EXAMINING THE PERFECTION OF THE METRIC SYSTEM
The metric system is perfect. How could the old-timers still believe in units based on body parts, like inches (length between two knuckles) and feet - with odd divisions of 4, 8, 12 and 36? Or a system based upon other oddball measures such as quarts, pints, and cups? To further complicate things, the old-timers use fractions like quarters, eighths, and sixteenths. How archaic!
Why can’t these anachronistic fools see the glorious decimal perfection of the metric system, which logically uses base 10 (decimal) divisions with logical prefixes (deca, centi, milli, etc.). It is known that the metric system is based on traceable units inherent to natural objects, like the circumference of the earth, and it ties the different weights and measures together, again using objects representing the natural order, such as the volume and density of water, to tie its basic units of weight and mass to its basic unit of length. Switching between units is as simple as moving the decimal place. Metrological perfection.
In contrast, the concept of using even denominator fractions (1/2, 1/4, 1/8) came from the ancient practice of ‘halving’ or being able to divide something evenly in two. This was used for the simple reason that in the case of length, halving provided symmetry. Also, since most ancient workers were illiterate, workers measured length with an unmarked string. Folding the string provided a simple way to divide it into equal parts - halves, quarters, eighths. Without mechanical spring scales, weights were measured by comparison to known objects, such as coins, using a simple balance. Half on one side, half on the other. Hence, the archaic system of these quirky even-denominator fractions. How could these antiquated methods still be used by the United States, the largest industrial nation on the planet? For the record, China is making a mark in the industrial revolution, but don’t kid yourself, they are still miles (or kilometers) behind. The answer to the question above is simple. The ‘perfect’ metric system - the iron colossus of flawless measure of all things - has feet of clay.
Let’s look at the cornerstone of the perfect system by which all nations can gather together in metrological bliss – the meter (or metre if you prefre). It seems the first chink in the armor of the perfect international system is that countries can’t agree on how to spell it.
The meter traces its roots to 1791, when the French Academy of Sciences agreed on the definition of the unit of length in the new metric system, the “mètre”, as being 10-7 (one ten-millionth) the quarter of the circumference of the earth. All measures based on this would follow a perfect base ten system. Wait! Did you say a quarter of the Earth’s circumference? That’s right, the entire perfect decimal system is, at its core, based on (gasp) one quarter, one of those despised, archaic, even-denominator fractions!
Continuing down the sordid history of the meter, we find that in 1792, two astronomers were sent by the French Academy of Science in opposite directions from Paris (the center of the universe, according to the French) to Dunkirk and to Barcelona to precisely measure the diameter of the Earth. It took them seven years. From the measurements of this intrepid duo, the ‘official’ meter standard was fabricated. It was a platinum bar (actually platinum alloyed with other metals for strength and stability), precisely cut to the distance of one ten millionth (10-7) the distance of the quarter circumference of the Earth, as measured through the longitude of Paris. With much fanfare, the French scientists declared the virtue of the new system, and its irrefutable tie to the greatest constant imaginable, the Earth. They invited scientists from all over the world in order to sell them on the worthy concept. However, upon the death of the astronomer who took the Barcelona measurements, it was revealed that while he was imprisoned in Spain (during this measurement adventure, Spain declared war on France), he was able to retake his original measurements in Barcelona. The two measurements didn’t match. For the life of him, he couldn’t reconcile the difference. He chose to alter the numbers in his report. Upon his death, the discrepancy was discovered. For the official report of the expedition, his colleague arbitrarily chose the concocted measurement, citing the following sentiment:
“We would not tell the public what it didn’t need to know.” “Because after all, does it matter if it is wrong? And can the meter be wrong? ”
To add insult to injury, the definitive meter measurements assumed an ‘Earth flattening’ equal to the fraction 1/334, which was shown to be in error shortly after the measurement expedition took place.
And, so it would seem, the entire foundation for the meter is based, not on accurate scientific measurements, but on mistakes that were hidden from society until after it was too late, coupled with a laissez faire attitude on the part of the metrologists who established it. For all intent, the meter - that perfect unit of metrology - like the ‘yard’ that preceded it - might as well have been based on the length of the king’s arm, as had been the ‘pre-meter’ custom.
The meter has been redefined several times since the ill-fated definition of 1798, with the latest definition of perfection being defined as the distance light travels in 1/299,792,458 of a second (in a nature-abhorrent vacuum). Ah, don’t we long for a measurement based on simple even-denominator fractions?
Disregarding all of the above, as the measure of all things, the meter is still deficient. Look at any scientific calculator. It likely has a button labeled ‘DRG’, which ingeniously converts angular measurement between degrees, radians and grads. Grads? What’s a grad? The official metric unit for angular measurement is the gradian (grad, or gon, to the metric purist familiar enough to call it by its nickname). A grad is 1/100 (or 0.01 to be metrically proper) of one quarter of a circle. Wait, one quarter? You mean the perfect decimal system has another decimal unit based on an even denominator fraction? Seriously? No matter. When was the last time anyone used a gradian? Never. That’s how useful it is. Now that you’re familiar with the grad, it might be nice to know that the conversion from grads to degrees is 9/10 (or 0.9).
