The Olde English Prefix Modifiers

I demand 1 billion, gagillion, fafillion, shabolubalu million illion yillion … yen.

By The Metric Maven

I’ve been over the fact that in SI, or the modern metric system, multiple prefixes should not be used. The idea of a Kilotonne I find to be just plain decanted of information. One should never use KiloMegaHertz or any compound prefixes. The only practice I find more fiendish is when this taboo is broken with ad hoc pre-metric conventions. For instance it is often stated that the distance from the Earth to the Sun is about 150 million Kilometers. The immediate desire to inject the word million to modify the metric prefix Kilo appears to be an irresistible Ye Olde English force. The word million itself is from words that mean one thousand, but it actually is used to mean one thousand thousand. 150 million Kilometers is essentially the same as writing 150 MegaKilometers, but with a space. No metric advocate would put up with concatenating metric prefixes, but little is ever said about million Kilometers. Clearly the introduction of million as a modifier is frivolous as the distance is compactly expressed in metric as 150 Gigameters. Astronomers are insistent on calling this distance an astronomical unit or au or sometimes AU, despite the fact that the metric system easily deals with astronomical dimensions.

Owners of Tesla electric cars are purported to have driven more than one billion gas-free Kilometers. Yet again, the press cannot help but place an unwelcome numerical modifier in front of a metric prefix. The word billion has its own sort of prefix. It originally stood for for bi-millions or a million millions, but now it “unambiguously” means 1000 million. One billion Kilometers is one GigaKilometer. Even more unambiguously it could be said that Tesla electric cars have collectively traveled one Terameter or 1 000 000 Megameters which allows one to immediately note that the circumference of the Earth is 40 Megameters and with a quick computation we see they have traveled around the Earth 25 000 times. The billion non metric ad hoc prefix only gets in the way of numerical understanding.

The light-year (don’t get me started) is about 9.5 trillion Kilometers, which could be rounded to 10 trillion Kilometers as a rule of thumb. In this case the concatenated metric “equivalent” would be 9.5 TeraKilometers.  Appropriately, and compactly expressed, it’s 9.5 Petameters and does not need any unwelcome trillion modification. Despite the belief that a light-year is a large value, the nearest star (other than the Sun) is over four times that distance or about 41.5 Petameters from Earth. I’m sure by now readers realize that injecting trillion so that a provincial dimension like Kilometers can be maintained only adds complexity if one wants to actually compare numbers, or use them in a computation. In my view, it is also wordy. This is true for the introduction of quadrillion, quintillion, sextillion and septillion so I will end my examples here. The inappropriate nature of millionth, billionth and so on for numerical reduction also applies. They are all verbose.

When talking about the ratios of numerical magnitudes, that is unit-less multipliers, the words million, billion, trillion and so on are also used and in this case people might think they are appropriate. One hears that something is a million times larger than something else, or a billion times larger and so on. For instance it was reported that a black hole which is 18 billion times as large as our Sun has been discovered in a galaxy known as OJ287. The phrase billion times is quite proverbial, but it could also be shortened. It could be said that this black hole is 18 Gigatimes as large as our Sun. The single word Gigatimes is clearly shorter than the two word description billion times.

Why not Kilotimes, Megatimes, Gigatimes and so on to describe ratios of dimensions in words? I think it’s at least Yottatimes as good of an idea as using confusing long scale or short scale expressions. There is compactness, consistency and instant magnitude recognition when using the metric prefixes in this manner. Brace yourself. I see myself using this expression in future essays, and I encourage you to do so as well.

Related essay:

A Kilotonne is How Much in Metric?

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.

13 thoughts on “The Olde English Prefix Modifiers

  1. Good suggestion Maven!

    Thus, the world population is about 7.2 gigapersons and that of the U.S. is about 320 megapersons.

    Somewhat relatedly consider this line from a recent biology-related paper on ligand-protein interactions:

    “The spatial scoring window was set, conservatively, at 2 angstroms, since that is a commonly accepted RMSD for significantly similar poses for ligands and synchronized with the poxel definition used.”

    Now, of course we don’t want to hear about angstroms anymore, and so should the writer have used 0.2 nm instead? Maybe 200 pm? From what I could ascertain about the concept, it looks like she and such biologists are stuck with the antediluvian angstrom unit here, especially in view of it being “commonly accepted”. (Wonder if this parallels using electron-volts for mass instead of yoctograms??)

  2. Sorry, section 5.3.7 of the SI Brochure requires powers of ten notation, not SI prefixes, for particularly large or small values of dimensionless quantities. An exception is made for the radian and steradian, basically pretending they are units and not dimensionless. Exceptions are also made if the units are shown such as using µL/L as a way to avoid the discouraged ppm by volume, even though the units actually divide out.

    Precisely contradicting requirements of the SI Brochure is exactly equivalent to random madeup abbreviations like kph in place of proper symbols, km/h, or multiple prefixes like kilomegahertz in place of gigahertz. If we pick and choose, we are back to Imperial mess.

  3. How will this go down? I hear all sides. There is the press and the rank-and-file, who are still under the influence of the old lingo, and there is the algebraist in those of us who flght for the metrication goal. I’m one who would like to see the metric ton or tonne replaced by the megagram, but there is a lot of journalistic pressure otherwise (tons of it! [grin]). The metric salesman in me would be contect JUST to see the Nation speaking in kilometers, meters, kilograms, and liters, with the occasional use of the cubic meter with knowledge of its connection to the liter.

    Can we start metric education all over again? I don’t think we could do it worldwide, and to what extent can we arithmetize American metric education to our liking? I’m not optimistic about the arrival of the pure SI to our lives, but at least we can ensure that it is studied in school, and certainly, that our children and grandchildren will be able to eyeball the number 500 on a meter stick and be able to interpret it mentally as 0.5 m and 50 cm.

