To Infinity…..and Beyond !

By The Metric Maven

Bulldog Edition

When I was a boy I had a friend who shared my interest in electronics. A new wonder device had been created around that time, it was called an operational amplifier or Op Amp. It was all new to me at the time. My friend stated with rapt excitement: “they have infinite gain!” I looked back at him in astonishment, and then thought “That can’t be possible.” A number of years later I was in a class on electrical circuit theory when the instructor began discussing Op Amps. He drew a diagram on the board and called it the “infinite gain mode” which suddenly caught my attention again. The Professor had a slight grin and said “actually the gain’s not infinite, it’s around 1000 to 100,000.” This is very, very large, but not infinite. In many cases one can assume it’s infinite and that’s a good enough mathematical approximation.

Last year I was watching a news report about Colorado flooding, and the large number of oil and gas structures which were flooded because of it. Some of the containers and rigs were toppled and releasing petrol-chemicals into the flood water. This alarmed a number of citizens who were quite concerned—but not the intrepid reporter. She offered a Cochranism to vanquish people’s fears: “the solution to pollution is dilution” the Very Serious Woman asserted. I cringed when I heard this. Like the Op Amp, I knew that the underlying assumption was that the amount of water on earth is infinite. To most people, this seems like a quite reasonable assumption, but it is a fantasy.

The amount of water in the oceans is given in Wikipedia as “1.3 billion cubic Kilometres … This can be thought of as a cube of water with an edge length of 1,111 Kilometres.” I’m sure these values are accurate within known evaluations, but they are expressed in a less than concise manner.  When I rework the figure to obtain a metric volume, I end up with 1.372 x 1021 liters. This may be compactly expressed as 1.372 Zettaliters (1.372 ZL) or 1372 Exaliters (1372 EL). I also wrote it as Exaliters, because by now most people have heard of Exabytes, which makes this prefix one which is now in general use. It will also be useful to write it this way for the explanations to come.

Water, water, every where, And all the boards did shrink ; Water, water every where, Nor any drop to drink.

The unfortunate fact is that from a human standpoint the oceans are already “polluted,” and there is no more pure water to dilute the oceans to the point where they are safe for humans. What I mean by this is that the oceans contain about 35 grams per liter of dissolved salt. This salt makes seawater unfit for human consumption. This, in the view of humans at least, is a form of “pollution.” To the life which lives in the sea, it is not pollution, salt for them is an essential compound. In our anthropocentric view, all but 3% of the water on the earth has not been polluted with salt. The assumption that the amount of water on earth is infinite breaks down, there is not enough “salt-less” water to dilute the oceans down to the point where they are safe to drink.

Of course “fresh water” is not salt-less. Wikipedia states:

Fresh water can be defined as water with less than 500 parts per million (ppm) of dissolved salts.[6]

What they have given is a number which appears numerically descriptive, but is next to impossible to use for any direct numerical comparison. The parts-per notation actually promotes innumeracy in my viewpoint. As Wikipedia states about the parts-per notation: “they are pure numbers with no associated units of measurement.” They are not SI. Wikipedia even calls them “pseudo-units” which I believe is appropriate.  We have been told there are 35 grams of salt per liter in sea water—but  how many grams of salt are there in a liter of “fresh water” If we knew that, we could easily make a direct comparison of the amount of salt in seawater and freshwater. The Wikipedia article does not express it in a useful numerical manner.

After considerable searching I came up with an unsubstantiated claim that seawater is 220 times saltier than fresh water. This would mean the amount of salt in fresh water would be about 159 milligrams per liter (159 mg/L). Now we can make a direct comparison:

Salt Water:  35 000 mg/L
Fresh Water:    159 mg/L

These values would, if scientifically stated, also have the temperature at which this data is accurate. The volume of water and the amount of dissolved salt depend on temperature.

