feasible and in one case the handle would become so hot it would burn anyone who simply used it to boil water. Many moons ago, it was apocryphally claimed that a raffle was held where the winner would get a sports car, such as a Corvette, as a prize. The winner did indeed receive a Corvette, but it was a  scale model worth only a few tens of dollars.

When really large numbers are expressed, such as those in astronomy, one generally ends up with concatenated pigfish such as billions of Kilometers. There are many examples of people who decide to use these large Olde English prefixes with incredibly small “everyday” units, in an attempt, I assume, to make the number something to which the average Jane and Joe can “relate.” As I’ve said before, large numbers are almost impossible to visualize, but with the metric system, their magnitudes can be categorized and metric worlds imagined.

I might ask, as a bit of a trivia question, if the Starship Enterprise, in the original Star Trek series, ever made a voyage that was more than a Zettameter? The answer is, probably yes, but not by much. The maximum extent of the Milky Way Galaxy is about 1000 Exameters or 1 Zettameter. TOS episode #51, titled By Any Other Name, has the Enterprise taken over by beings from the Andromeda Galaxy. The aliens were in the Milky Way looking for planets worth taking over or conquering. Their ship was destroyed and so the aliens duped the Enterprise crew into stopping by and then took over their ship. The alien beings, called Kelvans, modify the Enterprise so that it will only take 300 years to reach their place of origin. The distance to Andromeda is given in Wikipedia as about 2.5 million light-years. The use of light-years is bad enough, but using a Ye Olde English prefix modifier really helps to obscure the distance value. The distance, when written out, is 2 500 000 light-years which does not really help that much. We can calculate the Kelvans would be traveling about 8333 times the speed of light to reach Andromeda in “only” years—ok—300 years. How far is Andromeda from us? Well, in metric it’s about 23.7 Zettameters. The Andromeda Galaxy is about 220 000 light-years across, or about 2.1 Zettameters (2081 Exameters).

With our galaxy about 1 Zettameter in extent, we immediately see that Andromeda is about twice the size of our galaxy. The distance from us to Andromeda is about 24 times the extent of our Galaxy. Now that is rather close—and it’s getting closer—in fact it’s going to “collide” with The Milky Way in the future. But it’s only coming at us at the anemic rate of 600 Gigameters per hour. The distance from the Sun to Jupiter is 778 Gm. At this rate, it will “crash into us”  in about 4.5 billion years. Andromeda’s yearly rate of encroachment is a mere 5.25 Petameters, or 525 Petameters per century. A “light-year” is 9.46 Petameters, and therefore Andromeda is about 23 650 000 Petameters distant.  Andromeda is definitely taking its time getting here at its 5250 Petameters per 1000 year rate. When we use Zettameters  for galactic dimensions (or we could use Exameters and drop the decimal points) it is intuitive how far the two galaxies are separated, and their overall extent. Other appropriate prefixes provide clear context for a reader. Milliards and Milliards doesn’t cut it for astronomy.

We can never voyage more than 1000 Exameters (1 Zettameter) and remain within our galaxy. One could argue that when the Enterprise is on an imaginary voyage only Petameters in distance, it’s a nearby journey, and a voyage measured in Exameters, is a far away journey. Beyond 1000 Exameters, we are outside of our “Island Universe.”  Once again, we could be faced with a lack of magnitude causing confusion. If we accept as proper practice, that one does not go beyond 1000 for each metric prefix, when informally discussing magnitudes, we would expect that a 1 000 000 Petameter journey, would not be considered a “Petameter Voyage.” If we discovered otherwise, we would consider this an exaggeration, or in some cases even fraud.

click to enlarge

Zettameters and Exameters are not just for galaxies, there are other instances in astronomy where they can effectively be used. The May 2016 issue of Astronomy has an article[1] that discusses hourglass shaped lobes that extend for 25 000 light-years either side of our galaxy. Well, just how big are these lobes? A light year is 9.46 Petameters, and they extend about 240 Exameters above and below our galactic disc, with a maximum extent of about 500 Exameters (approximately half the maximum length of our galaxy). These structures are currently known as Fermi Bubbles. They could possibly be jets of material ejected by supermassive black holes found at the center of many galaxies, including our own. The Exameter sized bubble is composed of silicon and carbon atoms.

Recently, Astronomers have located unusual radio bursts “from beyond our galaxy.” These signals are called Fast Radio Bursts (FRB), and one of them, FRB 121102 is located in dwarf galaxy, dimmer than our own, over three billion light years away. But just how far is that?  It’s about 28 Yottameters! Remember our Universe has a diameter
of about 880 Yottameters. 28 Ym is a long way from Kansas.

The metric system is so well-suited for taming and categorizing astronomical distances, it’s a shame Astronomers refuse to use it in their work without Ye Olde English
prefixes, and generally after a light-year value has been alternatively presented. Perhaps Grade School and High School teachers could adopt the use of metric when expressing astronomical distances, and their students in turn might eventually become astronomers, and question why an infinitesimal yardstick the size of a light-year is used to measure the entire Universe. If you are an instructor, and have read this essay, please consider doing so.

