When I first began work as an Engineer, much measured data was still read from instruments, and then written by hand onto paper. What I noticed when presenting numbers to other engineers was that there would be a constant questioning. Had the number after the decimal point been switched, or was the number written down wrong? Did my technician or myself actually write down 5 whereas the number was 2. A very talented older engineer with whom I worked, told me he had figured out how to deal with that problem. It was the early days of computers, so he would take the handwritten numbers, type them into his computer, and make a lovely table. This poetic license has no effect on the accuracy of the numbers. It only changed the technical reviewer’s perception of them. Only within the mind of those evaluating the numbers would it produce a modification.
When the numbers were put into computer typefaces, even with dot matrix output, there was an immediate assumption by others that the numbers had to be right. Every time my friend did this, he was able to sit down and talk about the data without the constant questioning about the accuracy of the numbers–yet nothing material about them had changed.
Reflecting on this made me wonder about the seeming desire to use excessive decimal points. Pat Naughtin pointed out that the use of integers, or simple numbers, as he often called them in his lectures, increased the ease with which a person’s mind could compare numbers. Why is simplicity often unnecessarily sacrificed for complexity when creating tables of numbers? This is often done by persons who are in vocations that are heavily number based. Chemistry Professor Jeffrey H. Williams has written a monograph called Defining and Measuring, subtitled The Make Of All Things. It was published in 2014.
For instance, if you look at a table he presents of ancient Mesopotamian measurement units, the comparisons are in my view rather muddled:
For instance the Grain seed is 2.7 mm, but the next size is 1.65 cm?–rather than 16.5 mm? Why switch to centimeters in this case (or in my view ever)? I believe this table is for comparison purposes, and a more meaningful presentation could have been accomplished by attempting to invoke Naughtin’s Laws. Do we really know these ancient units to micrometer precision? The value 2.7 mm looks authoritative, and 16.5 mm also looks very authoritative. It says Modern Metric Equivalent, but wouldn’t these numbers, in their contemporary times, that is ancient Mesopotamia, have had uncertainties that were larger than 700 to 500 micrometers? One could actually use millimeters and meters up to the kilometer equivalent and separate them by prefixes:
Do we believe numbers are more accurate if we see decimal points? When comparisons are made, simple numbers are the easiest for the mind to readily compare, but sometimes large dynamic ranges can make it difficult to use pure integers, and maintain a single unit.
Williams makes this assertion in his text:
The Ancient Chinese used (and modern Chinese still use) a foot as their fundamental measure of length.
Then he goes on to state:
“…that the length of the ancient Chinese unit of measurement, the foot, increased from 0.195 m to 0.308 m over the last three millennia.”
Beyond my surprise at Williams’ assertion that the foot is still used as a fundamental length in China (I would like to see some documentation) I could not see why he didn’t say: “the foot, increased from 195 mm to 308 mm over the last three millennia” rather than introducing a decimal point with a leading zero. Does 0.195 meters seem more precise and accurate than 195 mm? Why did he introduce the decimal version? Was there a psychological reason more than a measurement presentation reason? I have no idea, but I’ve noticed this manner of numerical change in many other contexts.
Williams appears to gush at the succinct nature of the metric system, but does cause me a moment of concern when he uses the phrase “language of science”:
In fact, today we have seven base units which may be combined to explain every known scientific phenomenon, and which would be used to comprehend scientific discoveries that have yet to be made. That is, it is through these seven base units that the true universal language, the language of science is formed.
Later Williams discusses the oft-cited Mars Climate Orbiter metric/Ye Olde English disaster under the heading: The consequences of mixing units.
In Chapter 8 Williams finally sets off some real alarm bells of concern in my mind:
Systems of units and the ability to convert between different systems of units; for example, to convert from units in the British Imperial System of units to SI units is something that is no longer taught to science students. This is a great shame, as the different systems of units are only dialects of the single universal language of science, and an inability to communicate with people speaking these different dialects can limit
a scientist’s world view.
The lack of a proliferation of measurement units could limit a scientist’s world view??? What a strangely “new age” type of statement for a scientist to make.
Williams goes on to argue that the cgs system of units is still: “…needed so as to facilitate reading of the vast and important literature published in this area of science since the early-19th century.”
I will not go into technical details, but the lack of uniformity in electromagnetism, has caused nothing but headaches, and I would far rather see the “vast and important literature” from the nineteenth century either rewritten with modern notation and units, or left for historians to puzzle upon the gaping incompatibility between cgs and SI electromagnetic units.
The final chapter of the monograph, Chapter 13, is entitled: Dialects of the Single Language of Science. This is where the professor seriously jumps the shark in my view. He states that the metric unit of pressure, the pascal, is just too small, which precipitates large numbers:
For example, the pressure in your car tire would be about 340 000 Pa…
Well, how about 340 kilopascals? Is this really a problem? Just use an appropriate metric prefix. This number seems large. In the U.S., most people set the pressure in their tires, to about 220 kilopascals (32 PSI). Perhaps there is a difference between a tire and a tyre?
