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:


John 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.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page

Whatever Happened To the Metric System?

Guest Book Review By Sven

Is the metrication of a nation a technical exercise, or a social problem? Of course it is both, but in practice, one or the other view predominates. This should be recognized as framing all underlying debate. The classic example of a nation that came late to metric, but approached the transition as a technical hiccup, is now among the most successfully metricated: Australia. The nation that briefly flirted with metrication at about the same time, the 1970s, but dropped it on the dubious grounds that it would have required too much penicillin, is The United States of America. The Metric Maven has always sided with Oz, sometimes to the point of testing the patience of long-time readers. Keep this in mind, because it’s crucial to what follows.

A new book, Whatever Happened to the Metric System? How America Kept Its Feet, by John Bemelmans Marciano, ostensibly on the failure of metrication in the US, has us here at in a quandary. If the subject matter matches the title, then we might be expected to have an opinion. Silence might even be misinterpreted. On the other hand, if the book is something else, we could find ourselves in the position of electrical engineers trying to make sense of a seriously bizarre piece of dilettante sociology.

The book certainly starts off at the right point: the early 1980s, when Ronald Reagan gave the coup de grâce to any hope for imminent US metrication, by abolishing the US Metric Board. The Board had been in existence for only seven years, and still represents the sole official attempt to bring US measurement into alignment with the rest of the world. (I can personally attest that it was a time when kids were told by teachers that, ten years out of high school, we would never have to worry about confusing an ounce weight with a fluid ounce again.) But the Board foundered early, for reasons that will not be easily explained to citizens of European democracies. (Long story short: some members of the Board apparently saw their function as more than purely nominal.)

Before exploring this failure, however, Marciano indulges in an extended historical digression: at least twelve of his sixteen chapters. Our first major stop is actually the French Revolution. And I do mean stop: we will be stuck in France from well before the Reign of Terror, and will be hanging around for at least two Napoleons after (numbers I and III, I’m pretty sure — I’ve forgotten if II gets a mention, and frankly it’s not worth checking). The French chapters run from at least three through six and beyond, with chapter two, on the francophile Thomas Jefferson, as a kind of preamble. This makes the French section well over one fourth of the book. Although the book’s title suggests a specific focus on the failure of the US, alone among the nations, to metricate, the bulk of the book takes place elsewhere, and has only tenuous relevance to the US failure. The book seems to be intended more as a capsule history of the metric system. And if this is indeed the intention, then there is a grave problem. To paraphrase Sherlock Holmes, there is a dog that didn’t bark in the night: the complete absence of John Wilkins (1614-1672).

Ten years ago, a book on the history of the metric system might have been excused for not mentioning John Wilkins, and parroting the conventional wisdom that the metric system sprang fully formed, like Athena from the head of Zeus, out of revolutionary France. But it is now known, largely from the research of Pat Naughtin, that the idea of systematized measures, divorced from any artifact, had been around long before: at least one hundred twenty years before the Revolution. In 1668 Wilkins published An Essay Towards a Real Character, and a Philosophical Language, which included a proposal for an integrated system of linear, volume, and weight measures. It was not an isolated effort. William Brouncker, and the far better known Christian Huygens, collaborated. But the man who came up with the technological device that made the system possible, the “seconds pendulum,” may have been Christopher Wren, not primarily a scientist (or “natural philosopher”), but the architect of London’s St Paul’s Cathedral. Wilkins’ book was widely read well into the 1800s, and the units for length, volume, and weight it advocated were remarkably close to those later arrived at by the French by more dubious means.

Marciano is aware of such devices as the seconds pendulum, and of Jefferson’s disgust at the French rejection of them, which makes his silence on John Wilkins even more puzzling. The same silence, incidentally, is found in Marcus du Sautoy’s recent BBC documentary, Precision: The Measure of All Things. Du Sautoy also makes the astonishing claim that the French insistence on basing the meter on the Paris meridian was somehow an act of cooperative internationalism. Marciano doesn’t go this far, and seems to understand that their seven-year exercise in trigonometry was ultimately pointless, but persists in calling this nationalistic reboot or retread of some very old ideas an act of invention. He also discusses problems with the seconds pendulum that were apparent at the time, but which could have been compensated fairly readily. (A seven-year study of the behavior of pendulums in various parts of the world would also have provided a lot of information on the precise shape of the earth.)

