Category Archives: Metric Reform

Long Distance Voyager

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By The Metric Maven

Bulldog Edition

When it comes to distance, the larger metric prefixes are generally neglected. Astronomers feel justified in using Astronomical Units to describe distances within the solar system. When distances become large enough, the ubiquitous light-year is then employed with great relish and awe. One of the arguments offered for the absence of the larger metric prefixes in astronomy, is that the distances are just too large, and the metric system is overwhelmed. The distances are just too astronomical for the metric system to handle!—or even convey their vastness! Generally, this manner of argument masks a provincial desire by a specialty of engineering or science to have its “own” special measurements. It is also stated that people can only relate to Km and smaller metric measures because the other distances are outside of their everyday experience.

I have had the privilege of working with some incredibly talented engineers, including the Engineer, who designed the high gain dish antenna which resides on the front of the Voyager spacecraft. His name is Michel, and I once shared an office with him. The Voyager antenna would at one time have been within millimeters of Michel, it was then moved about 4000 Kilometers away from him so it could be launched into space on September 5, 1977 (1977-09-05). It ascended from our planet, which has a circumference of 40 Megameters. Michel’s antenna then passed the orbit of the moon which is about 384 Megameters from Earth. One could argue that the Voyager spacecraft was now in the realm of the solar system. At that point, its distance from the sun might be a more meaningful reference point to describe its distance from us. The Earth is approximately 150 Gigameters from the sun.

Gigameters is a useful length to describe the distances of our planets from the sun, as well as the current location of the Voyager spacecraft (2014-04-04). Michel’s antenna is part of the singular human-constructed object we call Voyager 1, and is further away from the Earth than any other space probe in history—and likely to remain so. Despite the fact that Voyager is now beyond our solar system, its distance is still readily describable in terms of Gigameters. Below is a table of planetary distances and Voyager 1 and 2:

I don’t recall any astronomers ever using Gigameters in school or on television, even though it is a convenient unit. Astronomers define their own “yardstick” which they call an astronomical unit. This astronomical unit is defined as the distance from the earth to the sun, therefore 1 AU = 150 Gigameters. I don’t see why modern astronomers, by which I mean astronomers who have been born after 1960, don’t use Gigameters instead. The prefix Giga was officially adopted in 1960. A Gigameter is certainly as convenient of a unit as an AU, and it’s tied to the meter, which is the universal measurement length used by science, and by 95% of the worlds population. When a person, even an American, sees the symbol Km, they see kilometers. The lack of use of the designation Gm for Gigameters by astronomers makes it unfamiliar and seemingly awkward. It is only the lack of general use which makes this so.

When Astronomers begin to describe distances outside of our solar system, they generally turn to another unit they coined which is unique to astronomers—the light-year. Wikipedia gives the definition of  a light-year as:

1 light-year     = 9460730472580800 metres (exactly)

This is where, if I were forced to write it in meters, I would use the three digit space convention to parse it. The three digit grouping allows a person to identify the appropriate metric prefixes with ease:

1 light-year     = 9 460 730 472 580 800 metres (exactly)

This expression allows one to immediately recognize the metric prefixes as one moves from right to left as: one, Kilo, Mega, Giga, Tera, Peta, and determine that 1 light-year = 9.461 Petameters (Pm). In my view the light-year is more of a “gee whiz” measurement metaphor than an actual length. It is like the kilowatt-hour. There is a metric prefix which is of sufficient magnitude to describe distances which have magnitudes in terms of light-years and it is Peta. The hypothetical Oort cloud is believed to be about 7.5 Petameters away, which when compared with stars, it not  far away.