Even metric system purists have to admit that angular measurement just works better using a base six system. If a circle is divided into six equal parts, the chord of each forms an equilateral triangle, useful in a lot of real-world scenarios. This means that six round shafts of the same diameter bundle together perfectly around a central shaft, again very useful. The trigonometric functions (sine and cosine) of a circle divided equally into sixths are simple fractions, such as 1/2, √3/2, etc. Even dividing into quarters or eighths gives simple functions. Dividing into 400-ths on the other hand… ick!
Time, of course, is based on angular motion of the earth, which also lends itself well to a base six system, or multiples of six. A decimal system of time was decreed by the French at the start of the metric system. A day was comprised of 10 hours, comprised of 100 minutes, comprised of 100 seconds. For reasons that seem obvious, the French officially stopped using decimal time after just 17 months. However, this didn't stop some ‘new-traditionalists’ from continuing to observe decimal time, and a few decimal clocks remained in use for years afterwards, presumably leading to many missed appointments.
Ah, but you argue that working calculations in metric is so easy because its inherent ‘decimality’ allows the user to switch measurement units by simply moving the decimal point. Thus, a length of 1.000 meter equals 10.00 decimeters and 100.0 centimeters. This reasoning, a possible advantage when using a slide rule, is as antiquated as the illiterate worker and unmarked string scenario mentioned above. Every person on the planet (at least every person who might be doing calculations more complex than measuring donkey dung) has access to a digital calculator. The author would wager that you can reach one right now without even getting out of your chair. Nay, I’ll wager you can reach two or more. Grab one, punch in a number, say 3,246 centimeters. Now convert it to meters. You punched in “÷ 100 =”. Five keystrokes (unless you’re using RPN, in which case you punched in something like “100 ÷”, for a savings of one keystroke). Now convert it to inches. You punched in “÷ 2.54 =”. Six keystrokes, assuming you need that kind of accuracy. For rough measure, you can save keystrokes by dropping the least significant digit, a trick that doesn’t work in the metric system. Of course, you can run any metric calculation without doing the conversions and keeping the decimal point shifts in your head, but for any decent series of calculations, the odds of a gross error would be high.
Ah, but you point out that the metric system is so easy when converting between weights and measures, since the liter equals one cubic decimeter, the kilogram equals the weight of one liter of water, and the Newton equals the mass of one liter of water. Thus, a tank of water containing one liter will weigh one kilogram (assuming all weighing is done on Earth) and exert one Newton of force in an inertial system. But the world does not run on water alone. If you need to measure any other substance; fuel, milk, honey, salt water, or the aforementioned donkey dung, you’ll be reaching for the conversion tables regardless of the measurement system in use. (Just for the record, donkey dung has an average density of 23.645 lbs/ft^3 or 378.76 kg/m^3, when in a compost pit.) [1]
But there is a core fault with the metric system - buried deep, yet also in plain sight - that renders moot any discussion of the system’s positive attributes. The entire concept of a base 10 system is flawed. Why do we use base 10? Again, the answer is simple – because we have ten fingers. So, just like the metrologically-appalling inch, foot and yard, the metric system’s core value is based on (wait for it) … body parts! Maybe this is understandable, since the base 10 system has been around so long, it is difficult to think in any other base. Or is it?
When scientists were finally able to invent thinking machines, did they choose to write the machine’s mathematical capabilities in a base 10 system? Hardly, and for good reason. Everyone understands that computers use the most basic of mathematical systems, base 2 or binary. While not practical for ‘human-readable’ calculations, the binary system converts quite easily into base 8 (octal) or base 16 (hexadecimal). These number systems are much more in tune with a system based on nature. Even the human hand really lends itself to base 8 if we only count the forward-facing digits, omitting the oddly placed, but quite useful, opposable thumb. Almost nothing in nature uses base 10. Look around and you’ll see numerous examples of base 3, 4, 5, 6, 7, 8, 9 and 12, but hardly ever 10. When the machines inevitably do take over the world, they will undoubtedly purge the world of the antiquated, useless metric system based solely on a peculiar number of appendages of imperfect biologicals, while pondering why the males of the biological species didn’t use base 11.
But still, shouldn’t the US convert to the metric system just to keep up with the rest of the world? That is the wrong question. The real question is this. Why should the US convert from one flawed measurement system based on fractions and body parts to another flawed system based on fractions and body parts? Once standardized as the national measurement system almost two hundred years ago, the IPS system has been working just fine, despite possibly needing an extra keystroke now and then. So, for the time being, or until the machines take over and concoct a system based on binary and real universal constants, the following truth stands:
There are two measurement systems on the planet. The metric system and the system that first put humankind on the Moon.
Long live Lunar Units!
-(c) Bob Carlton February 2023
Footnotes: [1] Physical and Frictional Properties of Donkey Manure at Various Depths in Compost Pit M. Chowda Reddy and M. Dronachari https://core.ac.uk/download/pdf/211015455.pdf (You really can’t make this shit up.)
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