Asimov and Metric Prefixes

Isaac Asimov (1920-1992)

By The Metric Maven

The late Isaac Asimov (1920-1992) was a great promoter of the metric system. In the early 1960s Dr. Asimov wrote an essay about the metric system entitled Pre-Fixing It Up. The essay appears to have been inspired by the official addition of new metric prefixes in 1960. Some of the essay shows its age, but Asimov makes an observation about the metric system which still seems lost on most people:

All other sets of measurements with which I am acquainted use separate names for each unit involving a particular type of quantity. In distance, we ourselves have miles, feet, inches, rods, furlongs, and so on. In volume, we have pecks, bushels, pints, drams. In weight, we have ounces, pounds, tons, grains. It is like the Eskimos, who are supposed to have I don’t know how many words for snow, a different word for it when it is falling or when it is lying there, when it is loose or packed, wet or dry, new-fallen or old-fallen, and so on.

We ourselves see the advantage in using adjective-noun combinations. We then have the noun as a general term for all kinds of snow and the adjective describing the specific variety: wet snow, dry snow, hard snow, soft snow, and so on. What’s the advantage? First we see a generalization we did not see before. Second, we can use the same adjectives for other nouns, so that we can have hard rock, hard bread, hard heart, and consequently see a new generalization, that of hardness.

The metric system is the only system of measurement which, to my knowledge, has advanced to this stage.

Asimov makes a point in the 1960s which appears to be completely absent from contemporary metric advocacy discussions. The metric prefixes themselves provide an intuitive set of relative magnitudes, expressed in literary form. People do not generally realize this because of the dismal manner in which “scientific journalists” present weights and measures in the media. I wrote a guest blog on the penetration of metric prefixes into our culture, but they only are vaguely understood, and their monotonic relationship is not clearly articulated.

There is only one technical area with which the public deals that has slowly introduced each metric prefix such that people have an idea of their relative magnitudes. That area is computers. In the early days of computing, a computer such as the Timex Sinclair 1000 came with about 2K of memory. That is, it has approximately 2 Kilobytes of memory. Memory escalation had begun and the Commodore 64 had—well—64 Kilobytes of random access memory (RAM). Soon computers would have Megabytes of RAM. The computer I’m currently using to write this essay has 2 Gigabytes of RAM. The use of the metric prefixes to describe computer memory has been a slight kludge as computer memory is in multiples of two. A Kilobyte is actually 1024 bytes instead of 1000 bytes as the metric prefix implies. There is an attempt to introduce binary name versions called the kibi, mebi, gibi and so on, which correspond to the actual metric prefixes, but exactly describe the number of bytes.

Metric prefixes have long been used to approximately count up all the ones and zeros available in computer memory, or on a disk drive. The RAM of a typical computer has increased from Kilobytes, to Megabytes, to Gigabytes. One knows that a file which is in the Kilobyte range is easily emailed. A file which is 1-2 Megabytes is pushing the email envelope a bit, and 10 Megabytes is a really large file to attach to an email. One would not even consider sending a 1 Gigabyte file, it is immediately apparent from the prefix that it is untenable.

As Asimov points out, the metric prefixes act like adjectives. Email attachment file sizes can be seen as small (Kilobytes), large (under 4 Megabytes), and too large (Gigabytes).

Computers use disk drives to store digital files.  5 1/4 inch floppy drives increased from 360 kilobytes to 1.2 megabytes. The 5 1/4 inch floppy drive was replaced by the 90 mm (~3.5″) floppy which held about 1.44 megabytes. Hard disk drives (HDD) with many Megabytes of space were introduced to the consumer. As time went on, Gigabyte sized hard drives were introduced. When compared with Megabyte sized drives, they seemed almost limitless in size. Currently 1-2 Terabyte drives are commonly available. The Greek roots of the prefixes are descriptive. Megas means “great,” gigas is “giant” and terras is “monster.”  Indeed a Terabyte drive is monstrous in size—at least as of this writing.