Almost everyone knows that alpha-centari is the star closest to Earth (other than the sun). It is 4.366 light-years distant. This is 41.4 Petameters. So even when we are discussing the distances to stars, there is a sufficient metric prefix. The light year is not required, at least not after 1975, when Peta was adopted as a metric prefix. Here is a list of nearby stars, and a more distant one also in Petameters:

Constellation of Orion Betelgeuse is the upper left star which is about 6 Em from Earth. Rigel is on the lower right and about 8 Em from Earth — Click to enlarge                    (Wikimedia Commons)

Betelgeuse is a red giant which is in the upper left corner of the constellation Orion. On a clear night in Montana, when I lived far away from the city lights, I could clearly see its red color. Stars beyond Betelgeuse are at distances that may require the introduction of another metric prefix.  This would be the prefix Exa.  One could categorize stars which are “near” earth as those up to 1000 Pm and those beyond 1 Em (Exameter) as “far away” stars. This would make Alpha-Centari, Barnard’s Star and Sirius all nearby stars. Far away stars would include Betelgeuse (6.1 Em) and Rigel (7.7 Em). The farthest currently known star which is still inside of the Milky Way Galaxy is  UDF 2457. It is 558 Em distant.

When we approach the dimensions of the Milky Way Galaxy, we may want to describe the distances from the galactic center. The diameter of our galaxy dwarfs the distance from the sun to Betelgeuse. It is 1 000 000 Petameters across or, shifting metric prefixes, is approximately 1 Zettameter (Zm) in extent. From this information, we know that no star within our galaxy is more than a zettameter away.

The Andromeda Galaxy is 24 Zm from Earth and is visible with the unaided eye.                      (Wikimedia Commons)

Interestingly, we can directly see a distance which is much farther than the dimension our galaxy with the unaided eye. The nearest spiral galaxy is Andromeda, and it can be viewed with the “naked eye.” The Andromeda Galaxy is 2 540 000 light-years away or approximately 24 Zettameters (Zm). This is rather close. It is only 24 times the diameter of our galactic disk. The Andromeda galaxy is expected to collide with our Milky Way Galaxy in 3.75 billion years and form a large elliptical galaxy. Andromeda is not the nearest galaxy overall. The Sagittarius Dwarf Elliptical Galaxy is actually a satellite Galaxy of the Milky Way, that is, it orbits our galaxy. It is only 0.77 Zettameters from our galaxy (or 766 Exameters). This places it just a couple of hundred Exameters beyond the farthest known star within the Milky Way Galaxy.

Here is a short list of local group galaxies which are over one Zettameter away:

The Sombrero Galaxy is 265 Zm from Earth (Wikimedia Commons)

Sextans B is near the end of what is known as the local group of galaxies. The local group encompasses a diameter of about 100 Zettameters (Zm). Clearly there are lots of galaxies which are further away, so which one is the farthest known? The current candidate for the furthest galaxy is MACS0647-JD which is a whopping  125 825 Zettameters (Zm). We can see that we are well beyond a 1000 difference. Has the metric system let us down because of this astronomical distance? No, it has not, at least not since 1991. In 1991 both the Zetta prefix, and the Yotta prefix were added. The Yotta prefix allows us to write the distance to the farthest confirmed galaxy as 126 Yottameters (Ym). The end of the observable universe is approximately 435 Yottameters (Ym). The diameter of the universe is 870 Ym. Astronomical distances do not crush the metric system. There is no need for astronomers to resort to a light-year or AU or parsecs to describe astronomical dimensions. The metric system can in fact be useful to classify astronomical distances. For instance:

click to enlarge
Neil deGrasse Tyson — Host of Cosmos

The latest incarnation of Cosmos has been interesting to watch, but I can only wince when I hear Neal deGrasse Tyson use miles, billions of kilometers, astronomical units, and light-years to describe the cosmos. This archaic measurement usage seems like a lack of respect for the metric system on the part of the Cosmos producers. It is 34 years after the original series was aired. When the original Cosmos aired, the Zetta and Yotta prefixes had not been added to SI. One could see why metric might not have been invoked. Indeed, SI was not large enough to encompass the universe, but like the universe, it expanded. Unfortunately, the root cause for the lack of the metric system in Cosmos could possibly have an even less desirable origin—it could just be unawareness. It is even possible it is the product of a culturally encouraged unfamiliarity. This culturally sanctioned ignorance, if that is the root source, was fortified at the same time as the first airing of Cosmos in 1980. It was in that year that Ronald Reagan quashed any possibility of measurement reform in the US, by disbanding the metric board. This disbanding was an attack on modernity and efficiency, mantled in a red herring of cost savings. It was a narcotic of intellectual flattery perpetrated by a cultural embargo, which has numbed the minds of the American public to the spectrum of metric prefixes, and in turn, it has cost lives. If there is another edition of Cosmos 34 years from now, I can only hope, that by then, it uses the metric system.

