Category Archives: Metric Education

On Beyond Yotta

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By The Metric Maven

Bulldog Edition

When I was a boy, I read a number of books by Dr. Seuss. One that immediately captured my interest was On Beyond Zebra. I don’t recall  much about the book at this point in my life other than the fact that it involved additional letters of the alphabet. Each new letter was introduced and illustrated by the author. The idea there might be unknown letters piqued my youthful interest. Here are the new letters that appeared in that book:

The first book I ever read by Isaac Asimov (1920-1992) was: The Universe, From Flat Earth to Quasar, which I recently re-read. The two books may seem far apart, but I made a connection between them when I came across a section on how the sun generates its energy. The Sun uses nuclear fusion to convert mass to energy. This process is understood using the famous equation E = mc2 developed by Albert Einstein (1879-1955).
The pressures at the center of the sun cause four hydrogen atoms to fuse into a single helium atom. After this process occurs there is a mass imbalance, the four hydrogen atoms have more combined mass than the resulting single helium atom, and the extra mass is converted into energy.

Dr. Asimov states that about 4.2 Tg (Teragrams) of mass is converted to energy every second inside of the sun. He uses pre-metric terms to describe this value as “4 600 000 tons of mass per second.” Unfortunately so does Wikipedia: “the Sun fuses about 620 million metric tons of hydrogen each second.” As I understand it 1 million is  106  and a “metric ton” is a Megagram or 106 grams for 4.2 x 1012 grams per second or 4.2 Tg per second. That’s a lot of grams. Dr. Asimov inquires: “Is it possible  for the Sun to support this steady drain of mass at the rate of millions of tons per second? Yes, it certainly is, for the loss is infinitesimally small compared with the total vast mass of the sun.”  The currently accepted mass of the sun is, approximately 2 x 1030 kg. This means it’s 2 x 1033  grams, and the proper metric prefix would be?—oh, well, there isn’t exactly a metric prefix for this value. The last magnifying metric prefix is Yotta, which allows the mass to be written as 2 000 000 000 Yg (Yottagrams). Which by current convention it appears there are about three extra metric prefixes needed to express the mass of the sun with a 2, and a minimum of two extra prefixes to use 2000 as a magnitude.

So what does “infinitesimally small” mean? Well the mass lost each second, divided by the total mass of the sun, is 4.2 x 1012 grams/2 x 1033  grams. This value is one divided by 476.19 x 1018 or 0.000 000 000 000 000 000 002 which is quite a tiny ratio. I believe this is indeed a small enough ratio to be “infinitesimally small.” Recall we are talking about 4.2 Tg per second of mass loss. Each gram has 90 TJ (Terajoules) of energy contained within it’s mass. If my computation is correct, then 378 x 1024 joules are released each second. This would be 378 YJ (Yottajoules) per second. We are approaching the limits of the metric prefix Yotta, and in only 1000 seconds we would have  378 000 YJ and see that a new prefix might be useful to describe the power released.

What is notable is that the mass of the sun is not readily expressed with a metric prefix, and it’s not all that massive for a star. It appears that the masses of stars are indeed astronomical. The most massive star is suspected to be R136a1 which is approximately 256 solar masses (a solar mass is the mass of the Sun). This means it has a mass of 512 x 1033 grams or 512 000 000 000 Yg. Clearly we are on beyond Yotta at this point. While I’ve made it clear in the past that astronomical distances are readily expressed with metric prefixes, this is not the case for stellar masses. One can see why R136a1 is described in terms of an equivalent number of solar masses and the metric system is not employed.

Asimov also makes this surprising statement:

Release of energy is always at the expense of disappearance of mass, but in ordinary chemical reactions, energy is released in such low quantities that the mass-loss is insignificant. As I have just said, 670,000 gallons of gasoline must be burned to bring about the loss of 1 gram (1/27 of an ounce). Nuclear reactions produce energies of much greater quantities, and here the loss of mass becomes large enough to be significant.

What I’ve been able find in my research on this subject is both minimal and contentious. It is mostly stated that the amount of mass lost in chemical reactions is “unmeasurable.” The few who venture to put numbers to paper (including a textbook example) end up with magnitudes on the order of 10-33 grams. One example computation has 70 x 10-33 grams as the amount of mass lost in the given chemical reaction. This would be 0.000 000 070 yg (yoctograms) and would indicate a possible need for at least two more metric prefixes. It appears that, at least in theoretical discussions, it might be useful to have two more metric prefixes on the dividing side of the prefixes.

Currently there are 20 metric prefixes from yocto to Yotta. Adding two more prefixes on the magnification side would be useful for some of this astronomical work. It would probably make sense to add a pair to the reducing prefixes also. This would increase the total number to 24 metric prefixes. This is a lot of prefixes, but is far less than the number of magnitudes scientific notation would allow, which would be 60. What I would propose is to consider adding the new prefixes, but at the same time remove the prefix cluster around unity: deca, hecto, deci and centi. They could be separated  and relegated into a set of atavistic prefixes which are no longer considered proper modern usage. They would be included as an appendix to the modern prefixes for historical reference, but discouraged for modern use. This simplification would reduce the number of prefixes back to 20 and also provide a larger dynamic range for scientific description.

In early grades it makes sense to me that only the prefixes micro, milli, Kilo and Mega would be taught as the Common Set of Prefixes. These would be the prefixes that students would generally encounter in everyday life (if the US was metric and fully engaged). In Junior High and High School the new set of prefixes I’ve proposed could be taught as the Complete Set of Prefixes. I would argue that all students (and their teachers) should have to memorize and use all these metric prefixes (without the prefix cluster around unity) in their instruction. Textbook authors should not shy away from using Megameters for planetary dimensions, Gigameters for the solar system, and all the other appropriate uses of metric prefixes.

People have objected to my proposal that we teach all students to use all the metric prefixes. They employ the argument that the Common Set of Prefixes is all that is needed for an ordinary person, and the Complete Set of Prefixes is for engineers, scientists and technical people. I reject this view entirely. It produces a scientific apartheid that keeps the public from understanding the important issues of the day, which involve engineering and science more and more everyday. What I have discovered when working with large questions, such as how much the salinity of the ocean would change if we dumped all our fresh water into it, or how much carbon is being belched into our atmosphere over a given period of time, is that these problems are tamed using appropriate metric prefixes. They allow an ordinary citizen to comfortably work with the magnitudes involved. If one talks about hundreds of billions of tons, that is a metaphor, and is not information. If the goal of education in the US is to create the most numerate population on the planet, then a good command of the magnitudes of all the metric prefixes is essential.

I would like to see a song which fixes the order of the metric prefixes in a person’s mind from the smallest to the largest, something similar to Tom Lehrer’s Element Song. Some manner of meaningless acrostic or other method of recalling the order of the 1000 based prefixes should also be developed. With the prefix cluster around unity eliminated, all the magnitudes will be of 1000 and any parsed base unit can be determined.  This would allow anyone to look at 1 000 000 000 000 000 grams and immediately relate it to the acrostic or song and “sound out” the size of the number as 1 Pg (Petagram), or conversely be able to take the 1 Pg and work out how many sets of three zeros one would need to express it. This would also be the case for 0.000 000 000 000 001 grams. It  could be “sounded out” as 1 fg (femtogram).

When all the metric prefixes no longer apply, that’s when a modern student should viscerally realize they are discussing dimensions that are so large or so small they are mind blowing, and on beyond yocto and Yotta. These values truly exist in an amazing far distant realm.

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.

Evanescent Measurement Policy

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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.

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.