Williams then details scientific and engineering “rules of thumb” that have been developed which are not SI and how their loss would be undesirable.
These are all expressions of the same piece of information, but expressed in the various dialects of the single language of science. In dialects which are useful for particular groups of technicians and scientists.
This is pure and simply an apologist’s rationalization for a proliferation of archaic units, without any good reason. It is an untenable argument for unit proliferation. Unit proliferation and poor definition were some of the reasons the metric system was developed in the first place. Then a flood of rationalization is offered by the author:
Such varieties of units exist for sound technical reasons: convenience in specialist branches of science, or convenience or facility of use in certain ranges of pressure, or because one profession refuses to change to another system of units, or because there is such an investment in technology that any change would be too expensive. The medical profession will, for example, not move away from using mmHg for blood pressure measurement, which is convenient for them and a sufficiently precise measurement for their patients, but this is not the case for the vast majority of physicists who gave up using mmHg as a unit for pressure early in the last century.
However, the question we have to ask ourselves is whether there is anything to be gained by attempting to force a large body of professionals to give up a system of units with which they have become familiar over many generations? There is certainly the possibility of serious adverse consequences arising from such a move. It would be far better to encourage the ability to use and convert between many of these systems of units—to celebrate the diversity of the dialects of the single language of science. A scientist or a technician who can convert between these units will be someone who will truly understand the science underlying the phenomenon, and will be less likely to make foolish errors; one dreads to imagine the consequences of the medical profession or drilling engineers getting their mmHg, their pascals and psis [sic] muddled up.
Comprehending these various means of expressing pressure, and being able to convert or translate between them is a great way of learning some basic science. Indeed, this was the reason that the Emperor Napoléon I mocked the decimal Metric System and re-introduced the old familiar, non-decimal units. The Emperor correctly thought that thinking only in factors of ten limits one’s perception of nature. There is more to science than being able to divide or multiply by ten.
Celebrate the diversity of the dialects of the single language of science‽‽‽ Where have I heard such tortured prose before? Oh yes, the absolutely indefensible reply offered by the head of NIST, when he rejected the We The People metrication petition. Dr. Gallagher argued that if measurement units are a language, we are bi-lingual and we should celebrate this measurement diversity.
Then Williams appeals to technical Darwinism, and some strange idea of heirloom units to further his rationalization:
The present SI is based on a beautifully coherent model of fundamental physics, but that does not mean that every measurement made everywhere on Earth should be made using only this system of units. There is merit to be found in the various nonmetric systems of units—otherwise they would not have evolved and would not have lasted as long as they have.
So, in Dr. Williams chosen field of Chemistry, would it make sense to also make certain that students know all the alchemical names for chemical compounds?—and if they don’t exist—create some? After all, the names must have utility, they’ve been around along time and also evolved. Flower of Antimony, Liver of Silver, Sugar of Lead, Lunar Caustic, how can one truly understand chemistry without knowing how to convert these names to and from the modern ones?
By now you may be asking yourself, why on earth is the Metric Maven getting so worked up about some small monograph written by a Chemistry Professor. Well, this is a fairly special Chemistry Professor. In the author’s bio of Jeffrey Huw Williams, which accompanies the monograph, it states:
Most recently, 2003–2008, he was the head of publications at the Bureau international des poids et mesures (BIPM), Sèvres. The BIPM is charged by the Metre Convention of 1875 with ensuring world-wide uniformity of measurements and their traceability to the International System of Units (SI). It was during these years at the BIPM that he became interested in, and familiar with the origin of the Metric System, its subsequent evolution into the SI, and the coming transformation into the Quantum-SI.
Yes, he was in a more influential position than the head of NIST, Dr. Gallagher. Williams was with BIPM, and is now seemingly arguing against the complete and unique adoption of SI. He was also the head of publications at BIPM, and almost certainly had input on style. In his monograph Williams is making the same poetic, as opposed to scientific arguments for “units as a language” which the head of NIST did. Here is Dr. Gallagher of NIST’s words:
if the metric system and U.S. customary system are languages of measurement, then the United States is truly a bilingual nation.
We measure distance in miles, but fiber optic cable diameter in millimeters. We weigh deli products in pounds, but medicine in milligrams. We buy gasoline by the gallon, but soda comes in liter-size bottles. We parcel property in acres, but remote sensing satellites map the Earth in square meters.
Metrology as language is the most inappropriate simile I can imagine. The length of a meter is not a poetic interpretation—no other base unit of length is needed. If SI is not flexible enough, then it should be augmented, but I’ve never encountered a situation where the seven base units which Williams celebrated earlier in his monograph have not been sufficient, when paired with the metric prefixes. The metric system is already beautiful, expressive and mostly succinct. The introduction of barleycorn lengths and poetry will only undermine the reason SI was developed originally. Please, leave the poetry and the endless interpretation of same to poets, and leave measurement as a unique set of seven singular and immutable base units, appropriately scaled with metric prefixes, to be used by all of engineering and science, along with the butcher, the baker and the candlestick maker, as their one and only description of the world.