[1] Kruesi, Liz “What’s Blowing Bubbles in The Milky Way?” Astronomy May 2016, pp 44-49.

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Related essays:

Long Distance Voyager

The “Best Possible Unit Bar None”

The October Report Three Decades On

GAO Report Edition

By The Metric Maven

The Beginning and The end

In October of 1978 The General Accounting Office (GAO) of the US issued a report titled “Getting A Better Understanding of The Metric System–Implications If Adopted By The United States.” It is a snapshot of the late 1970s solipsistic view of US metrication as the rest of the world converted to the metric system. The report seems very uneven in its views and understanding of the metric system. It has the look of a report by committee where those who wrote each chapter might have been insulated from one another.

The report is clear on asserting that a decision has not been made to convert to the metric system by the United States of 1978. My reading of the 1975 Metric Hearings are in line with that statement. “…the national policy is not to prefer one system over the other but to provide for either to be predominant on the basis of the voluntary actions of those affected.” It is also stated by the GAO that:

“The [metric] Board is not to advocate metrication, but is to assist various sectors when, and if, they choose to convert.” It is also “…to encourage retention of equivalent customary units (usually by way of dual dimensions) in international standards or recommendations;” (1-10)

The methodology used by the GAO was essentially to undertake extensive polling of multiple US industries, and finally the public, about how they thought metrication would affect them. The polls could only measure emotions as their targets of the inquiry. The US had not experienced any metric change and therefore the participants could only provide a visceral viewpoint. Not surprisingly, small businesses believed the disadvantages would outweigh any benefits.

The GAO begins with responses that are congruent with long-time US economic mythology:

Present sizes have developed over the years in the marketplace to meet demand.  … There is little doubt that increased standardization and rationalization could result in benefits, although this objective could be achieved using the customary system.

This is the sort of false equivalence that can be asserted when no specifics are studied. One can imagine a person who currently uses Roman Numerals, and has never encountered Hindu-Arabic ones, might make the same statement.

The beginning of the report seems like a strange loop of inconsistency (pg vii):

The total cost of metrication in indeterminable in spite of various estimates that have been cited in the last decade by various organizations  and individuals.

and two paragraphs later:

However, based on the limited cost data that was available to the GAO and the input from various representatives from a wide spectrum of organizations throughout the country, the cost will be significant–in the billions of dollars.

In a swelling of ersatz democratic pride the report indicates:

Since a decision will affect every American for decades to come, GAO believes the decision, which is to continue with the current policy or change it, should be made by the representatives of the people–the Congress.

The beginning of the report continues its emphasis on what the current policy is and launches into a short history of the metric system. The Adams Report of the 19th century is quickly encountered. The GAO points out:

Adams concluded in his report that the Congress should not change the existing system but should fix the standards for the units. …. He believed that the time had not yet arrived in which he could recommend

* * * so great and hazardous an experiment * * *, as that of discarding all our established weights and measures, to adopt those of France in their stead.

A discussion of Adams’ Report on Weights and Measures may be found here.

The GAO quickly mentions that the Mendenhall Order was “an administrative action.” In light of their democratic stance, that only Congress should make changes, one might question their view of the validity of the Mendenhall Order. The technical superiority of the contemporary 19th century metric standards and the failure of the British ones was not mentioned as the driving force for this ad hoc legal patch by Thomas Corwin Mendenhall (1841-1924) which Congress ignored.

The 1971 National Bureau of Standards Report  A METRIC AMERICA, A Decision Whose Time Has Come is mentioned with this interjection:

A major area of controversy was the impartiality and completeness of the NBS metric study. The critics, which included former members of the study group and its advisory panel, contended that NBS was biased in favor of conversion while performing the study and reporting the results.

Then an interesting historical tidbit is related:

Metric conversion legislation was passed in the Senate in 1972 providing for a predominantly metric America within a 10-year period. It was introduced into the House where no action was taken.

This may be the closest the US has come, from a legislative standpoint, to becoming a metric nation.

The GAO report generally interprets the metric system through Olde English measurement usage, and not as a new and upgraded way of implementing measures. The report states “Millimeters and centimeters would be used instead of inches and feet.” (2-2) They then offer an inch/centimeter ruler as an example. Think about the statement and it should be clear that millimeters are not like inches or feet, not even with a shoe horned barleycorn. The reader is told that “The metric system is decimal because prefixes are used to indicate multiples and sub-multiples of 10. The majority of metric prefixes use 1000 and this is clearly the best practice for implementing metric quantities. Yes, this practice was known and encouraged in 1978, see the essay: Who Says!?. The GAO has an objection to the pascal that is frivolous: “The major objection to the pascal is that it is too small of a unit with which to work. It takes about 1,000 pascals to equal 1 pound per square inch.”  So a Kilopascal would be about 1 pound per square inch?—and this is a problem how? Just use Kilopascals. That’s a unit.

A more legitimate complaint is that a pascal is rather abstract (a view that I share). This can be remedied easily by using newtons per square meter instead of pascals.