Related essay: Neil deGrasse Tyson and The Metric System

This essay was edited on 2016-10-15 to conform with The Elements of Bile.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page and contribute. Also purchase his books about the metric system:

The first book is titled: Our Crumbling Invisible Infrastructure. It is a succinct set of essays  that explain why the absence of the metric system in the US is detrimental to our personal heath and our economy. These essays are separately available for free on my website,  but the book has them all in one place in print. The book may be purchased from Amazon here.


The second book is titled The Dimensions of the Cosmos. It takes the metric prefixes from yotta to Yocto and uses each metric prefix to describe a metric world. The book has a considerable number of color images to compliment the prose. It has been receiving good reviews. I think would be a great reference for US science teachers. It has a considerable number of scientific factoids and anecdotes that I believe would be of considerable educational use. It is available from Amazon here.


The third book is called Death By A Thousand Cuts, A Secret History of the Metric System in The United States. This monograph explains how we have been unable to legally deal with weights and measures in the United States from George Washington, to our current day. This book is also available on Amazon here.

Metric Esperanto

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By The Metric Maven

When I first began work as an Engineer, much measured data was still read from instruments, and then written by hand onto paper. What I noticed when presenting numbers to other engineers was that there would be a constant questioning. Had the number after the decimal point been switched, or  was the number written down wrong? Did my technician or myself actually write down 5 whereas the number was 2. A very talented older engineer with whom I worked, told me he had figured out how to deal with that problem. It was the early days of computers, so he would take the handwritten numbers, type them into his computer, and make a lovely table. This poetic license has no effect on the accuracy of the numbers. It only changed the technical reviewer’s perception of them. Only within the mind of those evaluating the numbers would it produce a modification.

Hand Taken Laboratory Data (circa 1982)

When the numbers were put into computer typefaces, even with dot matrix output, there was an immediate assumption by others that the numbers had to be right. Every time my friend did this, he was able to sit down and talk about the data without the constant questioning about the accuracy of the numbers–yet nothing material about them had changed.

Reflecting on this made me wonder about the seeming desire to use excessive decimal points. Pat Naughtin pointed out that the use of integers, or simple numbers, as he often called them in his lectures, increased the ease with which a person’s mind could compare numbers. Why is simplicity often unnecessarily sacrificed for complexity when creating tables of numbers? This is often done by persons who are in vocations that are heavily number based. Chemistry Professor Jeffrey H. Williams has written a monograph called Defining and Measuring, subtitled The Make Of All Things. It was published in 2014.

For instance, if you look at a table he presents of ancient Mesopotamian measurement units, the comparisons are in my view rather muddled:

For instance the Grain seed is 2.7 mm, but the next size is 1.65 cm?–rather than 16.5 mm? Why switch to centimeters in this case (or in my view ever)? I believe this table is for comparison purposes, and a more meaningful presentation could have been accomplished by attempting to invoke Naughtin’s Laws. Do we really know these ancient units to micrometer precision? The value 2.7 mm looks authoritative, and 16.5 mm also looks very authoritative. It says Modern Metric Equivalent, but wouldn’t these numbers, in their contemporary times, that is ancient Mesopotamia, have had uncertainties that were larger than 700 to 500 micrometers? One could actually use millimeters and meters up to the kilometer equivalent and separate them by prefixes:

Do we believe numbers are more accurate if we see decimal points? When comparisons are made, simple numbers are the easiest for the mind to readily compare, but sometimes large dynamic ranges can make it difficult to use pure integers, and maintain a single unit.

Williams makes this assertion in his text:

The Ancient Chinese used (and modern Chinese still use) a foot as their fundamental measure of length.

Then he goes on to state:

“…that the length of the ancient Chinese unit of measurement, the foot, increased from 0.195 m to 0.308 m over the last three millennia.”

