The Metric System and Coincidence

By The Metric Maven

On July 4th, many, many years ago in Montana, I went out with a group of people to shoot at prairie  dogs. This was a common activity in rural Montana. It was common enough that the prairie dogs understood what was happening and would not surface above their burrow unless they were certain the hunters were far enough away so a .22 rifle was ineffective. It was very hot, and the prairie dogs seemed to have out-smarted us. We were about to leave, when one of us pulled up their rifle and aimed it at a far-off prairie dog. The target was but a tiny shadow on top of its mound, but stood up high, and defiant in the certainty that it was safe. The entire group began laughing and deriding the fellow with the rifle. “You might as well shoot popcorn at that gopher. You’re just wasting a round” they said with ridicule in their voices.  (Montanans sometimes called prairie dogs gophers) This only strengthened  the resolve of the varmint hunter who said “Oh, yeah, well at least I’ll scare him good.”  It must have been 150 meters to the tiny silhouette. He squeezed the trigger and the Prairie dog flopped over instantly. The entire crowd was stunned. One person said “That’s the most incredible shot I’ve ever seen!”  Three people began running over to inspect the scene. They were about three meters from the mound when they all put on the brakes and started screaming: “rattlesnake!  rattlesnake!” and retreated faster than they had arrived. The prairie dog had not been hit by a bullet, but instead, at exactly the same time the shot was fired, a rattlesnake had struck the unfortunate animal. This incident has always stood out in my mind as one of the strangest coincidences I’ve witnessed.

This coincidence however seems tame in comparison to some metric coincidences I’ve come across. One of the strange arguments that is offered by those against metric has been “metric lengths are unnatural” and the sizes of metric products aren’t a product of “natural” dimensions like those of imperial sizes. In his very first newsletter Pat Naughtin states in his Hidden Metric section:

As vinyl records developed, in the 1920s, they were designed and made 250 millimetres and 300 millimetres in diameter. In English speaking countries, they have been called 10 inch and 12 inch records ever since.

This seemed incredibly implausible. I took my trusty Australian mm ruler and measured a 33 1/3 LP. Wow, it was almost exactly 300 mm!–but not quite. It was actually 301 mm. I kept looking at the discrepancy and wondered if the extra mm was from the pressing process. It was hard to imagine if the specification was 300mm that any company would allow 1 mm of waste on each pressing. I did a web search and to my surprise found RIAA specifications for records. In the tradition of American Medieval Unit standards, it is written in the strange and tangled world of fractions:

The Diameter of a 12″ record is: 11 7/8″ + 1/32″ Now assuming the 1/32″ is a one sided tolerance we have in mm:

12″ => 301.625 mm + 0.79375 mm = 302.42 mm

Average = 302.02 mm

This is very close to 300 mm but LP records almost certainly are not based on metric. In the case of a Big Ten Inch Record, the specification is 9 7/8″ + 1/32″ which in mm is:

10″ => 250.825 mm + 0.79375 mm = 251.6187 mm

Average = 251.42 mm

Once again this is really close to 250 mm, but not quite, again it looks like an Olde English specification, that could be confused for a metric one. The other standard size (45 RPM) is 7″ which is 6 7/8″ + 1/32″ according to the specification.

7″ => 174.625 mm + 0.79375 mm = 175.418 mm

One can easily see that Pat might have mistakenly been told that records were 300 mm, 250 mm and 175 mm in diameter. A quick measurement would seem to verify this fact—except if you are a reasonably exacting Engineer like the Metric Maven, the small discrepancy would begin to bother you. Although it was a German-American inventor, Emile Berliner,  who is credited with developing disc records, there is no mention of metric sizes in Wikipedia.  It is quite interesting that these “metric sizes” appear quite natural and have seemed so to American citizens over the decades. Much to my surprise, vinyl is not dead, and seems to be expanding. Every time I ask for an album at my local independent music store the first question is: “vinyl or CD.”