The problem is that only in the computer industry have we been inculturated with the metric prefixes. As I pointed out in an earlier essay, I was not pleased that the producers of Cosmos chose to use Kilometers, light-years and astronomical units to describe celestial distances. Dr. Asimov encouraged metric usage in astronomy over forty years ago. He begins with the meter, then describes the Kilometer in terms of distances in Manhattan, “…a kilometer would represent 12 1/2 city blocks.” He moves on to the Megameter:

This is a convenient unit for planetary measurements. The air distance from Boston, Massachusetts, to San Francisco, California is just about 4 1/3 megameters. The diameter of the earth is 12 3/4 megameters and the circumference of the earth is about 40 megameters. And finally, the moon is 380 megameters from the earth.

Passing on to the gigameter, ….this comes in handy for the nearer portions of the solar system. Venus at its closest is 42 gigameters away and Mars can approach us as closely as 58 megameters. The sun is 145 gigameters from the earth and Jupiter at its closest, is 640 gigameters distant; at its farthest, 930 gigameters away.

There is no need for Asimov to have qualified the Gigameter as only being “handy for the nearer portions of the solar system.” This is a pre-Naughtin’s Laws view of the metric system. The Gigameter is completely useful for describing the distance to Pluto and the position of the Voyager 1 and 2 spacecraft. Asimov continues:

Finally, by stretching to the limit of the newly extended metric system, we have the terameter…this will allow us to embrace the entire solar system. The extreme of Pluto’s orbit, for instance is not quite 12 terameters.

Two factors that Asimov did not foresee was that Neil deGrasse Tyson would “kill Pluto” and the introduction of Naughtin’s 3rd Law: Don’t Change Measures in Midstream. The extreme of Pluto’s orbit quoted in Asimov’s essay is 12 000 Gigameters. If the Australian construction industry can handle this large of a number in millimeters, I’m sure astronomers can muddle through with it in Gigameters.

One cannot fault Asimov for not pushing matters further. It would not be until 1991 when enough metric prefixes would be added to encompass the entire observable universe.  Asimov does realize the limitations of light-years and parsecs (3.2 light years):

Even  these nonmetric units err on the small side. If one were to draw a sphere about the solar system with a radius of one parsec, not a single known star would be found within that sphere. The nearest stars, those of the Alpha Centauri system, are about 1.3 parsecs away.

The current version of the metric system has no problem describing the macroscopic universe. Here is a table from an earlier essay on the subject:

click to enlarge

The overall point is that if the metric system was completely adopted in the US without dilly-dallying, we would use the metric system, and its appropriate prefixes, to describe all important scientific discoveries and ideas. Children would grow up memorizing metric prefixes (without the prefix cluster about unity) as earlier children committed multiplication tables to memory. This exclusive metric ecosystem would soon provide  a reinforcing context for the relative sizes of the metric prefixes, and make the public as well as people in technical vocations, much more numerate. Astronomy texts would use metric to describe distances, and only mention light years as a gee-whiz! metaphorical supplement to actual measurement units.

Dr. Asimov died in 1992, just after the new set of metric units from yocto to Yotta were adopted. They describe the world which engineering and science encompass at this time. It is sad that the gentle doctor has been gone for over 20 years, and we are no closer to adopting metric units for everyday engineering and science, let alone in our public news media. Dr. Asimov expressed his frustration that no one was listening to his appeals for the metric in the early 1960s in his essay Forget It!. The US has continued to ignore the metric system for over 50 years since that essay first appeared. Will metric adoption take 200-300 more years to occur in the US? I don’t know. What I do know is I don’t have time to wait around that long, and neither did Dr. Asimov.

Isaac Asimov’s birthday was on January 2.

14 thoughts on “Asimov and Metric Prefixes

  1. It’s a pity that the metric multiplier and sub-multiplier prefixes follow no coherent plan. Their arbitrariness is a problem. Who would know without learning and committing to memory whether yocto is larger or zepto or what comes after Exa?
    If instead 10^3 was (as it currently is) Kilo and 10^6 perhaps bikilo (or bilo which ever you think sounds best), 10^9 trikilo (or trilo), 10^12 quadkilo (or quadlo) etc… then we wouldn’t need a board or committee to select new names or an additional learning of prefixes.
    The metric system in the late 18th/early 19th century introduced, for the first time, regularity in the relationship between units (10 initially in pre-SI and 1000 since SI). If this rationality had been applied to the prefixes too then the arbitrariness in needing users to have to commit to memory the prefixes as one previously would have with unit relationships in previous unit-systems would not exist.
    Your blog of 2014/11/20 highlights of some of the problems with naming units which introduces cultural habits and that also applies with naming the prefixes too.