Beyond my surprise at Williams’ assertion that the foot is still used as a fundamental length in China (I would like to see some documentation) I could not see why he didn’t say: “the foot, increased from 195 mm to 308 mm over the last three millennia” rather than introducing a decimal point with a leading zero. Does 0.195 meters seem more precise and accurate than 195 mm? Why did he introduce the decimal version? Was there a psychological reason more than a measurement presentation reason? I have no idea, but I’ve noticed this manner of numerical change in many other contexts.

Williams appears to gush at the succinct nature of the metric system, but does cause me a moment of concern when he uses the phrase “language of science”:

In fact, today we have seven base units which may be combined to explain every known scientific phenomenon, and which would be used to comprehend scientific discoveries that have yet to be made. That is, it is through these seven base units that the true universal language, the language of science is formed.

Later Williams discusses the oft-cited Mars Climate Orbiter metric/Ye Olde English disaster under the heading: The consequences of mixing units.

In Chapter 8 Williams finally sets off some real alarm bells of concern in my mind:

Systems of units and the ability to convert between different systems of units; for example, to convert from units in the British Imperial System of units to SI units is something that is no longer taught to science students. This is a great shame, as the different systems of units are only dialects of the single universal language of science, and an inability to communicate with people speaking these different dialects can limit
a scientist’s world view.

The lack of a proliferation of measurement units could limit a scientist’s world view??? What a strangely “new age” type of statement for a scientist to make.

Williams goes on to argue that the cgs system of units is still: “…needed so as to facilitate reading of the vast and important literature published in this area of science since the early-19th century.”

I will not go into technical details, but the lack of uniformity in electromagnetism, has caused nothing but headaches, and I would far rather see the “vast and important literature” from the nineteenth century either rewritten with modern notation and units, or left for historians to puzzle upon the gaping incompatibility between cgs and SI electromagnetic units.

The final chapter of the monograph, Chapter 13, is entitled: Dialects of the Single Language of Science. This is where the professor seriously jumps the shark in my view. He states that the metric unit of pressure, the pascal, is just too small, which precipitates large numbers:

For example, the pressure in your car tire would be about 340 000 Pa…

Well, how about 340 kilopascals? Is this really a problem? Just use an appropriate metric prefix. This number seems large.  In the U.S., most people set the pressure in their tires, to about 220 kilopascals (32 PSI). Perhaps there is a difference between a tire and a tyre?

Williams then details scientific and engineering “rules of thumb” that have been developed which are not SI and how their loss would be undesirable.

These are all expressions of the same piece of information, but expressed in the various dialects of the single language of science. In dialects which are useful for particular groups of technicians and scientists.

This is pure and simply an apologist’s rationalization for a proliferation of archaic units, without any good reason. It is an untenable argument for unit proliferation. Unit proliferation and poor definition were some of the reasons the metric system was developed in the first place. Then a flood of rationalization is offered by the author:

Such varieties of units exist for sound technical reasons: convenience in specialist branches of science, or convenience or facility of use in certain ranges of pressure, or because one profession refuses to change to another system of units, or because there is such an investment in technology that any change would be too expensive. The medical profession will, for example, not move away from using mmHg for blood pressure measurement, which is convenient for them and a sufficiently precise measurement for their patients, but this is not the case for the vast majority of physicists who gave up using mmHg as a unit for pressure early in the last century.

However, the question we have to ask ourselves is whether there is anything to be gained by attempting to force a large body of professionals to give up a system of units with which they have become familiar over many generations? There is certainly the possibility of serious adverse consequences arising from such a move. It would be far better to encourage the ability to use and convert between many of these systems of units—to celebrate the diversity of the dialects of the single language of science. A scientist or a technician who can convert between these units will be someone who will truly understand the science underlying the phenomenon, and will be less likely to make foolish errors; one dreads to imagine the consequences of the medical profession or drilling engineers getting their mmHg, their pascals and psis [sic] muddled up.

Comprehending these various means of expressing pressure, and being able to convert or translate between them is a great way of learning some basic science. Indeed, this was the reason that the Emperor Napoléon I mocked the decimal Metric System and re-introduced the old familiar, non-decimal units. The Emperor correctly thought that thinking only in factors of ten limits one’s perception of nature. There is more to science than being able to divide or multiply by ten.