The author’s Tilt-A-Whirl approach to history is engaging, his chapters on the French Revolution more fun than a free ride in a tumbrel, but perhaps not by much. It’s actually hard to find much in the book that has anything to do with SI, today’s metric system, or even measurement per se, except by implication — possibly invidious. There are long sections devoted to such things as English spelling reform: Noah Webster’s partially successful efforts to redefine American English; and the completely unsuccessful attempts of such disparate characters as the rather pathetic Melvil Dewey (of Dewey Decimal fame), and Teddy Roosevelt. The efforts of advocates of artificially constructed languages, Esperanto, and its less-known predecessor Volapük, are detailed. One entire chapter is devoted to the development of standard time; and another is on attempts to rationalize the calendar, which continued through the 1920s. Cranky figures take the front row, including extended discussions of perhaps the greatest of nineteenth-century crackpots, Charles Piazzi Smyth, and his obsession with the Great Pyramid. Yet another chapter is given over to a man who, although no crank, is no more than a footnote in metric history: John Quincy Adams and his pointless and unreadable Report on Weights and Measures.

A great deal of the book concerns something that most people today wouldn’t think of as measured at all: money. This is justified on the grounds that “In the late eighteenth century, coinage was not only a part of weights and measures, it was the most vital part, and had been for thousands of years.” This is arguable (although some of us might point out there was an awful lot of measurement-based engineering going on in the ancient world, and when buildings and aqueducts fail, people die). But even granting this, money today is counted rather than measured: a very different thing. Neither SI, nor any of its several predecessors has a monetary unit. This doesn’t mean, however, that we aren’t going to be spending some time in Bretton Woods.

Eccentrics and guru-like figures continue to dominate in the “contemporary” section, from about 1970 onward (essentially just the last three chapters). Two of these are introduced in chapter one: Stewart Brand, described as a “libertarian prototechie,” and Tom Wolfe, a “literary icon in a white suit.” Brand, editor of The Whole Earth Catalog in its myriad forms (all of them aging ungracefully, or thankfully forgotten) specialized in demagoguery by using metric system and nuclear power in the same sentence on all occasions. Wolfe then apparently dealt metric a crushing blow when he judged a “Most Beautiful Foot” contest at a party called a “Foot Ball.” Yet another oddity: the editor of the American Journal of Physics (actually a teaching journal) is cited, apparently with approval, for using such units as the “jelly doughnut” (106 joules) in an attempt to make science more understandable. (Last time I looked, the joule was an SI unit, and 106 was the prefix mega-. I like reporting food energy in megajoules, and I’m completely on board with making science understandable. I’m just not sure rebranding the megajoule as a jelly doughnut is the best way to do this.) The book also degenerates into reporting anti-metric t-shirt slogans and schoolyard taunts of the era.

Does the book address any technical issues at all? Very few, but one comes up at least twice, attributed to Tom Wolfe: “NASA had gone to the moon on inches and pounds and had never considered any other system.” Not true, of course. The computers aboard the Apollo spacecraft performed all calculations in metric. Only the displays were in archaic units. Considering the low speed of those early computers, that unit conversion must have been a significant extra computational load. But it is true that NASA was and is hostile to metric.

The author is under the curious impression that NASA learned a lesson from the Mars Climate Orbiter: “America has gone metric where it has been useful to do so. Thankfully, this now includes space travel.” Sorry, but again no. Official policy to the contrary, NASA and its supporting industries are as intransigent as ever. For as long as the Space Shuttle was in service, NASA baulked at any attempt at metrication, on the grounds that the conversion of drawings would have been too expensive. Now the Shuttle is retired, and the US has no manned spacecraft. American astronauts thumb rides on Russian spacecraft. NASA has as near a clean slate as it will ever have. But the contract for Orion, the manned spacecraft intended to replace the Shuttle, was awarded to Lockheed Martin, at least in part because Lockmart specified in its proposal that archaic units would be used whenever possible.

And our poster child for rational, democratic metrication? Australia gets one mention, and only to say that it had found metrication a “relatively straightforward project.” Come to think of it, there is another dog that didn’t bark lurking here. The Australian experience was that metrication costs were so low they were instantly swallowed up in the benefits. Considering how money-oriented this author is, it’s strange he never considers such terms as one-time costs, or ongoing benefits.

The book ends on a weirdly inverted triumphalist note. In fact, the entire book is a kind of celebration of technical and economic eclipse as social triumph. When I picked it up, I had in mind a map of a metric world with one obvious, US-shaped black hole in it, and the question “What happened?” Now that I’ve put the book down, I still have the same question.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page

Related essays:

John and the Argot-nauts

Bonfire of The Vanity Units