Chapter 3 of the Report highlights ascribed advantages and disadvantages of metric. The initial positive aspects related by the GAO have been covered by Pat Naughtin many times: 1) Conversion would provide opportunities for worthwhile changes [needed industrial reforms to implement efficiency] and 2) Conversion would stimulate the economy. There is no discussion of the advantage of using millimeters versus centimeters, no discussion of whole number usage with milliliters, and grams and how that could simplify matters, just vague platitudes.

The ascribed disadvantages of the metric system begin with an appeal to the mythology of technical Darwinism, and an appeal to the “practical” over the theoretical:

The Customary System is a better measurement system

The U.S. customary system is tailored to meet practical everyday needs of human beings. It is firmly established, and is not obsolete or complex. It came into being by natural selection. Although use of the metric system has been legal in the United States since 1866, the customary system survives because it meets a need. …. “

The same old Goldilocks pseudo-arguments about Ye Olde English measures are paraded about:

The meter, about 4 inches longer than the yard, is too great a length for general application, and the gram is too small to be practical. Metric names are more difficult to say and remember.”

Without a pottle of porrige in an 18 barlycorn wide bowl for Goldilocks, how could she fathom what 250 mL might be?

The Report has no clear conclusions on US trade, as that is the answer which came back from the questionnaires sent to representatives of the Fortune 500. The GAO surveyed people in Business, and discovered that:

“Few of the respondents knew the U.S. policy on metric conversion. As the following chart shows, almost half of the respondents believed conversion to be mandatory.” (5-13). and “Few believed the Government should legislate or enforce conversion.” (5-21).

There are many other chapters in the 1978 GAO Report, but the information they contain would be best examined in separate essays. Here we will look at the overall view of the GAO toward metric conversion. We will now skip to the end of the Report and look at the GAO conclusions for an answer. Chapter 30 of the Report examines lessons learned by foreign countries. If the US decided to become metric, here is the GAO’s list of what we should embrace:

— A firm Government commitment to convert is necessary.

— A central body should be established early to plan and coordinate the conversion and inform the various sectors of the economy and the public of metric activity.

— A well-developed plan and effective coordination by industry and all sectors of the economy must be accomplished.

— A voluntary conversion must eventually become mandatory through laws and regulations, etc., in order to complete the metrication program.

— Overall and specific target dates must be used.

— The public must be adequately informed and educated, and responses must be made to consumer concerns because conversion of the retail sector is most difficult.

— Letting costs lie where they fall can be adopted in whole or in part.

— Government purchasing power can be used to propel the conversion.

— The conversion of certain sectors, such as in sports and weather forecast, can aid in metric education.

— Periods of dual marking should be kept to a minimum

— Hard conversion of products is more desirable than soft conversion whenever practicable to obtain benefits.

I was quite surprised. The list makes for a set of very good guidelines for the most part. I would not allow dual marking at all. Whoever wrote this section has a good understanding of the problems involved. What I was not prepared for was a very self-introspective view:

Another difference between these countries and the United States is the type of governments. Basically, the foreign countries have a parliamentary type of government in which the executive is also the leader of the legislative branch. Two of the foreign countries only had to change national laws to effect metrication. Australia, with six State governments, and Canada, with ten Provinces, had to change some local laws. The changes appeared to be well coordinated. The United states has a Federal Government and 50 State governments. Metrication would necessitate revisions in the laws of each of these government entities. Because of the differences in government, the other countries’ decision making process, including changes to laws, regulations, ordinances, and codes, is less complex than the United States.” (30-4)

The Report points out the frozen nature of our Republic:

Other countries established their metric organizations early in the conversion process. One month after Australia enacted its metric legislation, the metric board had its first meeting. In New Zealand the metric board had its first meeting 10 months after the decision to convert had been made.

The Metric Conversion Act of 1975 provides for a U.S. Metric Board to coordinate the voluntary use of the metric system. …. However, the Metric Board had not become fully operational at the time this report went to print, more than 2 years after passage of the act.” (30-7)

In Chapter 31 the GAO exposes the misuse of the word voluntary in 1975:

In other countries that are converting, “voluntary” means that the various sectors voluntarily agree on how and when to convert within the over-all parameters of a national commitment to convert to the predominant or sole use of the metric system during a specific period of time, usually within 10 years or less.  In other countries voluntary was not a choice of whether to convert or not, as in the United States.

In the 1975 metric hearings, this confusion about the word “voluntary” was used to disingenuously equate the legislation passed by the US Congress with that of Australia and other countries.

The GAO Report then provides a side-by-side summary of the differences between the US approach and other countries. Here I reproduce them in full:


The idea that “we tried to go metric” in the 1970s is simply ludicrous. What is most interesting is the fact that the GAO Report, which starts out as a very anti-metric document, ends by explaining what should be done for the US to become metric. It also lays out the hurdles involved with the legislative molasses known as our government that keep any meaningful reform from occurring.

The GAO report is a 767 page tome of a document. It contains many interesting metric stories which I plan to focus on in future essays. This essay demonstrates that the anti-metric GAO Report is much more complex (and muddled) document than it is generally thought to be. It has some information that is quite relevant to our current zero-kelvin metric situation.

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