Category Archives: International Standards

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.

The Metric Mess is Hard Wired in The US

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Skeez

By The Metric Maven

Bulldog Edition

Skeez was a person who seemed to be born interesting. He obtained his nickname from a character called Skeezix in the comic strip Gasoline Alley. The comic strip itself is unusual in that Skeezix arrives as a baby on a doorstep and ages as time goes on. Skeez spent much time at his cottage on the shore of a nearby lake. One day I noticed a new bust among his eclectic collection of objects; it was Charles Dickens. Skeez then told me that Dickens had a story about an innkeeper who was so cheap he counted the number of beans he put into his soup, and that’s where the term “bean counter” arose. He was as close to a polymath as I have ever known. When he passed away I ended up with small gargoyles that he had brought back from France during World War II. I have an African shield with a weapon which was used to kill tigers, as well as other books and notes he left behind.

Recently I ran across a an RCA Radiotron Reference Book from 1940 which Skeez had owned. Inside, it contains a small snapshot of how the metric system was viewed by electrical engineers in 1940. It appears that US engineers saw the metric system as a simple drop-in substitute for Olde English measures. For instance, under pressure they equate pounds per square inch to Kilograms per square centimeter. No pascals. The equivalence of kilograms (mass) with pounds (force) is a strange misunderstanding in a reference like this—unless they meant Kilogram-force. It is clear that again Americans see the centimeter as a pseudo-inch and just substitute away without any measurement introspection. I’ve not found a millimeter mentioned in this reference.

It also has a list of miscellaneous conversions that have a couple of interesting aspects. First I had no idea there was a unit of metric horsepower. Apparently notion of horsepower was still considered so important in 1940 that a metric version needed to be defined. Apparently metric horses have less strength than Olde English horses. The definition does not seem to even involve a horse:

DIN 66036 defines one metric horsepower as the power to raise a mass of 75 kilograms against the earth’s gravitational force over a distance of one metre in one second;[13]

The other odd aspect is that meters show up with an er ending, but litre is spelled with re. I’ve often wondered when it was decided, and by whom that in the US we would use er rather than re. Here the situation is mixed.

What really caught my attention, and is the actual subject of this essay, are the tables on wire.  American copper wire is designated in American Wire Gauge (AWG). I have made my view known concerning the vacuous non-term gauge in a previous essay. We note that along the left column is the AWG number. AWG was first used as a designation in 1857. The diameter of the wire is then given using the informal feral unit known as the mil. A mil is a slang term for one-thousandth of an inch—at least in the US. In metric countries it’s a slang term for a millimeter as I understand it. As the gauge number increases, the diameter decreases.

There is also a column to the right of the diameter of the wire in mils, which is the area in circular mils. Let’s take an easy example, say AWG 10, which is a solid wire with  a diameter of 101.9 mils. Now we know the area of a circle is π multiplied by the radius squared.  The answer to the computation is 8155 square mils. But wait–the value in the area column is actually 10 380 circular mils. Well, that’s because apparently our engineering founding fathers, in their infinite wisdom, decided that dividing the area up into the number of circular areas of one mil was the best way to do it. To get circular mils you just square the wire diameter in mils. This produces a value that is not directly usable for any common engineering calculations. The resistance of a solid wire is proportional to the cross-sectional area, and circular mils are essentially a gauge number for area and not a defined area. We have inherited this strange way of determining the area of solid copper wire without questioning its sanity. It also illustrates once again that our Olde English set of measurements has nothing in common with a system. To make matters worse, Wikipedia decided to use the term kcmil for kilo-circular-mil in their wire table. I wish metric prefixes would only be used with metric units, and not feral ones, or medieval ones.

Another page in the RCA Radiotron Reference Book has the number of winding turns which make up a linear inch. For example, the Brown and Sharpe (i.e. AWG) Gauge Number is given on the left. We then see that for enamel coated wire one needs 7.6 turns of AWG 8 wire to have a coil which is one inch in length. This data is useful for computing how long an inductor might be for an electrical engineer.

If one were rationally using the metric system, one could easily compute any of these values from a table which gives the wire diameter in millimeters and the area in millimeters squared. If the wire manufactures were to use preferred numbers with metric diameters, then it would simplify matters further. Their would be no more indirect designation of sizes with meaningless gauge numbers. The values would be directly understandable in millimeters. Let’s suppose we have a wire of 1.25 mm diameter, we would know immediately that ten turns is 12.5 mm. We could use AWG 16 which after we consult the table is seen to have a diameter of 50.8 mils. We then know that ten turns is 500.8 mils, divide by 1000 to get the value in inches or 0.5008 inches. Alternatively, we could have started with a direct metric designation of 1.291 mm and ten turns is immediately seen to be 12.91 mm. Starting with the metric diameter, one knows this is the width of a single turn. Using this, one can quickly evaluate 1/1.291 mm on a calculator which is 0.775 turns per millimeter. To get 10 millimeters it would take 7.75 turns. start with a metric wire diameter and one can quickly compute anything one needs–using common mathematics.

Incidentally the gauge designations for copper wire are not standard across types of wire, so one can’t be certain what diameter other wires might be when  given a gauge number. Clearly,  if the diameter of a wire in milimeters is given, or another appropriate metric length (e.g. micrometers), this allows one to immediately compute any appropriate parameter. Here is an illustration from a vendor who sells wire in Australia:

The wire industry in the US has been using this kludged up system since 1857 and has done nothing to introduce reform. This clearly shows to me that one needs to have a government mandate, like that implemented by Australia, which mandates metric. The voluntary part for industry is how they will introduce metric. If they have any sense they would take the opportunity to reform their industry with preferred numbers, or in some other rational manner. Standard DIN Sizes using ISO6722 in terms of mm² look like a good idea to me. But how they would implement the change would would be up to them—and in ‘merica they just might use “soft” metric and preserve familiarity over simplicity along with 19th century measurement practice. Until then, this mess is hard wired in the US.

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.