But at least we can now compare values—if only approximately. When numerical values are presented as they are in the media, or as often occurs in Wikipedia, these offerings  obscure actual numerical understanding, by presenting an artificial, but  seemingly intuitive number, which is accepted as information by the public. It is a literary metaphor masquerading as information.

The Great Lakes are massive, and contain a large amount of the world’s fresh water. Wikipedia claims they have 22 671 cubic kilometers of water. Provided I have converted correctly this is 22 671 x 1015 liters or 22.671 Exaliters. The Great Lakes contain about 21% of the world’s surface fresh water so, the total fresh water would be about 110 Exaliters. So the amount of water in the oceans compared with that of the great lakes in terms of Exaliters (EL) is:

Ocean: 1372 EL
Great Lakes: 23 EL
Total Fresh Water: 110 EL

The total amount of salt in the ocean would be about 48 000 Exagrams (Eg) according to these estimates. The fresh water salt total would be 17.49 Exagrams which we will round to 18 Exagrams. So the total amount of water on Earth would be approximately 1482 Exaliters, and the total amount of salt found in the world’s oceans and fresh water would be 48 018 Exagrams.

If we divide 48 018 Exagrams/1482 Exaliters the Exas drop-out and we have 32.4 grams per liter if we used all the fresh water in the world to dilute the ocean’s water. The use of appropriate metric units and prefixes, with Naughtin’s Laws, show very easily that in the case of salt as a water pollutant, there is not enough fresh water on the planet to dilute all the water below about 32.4 grams per liter. All the water on the planet would then be undrinkable by humans.

In short:

Oceans Contain: 35 grams of salt/liter
Oceans + Fresh Water Contain: 32.4 grams/liter

Dilution only provides more pollution.

Alan Weisman in his book Countdown, which is about resource limitations and population, has this to say on page 29:

Yet techno-fixes for what limits Israel and Palestine’s existence crash into certain realities. Eilat’s desalination plants are now surrounded by by giant mounds of salt. Some gets sold as Red Sea salt for aquariums, some as kosher table salt, but markets can absorb only so much, and dumping the excess back into the Gulf is a hypersaline hazard to marine life.

It is my understanding that Australia has resorted to desalination plants to provide fresh water for their population. When information is reported by the media and others using non-SI methods to express it, these values are simply made opaque and unusable for the common citizen, but provides them with the illusion of information. The woman reporter offered an aphoristic rhyme in place of an analysis. Perhaps the Rime of the Ancient Mariner might be a good reading assignment for her if she insists on literature in place of information. Go forth Ms Anchorwoman and wander the earth. Tell all the people you see about SI,  Naughtin’s laws and The Elements of Bile.

An important point of this calculation is that polluting fresh water with anything that makes it undrinkable, such as petrochemicals, reduces the small reserve of drinkable water that exists on the earth which does not have salt in it.

It was a complicated and tortuous route for me to collect all the information available and convert it to a metric form which was easily compared and useful for computational comparison. The sad fact is that our teachers and educators appear ignorant about the metric system and its effective use. To my knowledge there is no public school instruction about the use of metric prefixes and units as proper ways to express quantities. Much time is wasted on unit conversions which utilize time which would be better spent on the proper expression of quantities for comparison. The lack of attention to this need is one of the basic reasons why “Johnny is innumerate” and cannot see through a false colloquialism such as “The solution to pollution is dilution.” This is an illusion. Proper use of the metric system promotes numeracy. Curiosity may have killed the cat, but innumeracy will quite probably kill the humans.

Postscript/Double Bulldog Dare Edition:

top-wimtba-logo-245x134John Bemelmans Marciano has written a supplementary article to his book Whatever Happened to the Metric System? Marciano’s book is a cherry picked collection of odd ideas and personalities which he conflates with the metric system, and makes no real effort to answer the question posed in its own title. Sven’s review addresses a few of these deficiencies, but is not exhaustive. Marciano’s current article (2014-12-15) rephrases the question: Why Won’t America Go Metric? It is given space on Time magazine’s blog, and is also cross-posted to a blog which has as its masthead: “What It Means To Be American.” It will probably not surprise readers that an essential part of what it means to be American is to cling to medieval units. Marciano opens with “We Americans measure things our own way” and chortles that they are “…measures that are all unfathomable to foreigners….”