This metric question of vinyl diameter has been superseded by the introduction in the 1980s of the metric defined CD which is 120 mm in diameter, and is indeed specified as metric, independent of the size of the standard case housings.

While LPs might be interesting, there are much bigger metric coincidences. The first has to do with the fact that John Wilkins, the British man who invented the system part of the Metric System, used the length of a seconds pendulum to define what later has become known as the meter. Early on it was suggested that a seconds pendulum be used to define the meter in order to tie its length to a scientific phenomenon. Unfortunately the length of  a seconds pendulum depends on its latitude, which became a point of contention. One can see in the figure below that a seconds pendulum from a 19th century clock is very, very close to the length of a modern meter. The alternating colored sections are 100 mm in length.

Pendulum from 19th Century Clock with Meter Stick

The next idea was to define a meter as one ten-millionth of the distance from the north pole to the equator. James Clerk Maxwell found the idea of using this distance across the Earth to be frivolous, and made sport of it in his understated way, in his famous Treatise on Electromagnetism. Clearly the distance of a meter, as defined by a seconds pendulum, would be quite different than one ten-millionth of the distance from the north pole to the equator—right? Well, no, amazingly enough the circumference of the Earth through the poles is slightly more than forty million meters (40,007,863 m) and the two suggested values of the meter are remarkably close. I find this a very surprising coincidence.

James Clerk Maxwell proposed that light is an electromagnetic wave and used his theory to predict the expected speed of these waves. His answer was 193,308 miles per second. Later in the 20th century the value would be accepted as 186,282.3959 miles/second. It was Albert Einstein who put the speed of light at the center stage of physics and directly related energy and mass using the speed of light in his famous equation E = mc2.

When the meter was finally defined with a scientific phenomenon, it was in terms of counting a number of wavelengths of light of a given color. The next metric coincidence is that the speed of light, when expressed in meters per second, is 299,792,458 meters/second. Don’t see the coincidence? Well this is only 0.07% from 300,000,000 meters per second. I use this approximate value almost daily in my Engineering work. Myself and my peers all use 3.0 x 108 meters per second for hand calculations. It is a nice round number and easy to remember. For instance, let’s compute the wavelength of an electromagnetic wave of 3 GHz (3.0 x 109 Hz) in free space. It’s 99.93 mm if one  uses the exact value for the speed of light. When the 3.0 x 108 m/s approximation is used it is exactly 100.00 mm. The error is 69.17 μm! Yes, micrometers!

When used for everyday engineering computations, there is no need to remember the exact value of the speed of light, as the approximate one is so close, there is no reason to bother. This is an amazing coincidence.

Another coincidence that I find quite interesting (and will discuss in a future blog) is that in Boulder, Colorado one cubic meter of air has a mass of almost exactly 1 kilogram. On the coasts it is about 1.2 Kg.

Here are some other metric coincidences:

The width of a human male hand is about 100 mm.

The length of a stretched human pace is about one meter (1 m)

The distance from the Earth to the Sun is almost exactly 150 Gigameters (150 Gm)*

The volume of the Earth is very close to one Yottaliter (1 YL).

The distance across the Milky Way Galaxy is about one Zettameter (1 Zm).

The diameter of the local group of galaxies is about one hundred Zettameters (100 Zm)

And one engineered non-concidence is that the circumference of the Earth is almost exactly 40 Megameters (40 Mm)

I find these metric coincidences far more interesting than the Fourth of July rattlesnake coincidence. The meter and its divisions seem to me much more attuned to the natural world than the contrived, inconsistent and almost uncountable units of the old remnants of the non-system of Olde English and Imperial, or the even more laughable American designation of same as: “standard.”

It is time for all of us in the United States to give up this unnatural, non-system of measurement for the one that nature clearly intended—the meter and the metric system.

* In other words the “astronomical unit” has a nice integer value in the metric system