    • I think the naming of the units is a minor issue. The structure of the system is perfect. If some future generation is not happy with the names of the units or prefixes, they can change them without damaging the integrity of the system.

      • Let’s be careful here: There is just One unit for length, One unit for mass, etc. The prefixes are just good conveniences.
        The Maven, referring to Dr. Asimov’s Pre-Fixing It Up essay, makes this clear with the adjective-noun analogy, where the noun is the unit, whether a base unit or a derived unit.

        Regarding another point the Maven made, the cover story of this Sunday’s NYTimes Magazine is about the mapping of the human brain by Sebastian Seung and others. Here’s a sentence from the article, written by Gareth Cook:

        “A typical human neuron has thousands of connections; a neuron can be as narrow as one ten-thousandth of a millimeter and yet stretch from one side of the head to the other.”

        Of course, why not one-tenth of a micrometer or 100 nanometers? My guess is The Times, which I go through each and every day, will “tolerate” millimeters but not units with smaller prefixes. (There’s some evidence for writing this.)

        Also, related to this essay, there’s the 1982 book by Philip and Phylis Morrison titled Powers Of Ten: About the Relative Size of Things in the Universe, which the authors have ranging from 10^25 meters down to 10^-16 meter without using the prefixes (although a list of such is given on Page 113 under “How to Write Numbers Large and Small”, with, as I’m confident the Maven will appreciate, centi-, deci-, deka-, and hecto- listed separately under “Not quite official”).

        [Now back to the Oregon-OSU game…]

  2. Is it possible that The Metric Maven posts some articles that investigate and explore the lack of commitment and the reluctance of Administrators in our Public School System (from elementary to public Colleges and Public Universities) to give even more information about the Metric System and its rejection to the metrication process with more emphasis?
    Actually, many educators from elementary to higher education do not care a bit on teaching well metric units and are careless on metrication in the U.S.
    One Federal Agency that is blocking information on metrication and metric units is NOAA and especially NWS, more specifically metric measurements in DISTANCE and SPEED. Meteorologists in general, around the country, who are working for local and national TV stations, are also very reluctant to provide “dual” measurements when they broadcast weather news. They can do it, however, they do not want to show this information to their viewers. An example is chief meteorologist Mr. John Patrick from ABC-2 in Fort Myers, FL who wrote in an email that the “official unit of measure in the United States is the Imperial Unit, not metric.” He also wrote and I quote: “While we, as meteorologists and scientists, use the metric system in our work,our viewers, the general population, do not.”
    Could the Metric Maven write about this? Is anyone in agreement with meteorologist John Patrick, ABC-2 in Ft Myers, FL? Is it true that the “OFFICIAL UNIT OF MEASURE IS THE IMPERIAL UNIT IN U.S.? Could the Metric Maven prove if this is true exploring U.S. metrication issues of being reluctant, lack of commitment, lack of interest, excess of apathy in our public schools as well as NOAA when they produce news for the “general population” as Mr. Patrick said?
    I strongly suggest these points as future writings in The Metric Maven.

    • The US does not use Imperial, it uses Customary (the units of fluid measure, dry measure, and mass units larger than pounds are different). If Customary were “official,” you would expect it to have well defined standards. The mile is defined as 5280 feet; however, the foot is officially defined as 0.3048 m. There are no primary physical standards backing the Customary units, they have been defined in terms of our metric standards since 1893. Still, they are in wide, everyday use.

      NOAA and NWS are not exactly leaders in metrication, but they are not laggards either, they are somewhere in the middle of the pack. The National Hurricane Center uses dual in its public advisories, miles and miles per hour but also kilometers and kilometers per hour. On the Internet, NWS text products tend to be Customary only, but their “point forecasts” (for an address, zip code, or city) have a link for SI units at the bottom of the page. If you navigate to the page for your “point” of interest, switch the units, then bookmark the page, your preference is saved and you have a metric weather page for your location. Hardly blocking information. However, the page initially defaults to Customary, so they are hardly leaders, either.