When it comes to citing the economic and societal advantages of the metric system, Marciano’s displays a seemingly willful lack of interest. Pat Naughtin’s metric information is available with a simple search, both in video and written form. My blog contains considerable information about the practices and advantages of metric, but it seems that Marciano is impervious to this readily available information. His book never touches upon the non-decimal use of the metric system in Australian and UK construction, which saves them about 10-15% compared with our medieval measures. This does not fit into his dyadic view that: “……foreigners, nearly all of whom have been brought up in a decimals-only [i.e. no fractions] environment.” have no other options. Marciano cannot contemplate the use of integers in place of fractions and their numerical benefit. He only sees usable numbers as decimals or fractions.

Marciano states that “The United States is metric, or at least more metric than most of us realize.” and goes on to claim: “The metric system is, quietly and behind the scenes, now the standard in most industries, with a few notable exceptions like construction.” (and transportation, and agriculture, and electronics manufacturing…..) This engineer has visited a number of U.S. commercial engineering design and manufacturing plants over the last five years, and found they still use Ye Olde English measures—as does all of Aerospace—and NASA—with the notable exception of JPL, which is allowed to use it, but only internally. We have Marciano’s perception and my anecdotes, and both are unreliable. Marciano offers no actual studies or data to substantiate the amount of metric which is used in the US, because as far as I know, there has been no funding or systematic attempt to study this. Nobody knows, and we are likely to remain ignorant indefinitely as metric seldom penetrates the national consciousness. When it does, it is ephemeral, and what general information is available hardly supports Marciano’s bald assertions.

So what is Marciano’s final answer to his own question?

Why is it that America hasn’t gone full-on metric? The simple answer is that the overwhelming majority of Americans have never wanted to. The gains have always seemed too little, and the goal too purist.

Yes, indeed, it’s obvious! That’s why we abandoned the idea of going to the moon in the 1960s—the goal was just too purist—and what of practical value would be gained? There is also an unstated assumption, that whatever the majority of Americans desire, our government quickly implements. But I do agree that the the answer he offers is simple. I might have said simplistic.

Marciano pulls out a favorite polemical chestnut used by anti-metric people when discussing metric change in other countries: “In all these cases, however, conversion was dictated by democratically deficient governments bucking the will of the people.” I want Australia to take note that you have a “democratically deficient government” according to John Bemelmans Marciano. He does not appear to have read Metrication In Australia, or if he did, found its information of insufficient importance to include in his book or note in his article. I guess the absence of any metric riots in Australia was just not worthy of note, as was his statement: “The 1880s imposition of the metric system in Brazil led to a full-scale uprising that lasted months.” And shame on you too New Zealand!—how can you live with yourselves!—no riots! Clearly you lack democratic values!

Marciano then delivers a bombshell: “The world’s most anti-metric nation–Great Britain–grudgingly began to ditch its Imperial system in the 1970s.” Marciano can say this with a straight face? I guess he couldn’t be bothered to read my blog where I publish UK junk mail with all housing and grocery store fliers given in metric ONLY. Marciano can claim Great Britain is the most anti-metric country on the planet, but in practice this champion of anti-metricism appears to be metric everywhere except when implementing highway distance signs. Logically, this also puts Great Britain on Marciano’s list of “democratically deficient” countries. Marciano is an American. Did he forget that America is always number one?—in everything—including anti-metrication!

Finally, this:

There is no question that a uniform global system of measurement helps cross-border trade and investment. For this reason, labor unions were among the strongest opponents of 1970s-era metrication, fearing that the switch would make it easier to ship jobs off-shore. (Which it did.)