  4. We have at least two problems, here: the BIPM is probably far too conservative – like any more or less bureaucratized institution – and thus seems to resist change, even when there are self-evident irrationalities in the current implementation of the SI (for example, for things such as the kilogram being a base unit with a prefix, the liter being based on the decimeter, and so on); and the SI prefixes, as they are now, are not really indefinitely scalable, as new names must be invented – and officially approved – for every new prefix: i.e., there isn’t a universal and extendable scheme for creating prefix names, as for example in the TGM system (which, apart from dozenalism, is anyway interesting; even if its meter, the “grafut”, besides sounding funny, is a much too short unit, IMHO: less than 300 mm).

    A more open source and scalable SI would be a possible solution – but when?

    If there is no real will for progress, both from below (the people) and from “above” (see institutions), it won’t happen, sadly – exactly as for metrication in the US…

    • Prefixes are convenient in speech and writing when generally understood. I’m willing to learn a few for orders of magnitude I commonly use. I’d prefer not to memorize an infinitely long list of them for the sake of being “scalable.” They are merely shorthand for scientific notation and scientific notation is already infinitely scalable. In calculations, it is normally necessary to drop the prefix and use scientific notation to go back to the base unit. Prefixed units are not coherent (with the exception for the kilogram).

      The liter is not officially an SI unit, it is a special name, like the tonne and hectare, allowed (tolerated?) for use with the SI in Table 6. The BIPM would like all table 6 units to go away, but they know that won’t happen so why flog the dead horse. They are concessions to commerce and to ordinary folks who would otherwise be more opposed to the SI. Purists can use 1 dm³, 1 Mg, and 10^4 m² (or 1 hm²).

      We could use a new, unprefixed name for the kilogram, (and a definition that doesn’t depend on a physical artifact) but I personally find the rest of the SI pretty usable, and have much more of a concern with those who don’t use it properly.

      • Yes, but an infinitely scalable prefix system would also have the big advantage of not having to memorize every prefix on its own: for example, in a TGM-like system, you just memorize 10 – in our decimal system – “modules” (easily based on ancient Roman and/or Greek), such as nil, un, bi, tri, quad, pent and so on, and then you can automatically build any prefix, from the smallest to the biggest, in a logical way, with far less effort.

        This would also be positive in order to create a SI that isn’t “yet another customary measurement system”, as it sadly is today, at least in everyday life (nobody uses megameters or megagrams, for example).

        As for renaming the kilogram, it might be a lost cause: so, why not adopt the tonne as the base unit of mass? As in the former MTS system… And 1 t/ms^2 would also be a more sensible unit for pressure (the Pascal is far too small).

        Not going to happen, currently – but IMHO interesting to discuss, anyway.

        • … Another interesting thing is this notation: for example, 1 km – or 1 Km (à la Maven) – can be written as 1 x 10³ m = 1 ³m (the positive exponent of 10 becomes a preceding superscript of the unit); while 1 mm can be written as 1 x 10⁻³ m = 1 ₃m (the negative exponent of 10 becomes a preceding subscript of the unit); in TGM-style language, it would be 1 triquameter and 1 triciameter, respectively; if one doesn’t like the “qua” and “cia” prefixes, better ones could of course be imagined.

          Adding such a coherent method of building prefixes – however large or small – would probably be a good thing for the SI; while the traditional prefixes could be retained for everyday use, but without the need to constantly invent and memorize new ones for very large or small numbers.

          (Just some personal ideas and points of view, of course…)

  5. It should be noted that the meaning of billion as 10^9 and trillion as 10^12 is not universal. Progressive countries like Germany use the more logical long form where milliard is 10^9 and billion is 10^12, followed by billiard, trillion, triliard, etc all the way up to noniliard 10^57.

    The long form is easy to determine, simply by taking the meaning of the Latin prefix of the number and multiplying by 6 to get the exponent or the number of zeros following one. One then adds 3 to get the higher -iard form.

    The short form is illogical and contributed to innumeracy.

    • Anyway, the current SI prefixes are based on powers of a thousand, while the long scale is based on powers of a million (from “milione”, or a “big thousand”), that is a thousand thousands.

      An alternative and more direct way – among others possible – could be: mille = 10^3 (kilo), bille = mille^2 = 10^6 (mega), trille = mille^3 = 10^9 (giga), quadrille = mille^4 = 10^12 (tera), and so on.

      But changing the way we name big numbers of course would require some form of planned cultural revolution, worldwide, which seems highly unlikely in these troublesome times.

      BTW, talking about the Germany, it might be a quite advanced country from a metric point of view, but has an enormous anachronism in the way it writes its language: probably the only Western language which still capitalizes substantives – rather irrational, indeed!

      Every country still has its problems, in other words…

      • … Sorry, a typo: Germany, and not “the” Germany, of course.

  6. The US is increasingly becoming a less technically intelligent society and this probably extends throughout the English speaking world. Proper use of SI prefixes and efficient use of the SI are not taught in most schools and thus it shouldn’t be a surprise when errors in numeration, prefix choices, symbols, etc are encountered.

    Also, SI units are just seen as a parallel system to the obsolete units they replace and the bad habits that were ingrained in the use of those units is carried over to SI. The kilometre is treated as just a metric mile and if you say something is a million miles away, it becomes a million and a half kilometres away. There must be too much effort to make it 1.5 Gm away. That is a two step difficult conversion, something most non-technical people can perform.

    Cars are strictly in kilometres in metric countries. They odometer does not switch to megametres once 1000 km is reached. So, is it any wonder people don’t have a feel for switching away fro kilometres only when dealing with large distances?

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