      NWS has no real control over “tv weathermen” (and weather ladies), although all the information used is originally from NWS. As pointed out above, that is readily available in metric or Customary form, so it is up to the tv station. However, it is true that most of the station’s viewers are more familiar with Customary and the station’s goal is viewer ratings and advertising dollars, not educating the American public on metric. If they used metric, they might attract USMA members, but would likely lose total viewers to competitors.

      • I’m referring to “blocking information” because it is not enough to have just a link to a webpage with metric units only. A good informative website for NOAA and NWS is to have both “dual” units of measurements in the same page besides such a “link” to a metric “only” webpage. We should not continue somehow giving them more reasons to not showing metric units any longer. It is not anymore a justification that because of the “general population” do not use metric units tv station news directors and meteorologists do not use these dual measurements. I strongly criticize those national and local tv stations that do not want to provide this information to their communities. CNN in Spanish shows both Celsius and Fahrenheit degrees at the bottom of the the screen. Why English TV Stations are “reluctant” to provide this information. For me and at this time, there are no excuses at all for not doing it. Why “educators” at all levels in our public educational system are rejecting such a measurement system including those teaching chemistry? Why “educators” at all levels, and in general, are reluctant to provide support to the metrication process when practically is a necessity in the U.S.? I’m also blaming our local, state and national “patriotic” politicians, both democrats and republicans including other political parties for omitting and relegating this academic subject for decades.

        • I used to believe that “dual” (metric and Customary side by side) was a useful transition step. Twenty years of it on food packages and most other commodities has not really helped Americans learn the metric system. I think only hard-core metric-only will make them learn it.

          Maybe if it had been announced as a two year interim step and then followed up with metric only, it would have helped. As an isolated action with no further steps, it hasn’t been shown to do much of anything.

  3. Sometimes we may have to put up with a non-SI unit. For example, consider a front-page article in today’s ScienceTimes, which focused on Rolf-Dieter Heuer, who is in his last year as director of CERN.

    Consider this from the article, written by Dennis Overbye:

    “It [The Large Hadron Collider] will start up again in March, running close to full strength for the first time, with proton bullets of 6.5 trillion electron volts –enough energy, scientists hope, to break into new ground.”

    Expressing this in terms of joules shows such is equal to about 1 microjoule, which doesn’t sound “large” like “6.5 trillion”. Thus, to make it sound large, we could change it to 1 trillion attojoules (1 aJ), but The Times would not likely tolerate such. Thus, what to do here???

    Later in the article, we find, “Last summer, Chinese physicists announced a proposal to build a pair of colliders 32 miles around, twice as big as CERN’s.” Of course, this is probably more of The Times’s anti-metrication nonsense as that 32 miles was likely 50 km in its source.

    A bit later machines up to 100 trillion electron volts were indicated, to which Dr. Heuer was quoted as follows: ‘This no-lose scenario does not exist for 100 TeV.’

    Well, I guess The Times will tolerate the prefix tera-, as long as it’s not associated with SI. (Also, unfortunately, it looks like physicists are staying hooked on electron-volts, perhaps because of what I wrote in the first sentence above…)

    [BTW, 100 TeV is abot 16 trillion aJ. (As an old prefix joke goes, “atto-boy!”)]

  4. Well, I think we need to put up with those “non-SI” units that the SI Brochure, itself, accepts (see Table 7). The electron volt is accepted for use with the SI and may use SI prefixes. The energy is still small compared to raising an apple a meter against gravity but a teraelectron volt is a lot of energy for a single atomic (or subatomic) particle. Photons over about 3.2 eV will damage you.

  5. The January/February 2015 issue of Money magazine uses SI units in two articles. Page 97 has an article comparing residential floor space in several countries using square meters. On page 144 the author describes her ride on a moped using kilometers. I consider these articles to contain small, but significant, positive steps. Could it be that the path to metricating the U.S. would best be through the business sector? Since most CEOs are bottom line oriented the movement to metric might be accelerated if they could be convinced of cost savings and greater efficiency by using SI.

    • Thanks EuroCity — well worth an extended look.

      (The only problem, again, is that lengths less than one meter expressed in terms of meters are singular, not plural; thus, for example, 2 x 10^-3 m is 2 x 10^-3 meter or 0.002 meter, not 2 x 10^-3 meters or 0.002 meters. (Of course it’s 2 mm, or two millimeters.)

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