If you would like to see an abbreviated version of what was actually said by the AFL-CIO about metric in the 1970s metric hearings, it is here. I really, really, really, would like to see a single study cited by Marciano supporting the notion that our embracing the metric system (which, as near as I can tell, we didn’t) made it easier to offshore jobs. (I would also caution Mr Marciano that one cannot just place what you believe to be a proverbial truth, without substantiation, in parenthesis, to make it true.) This throwaway assertion that metrication was a significant contribution to the offshoring of US jobs, combined with the lack of information of how metric the US actually is, causes his article, in my view, to degenerate into farce. His “measurements as culture” trope is becoming the last refuge for those without a reasoned argument.

12 thoughts on “To Infinity…..and Beyond !

  1. A “pseudo-unit” in the healthcare world is the “one to…” Some drug products retain the metrology of eras gone by, either by retaining the relics of apothecary units (straight conversion from apothecary to metric, e.g., 1 1/2 gr. becomes 97.2 mg as the declared strength of the tablet). Epinephrine injection is still described in strengths of one to one thousand or one to ten thousand, written, respectively, 1:1000 and 1:10000. These “one to..” statements mean grams per milliliters, so 1:000 and 1:10000 mean, respectively, 1 g/1000 mL and 1 g/10000 mL, or simply, 1 mg/mL and 0.1 mg/mL. I don’t have a story handy in which, due to the “one to..” expressions, the more concentrated solution was used by mistake, but anyone can see that the explicit concentrations expressed in SI units are MUCH safer statements of the products’ strengths! The explicit SI strengths are still on the label, but the “one to…” nomenclature heads the description.

    (corrected 2014-12-20)

  2. CORRECTION OF PREVIOUS COMMENT:

    “pseudo-unit” in the healthcare world is the “one to…” Some drug products retain the metrology of eras gone by, either by retaining the relics of apothecary units (straight conversion from apothecary to metric, e.g., 1 1/2 gr. . becomes 97.2 mg, which is where we sometimes get phenobarbital 97.2 mg tablets), or the use of an antiquated expression of concentration. Epinephrine injection is still described in strengths of one to one thousand or one to ten thousand, written, respectively, 1:1000 and 1:10000. These “one to..” statements mean grams per milliliters, so 1:000 and 1:10000 mean, respectively, 1 g/1000 mL and 1 g/10000 mL, or simply, 1 mg/mL and 0.1 mg/mL. I don’t have a story handy in which, due to the “one to..” expressions, the more concentrated solution was used by mistake, but anyone can see that the explicit concentrations expressed in SI units are MUCH safer statements of the products’ strengths! The explicit SI strengths are still on the label, but the “one to…” nomenclature heads the description.

    Ever wonder why we have 81 mg tablets of aspirin, and 325 mg tablets of aspirin and acetaminophen? Again, straight conversion from the apothecary amounts, 1 1/4 grains and 5 grains. I don’t recall seeing these odd strengths in Australia, arguably one of the most thoroughly metricated countries in the world.

  3. The actual cube root of 1.3 billion km³ is about 1091.4 km. That may be how you got from 1.3 ZL to 1.372 ZL, and two more “apparently significant” figures, but the difference is minor. I don’t find liters with large prefixes very easy to visualize. I would prefer to write 1.3 billion km³ as 1.3 Mm³ (megameters), using cubic measure with suitable prefixes.

    Salinity of the ocean is typically taken as 35 g/kg, not 35 g/L. The density of seawater is around 1.025 kg/L. The mass/mass form has the advantage of being independent of temperature (as long as nothing actual breaks down).

    The real problem with ppm notation is that it can be based on mass, volume molar, or mixed ratios (mixed is usually mass/volume, mg/L). If the basis is not defined, then you don’t know what the hell it means. You might wish to read all of section 7.10 (several subsections) of NIST SP 811. They strongly prefer explicit notations that make the basis clear such as 35 g/kg for ocean salinity. Wikipedia’s article on salinity uses that for the ocean and 0.01 – 0.5 g/kg for fresh water. I would write the upper limit as 500 mg/kg which is 500 ppm on weight/weight basis. This is probably sufficient dilute to approximate density as 1 kg/L.