Celebrate the diversity of the dialects of the single language of science‽‽‽ Where have I heard such tortured prose before?  Oh yes, the absolutely indefensible reply offered by the head of NIST, when he rejected the We The People metrication petition. Dr. Gallagher argued that if measurement units are a language, we are bi-lingual and we should celebrate this measurement diversity.

Then Williams appeals to technical Darwinism, and some strange idea of heirloom units to further his rationalization:

The present SI is based on a beautifully coherent model of fundamental physics, but that does not mean that every measurement made everywhere on Earth should be made using only this system of units. There is merit to be found in the various nonmetric systems of units—otherwise they would not have evolved and would not have lasted as long as they have.

So, in Dr. Williams chosen field of Chemistry, would it make sense to also make certain that students know all the alchemical names for chemical compounds?—and if they don’t exist—create some? After all, the names must have utility, they’ve been around along time and also evolved. Flower of Antimony, Liver of Silver, Sugar of Lead, Lunar Caustic, how can one truly understand chemistry without knowing how to convert these names to and from the modern ones?

By now you may be asking yourself, why on earth is the Metric Maven getting so worked up about some small monograph written by a Chemistry Professor. Well, this is a fairly special Chemistry Professor. In the author’s bio of Jeffrey Huw Williams, which accompanies the monograph, it states:

Most recently, 2003–2008, he was the head of publications at the Bureau international des poids et mesures (BIPM), Sèvres. The BIPM is charged by the Metre Convention of 1875 with ensuring world-wide uniformity of measurements and their traceability to the International System of Units (SI). It was during these years at the BIPM that he became interested in, and familiar with the origin of the Metric System, its subsequent evolution into the SI, and the coming transformation into the Quantum-SI.

Yes, he was in a more influential position than the head of NIST, Dr. Gallagher. Williams was with BIPM, and is now seemingly arguing against the complete and unique adoption of SI. He was also the head of publications at BIPM, and almost certainly had input on style. In his monograph Williams is making the same poetic, as opposed to scientific arguments for “units as a language” which the head of NIST did. Here is Dr. Gallagher of NIST’s words:

if the metric system and U.S. customary system are languages of measurement, then the United States is truly a bilingual nation.

We measure distance in miles, but fiber optic cable diameter in millimeters. We weigh deli products in pounds, but medicine in milligrams. We buy gasoline by the gallon, but soda comes in liter-size bottles. We parcel property in acres, but remote sensing satellites map the Earth in square meters.

Metrology as language is the most inappropriate simile I can imagine. The length of a meter is not a poetic interpretation—no other base unit of length is needed. If SI is not flexible enough, then it should be augmented, but I’ve never encountered a situation where the seven base units which Williams celebrated earlier in his monograph have not been sufficient, when paired with the metric prefixes.  The metric system is already beautiful, expressive and mostly succinct. The introduction of barleycorn lengths and poetry will only undermine the reason SI was developed originally. Please, leave the poetry and the endless interpretation of same to poets, and leave measurement as a unique set of seven singular and immutable base units, appropriately scaled with metric prefixes, to be used by all of engineering and science, along with the butcher, the baker and the candlestick maker, as their one and only description of the world.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page and contribute. Also purchase his books about the metric system:

The first book is titled: Our Crumbling Invisible Infrastructure. It is a succinct set of essays  that explain why the absence of the metric system in the US is detrimental to our personal heath and our economy. These essays are separately available for free on my website,  but the book has them all in one place in print. The book may be purchased from Amazon here.


The second book is titled The Dimensions of the Cosmos. It takes the metric prefixes from yotta to Yocto and uses each metric prefix to describe a metric world. The book has a considerable number of color images to compliment the prose. It has been receiving good reviews. I think would be a great reference for US science teachers. It has a considerable number of scientific factoids and anecdotes that I believe would be of considerable educational use. It is available from Amazon here.


The third book is called Death By A Thousand Cuts, A Secret History of the Metric System in The United States. This monograph explains how we have been unable to legally deal with weights and measures in the United States from George Washington, to our current day. This book is also available on Amazon here.