    You slipped a prefix (3 digits) in conversion of Great Lakes, 22 671 km³ is 22.671 x 10^12 m³ or 22.671 PL. This affects all your computations derived from the figure.

    There is some truth to “the solution for pollution is dilution,” not for salt, but there are bacteria that thrive on petrochemical waste provided it is fairly dilute. In general, the freshwater we use comes from precipitation and is deposited above sea level and runs downhill to the sea at some rate, thus is renewed by the evaporation/precipitation cycle. Some pollutants can be dealt with by organisms and broken down, when the pollutant is dilute, some can’t (inorganic salts). Still, the water would be more useful and reusable, all the way to the sea, if we didn’t pollute it.

    • Indeed I did incorrectly convert the volume of water in the Great Lakes. The value is about 23 Petaliters. The volume of all the fresh water lakes in the world is about 176 Petaliters.

      The total amount of fresh water on Earth has inconsistent estimates. If one uses this Wikipedia page as a reference, one obtains about 35 Exaliters of fresh water and 1351 Exaliters of saltwater. The total salt is about 47 300 Exagrams.

      These figures when divided out give a value of 34.14 grams of salt per liter. My original estimate was 32.4 grams of salt per liter. This recalculation considerably strengthens my point. The solution to pollution is not dilution.

  4. “The 1880s imposition of the metric system in Brazil led to a full-scale uprising that lasted months.”

    But Wikipedia, a USMA article, and some other sources all assert Brazil adopted the metric system in 1862, and many South American countries did so at or around the same time. Does this speak to the “accuracy” of Marciano’s research?

    • Perhaps it speaks as to the accuracy of the propagandistic fluff of the “date of metrication” chart, that erroneously claims that the US never officially adopted the metric system (it did, in the 1860s), and omits several other nations, that continue to use customary units, some who are less metric than the United States, like Belize.

  5. As stated above – the petrol residue is not a problem – Bacteria love to eat it up.

    And the salt is also not a problem compared to the amount of salt used on roads. I find the anti fracking propaganda interesting – this is about the only bright spot in our economy – and did not come from the government, but only from the private sector. Basically it means about $1T/year is staying in the USA – we would be facing economic collapse with out it – yet it is seen as an evil. And for those that want to say it is causing earthquakes – it is true that it causes very small quakes – which is good as it is reducing the built up stresses that would power major quakes.

    • Bacteria don’t eat petrol chemicals immediately, and your statement about the impact is a simplistic assessment.

      The spreading of the element mercury around the Earth is an even better example where the solution to pollution is not dilution. Krill love to eat it up, and other fish eat krill until long lived fish become toxic. In the Midwest the invisible rain of mercury from coal fired power plants concentrates itself enough in fish that some retired people who often catch and eat them have become seriously ill.

  6. Just my opinion, but when I think of “the U.S. adopting the metric system,” in my gut I think of America being as metric as Australia. But, in 1866, the U.S. did pass the Metric Act, which legalized the use of the metric system throughout the country but also made the point that “no contract or pleading in any court” can be invalidated because the weights and measures used therein are metric. My opinion again: this came about because some tough lawsuits were thrown out on the technicality that you couldn’t use meters or grams in a U.S. court, and the Metric Act prevented that from happening in the future.

  7. The gain on an op amp is calculated by dividing the value of the external input resistor into the value of the feedback resistor. If the input resistor value is zero (shorted) or the feedback resistor is infinite (not present), then theoretically the gain is infinity. That is where the claim originates. But in reality, the output voltage with an infinite or extremely large gain would clip at the rails. If you supply +/- 15 V dc to the power terminals, the output would clip at this value and a sign wave would become a square wave.

    This is from what I was taught and experienced.

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