My Olde English GPS Adventure

Don't look in the trunk, it's Olde English in there

By The Metric Maven

Bulldog “Moon Landing” Edition

When I finally purchased a GPS for my automobile, the impact it had on how I drove around my city was enormous. I also immediately set it for kilometers instead of miles. Within a few weeks I had a good idea how far 100, 200 and 500 meters is and about how far I could see was often about a kilometer. For the next few years I merrily drove multi-state road trips and local ones with the GPS piloting my excursions.

My father did not own a GPS at the time I purchased mine and was curious. At his request I brought it with us on an errand and we set it to find the address where an old family friend had lived at a nearby lake. It immediately told us to proceed 200 meters to a nearby stoplight. My father’s face contorted, and some very disapproving prose was uttered. I don’t recall what he said, but I do recall laughing out loud. Despite my father being “metrically challenged” the test trip went smoothly and we arrived at our destination.

Because I had not estimated drive times in metric before, I had to adapt. A useful benchmark in Ye Olde English is 60 miles per hour or a mile per minute. 40 miles is about 40 minutes. If I saw a road sign which stated it was 270 miles to a destination, I would have to multiply out integer values of 60 and figure the remainder. “Let’s see 240 miles is four hours and 30 left over is 30 more minutes. so four and one half hours.” I immediately realized I had lost the mile per minute guesstimate in metric, but hours were instantaneous to determine. A good guesstimate of an average speed is 100 Km/h Kph . So let’s suppose a kilometer marker states it’s 450 Km* to a destination, immediately we know it’s 4.5 hours. For short trips I know that 0.1 hour is six minutes. If it’s 10 Km to a destination it’s about six minutes, 25 Km is 15 minutes, 50 is 30 minutes and 75 is 45 minutes.

I happily continued my GPS guided metric motoring over the last few years without incident. Then, this last winter I had a disruption. It had been hovering about zero degrees Fahrenheit or about -18 Celsius outside. I went to my car and drove to a battery store on a side of town with which I’m unfamiliar but was straightforward to find. I needed to go to a market next, and wanted to take the most direct route. I fired up my GPS. There was just one problem, it had been so cold the battery went dead and reset the unit. I had to tell the unit I was in the US and other information. I could not find my stored addresses. I tried cycling the power. All my saved addresses re-appeared!  Great! I selected the market and began driving. The GPS display indicated I needed to drive 7 Km and make a right turn onto an interstate highway. I thought to myself “that’s not too far.” It seemed like it took quite a while to cover the 7 Km, but I took no real notice. When the turnoff onto an interstate highway arrived, the voice instructed me to “turn right in 0.4 miles.” Suddenly I had no idea how far that was. Even though I could see the turnoff, it bothered me I had no correlation with distance. As I entered the highway I was told to drive 7 miles. When I approached the off ramp to the secondary street leading to the market it again gave the distance in tenths of miles. They had no meaning for me.

I was completely familiar with this road and the turnoffs in metric, but the correlation with the Olde English distances on my GPS were giving me a sort of unexpected vertigo. As I approached the market I looked up at the distance display and all I could read was 600. I was so used to seeing meters there that my mind rejected what it was seeing. I thought it can’t be yards, they’re like meters, it must be feet. When I pulled into the parking lot I could barely read a tiny ft stacked up on the GPS units after the number. But it had been tenths of miles previously when I was turning. When did the units switch?

Driving with my GPS set to kilometers caused me to pay little attention to the distances on signs. Without metric for a touchstone, the craziness of US road signs became stark. I noticed this sign which indicates the left lane will end in 1/2 mile. You will note there is a second follow-up warning sign, which can be seen along with the first but not read:

This Lane Ends 1/2 Mile (note the second warning sign in the distance)

Here is the second warning sign in the distance:

This Lane Ends in 1000 feet

The first sign tells me that the left lane ends in 1/2 mile or 5280 feet/2 which is 2640 feet. The second sign, whose presence is clearly seen from the first, next tells us the left lane ends in 1000 feet, which is of course 1000 ft/5280 ft/mile or 0.19 miles approximately.  Wow! How had I not noticed this crazy set of signs before?—oh—I was using metric with my GPS and ignoring them. If they had been in metric the first sign might have said:  This Lane Ends in 800 meters, the second sign could then say This Lane Ends In  300 meters. This is much easier to read than 0.8 Km and 0.3 Km. Nice Naughtin friendly integers, and the same units for both signs.

One never hears cries of the “implied precision fallacy” when feet are used in a context like this. In this case the first sign is in miles, the second is in feet. This is a ratio of 1:5280. Where are the cries that feet are too small of a unit?—they imply too much precision for this usage—or that miles are too large?  In the case of kilometers and meters, the ratio is only 1:1000.

When I returned from shopping, I set my GPS unit back to kilometers. As soon as I heard proceed 500 meters and take a left, I was calm again. As I drove home I noticed something else. I had not been  looking at the distances on the road signs as my GPS provided distances to exits in metric. Apparently, when I was looking at the signs, I had been just noticing the road name and the exit numbers. With the interruption of my GPS unit still firmly in my mind, I realized that the road signs all had fractional distances. Harlan street 3/4 mile, or Jessman Drive 1/2 mile, yet the GPS would output decimal miles—-0.75 miles or 0.5 miles—-it did not match the fractional expression on the signs. This was but one more reminder that we have not even fully embraced decimals in this country, let alone the metric system. No wonder it seemed so odd.

Once I used a GPS with metric measurement, I embraced a system which has a dimensional continuum. I understood meters, and if I was told it was 1000 meters to a destination (which it has) or  alternatively 1 kilometer, this created no distance discontinuity in my mind. They both cognitively registered as the same distance without distraction. Metric forms a continuous expression of sizes. When using Ye Olde English/USC/ACSOWM one may choose whatever unit you feel like, in fact we are encouraged to do this by our grade school pedants, but this farrago of units creates discontinuities in cognitive quantity comprehension. The sudden change from tenths of miles to hundreds of feet was a jolt. I was so happy I had my meters back.  Olde English has hundreds of units from which one can choose. A false maxim of The Ye Olde English Arbitrary Grouping of Weights and Measures, is to choose a unit that fits the closest to what you’re measuring. This multi-card measurement monte encouraged massive unit proliferation, which in turn allows massive opportunities for fraud and confusion.

The metric system has but one base unit for length, the meter. The prefixes describe units which are multiplied or divided by 1000. The length of an object falls on the metric measurement continuum. If its length is near a prefix boundary, Naughtin’s Laws help to keep one’s intuition of magnitude continuous by smoothing out discontinuities. (This is also a reason I’m against the use of centimeters, and believe they should be discontinued for actual computation)

I had an unexpected realization from my GPS reset. Suppose you were from another country—ok any other country sans Liberia and Myanmar, and visited the US. You have been brought up on the metric system, and suddenly you are confronted with US roadsigns. You first must contend with miles, and signs with fractions of miles, not decimals. Then  you suddenly encounter a sign that says: Right lane ends 500 feet. We switched units on you from miles to feet, and possibly even yards. You have no idea if that is near or far as the base unit of length has been changed–radically. One can see how this switching of units could cause panic, measurement vertigo, and uncertainty for a visiting driver. I had somewhat experienced their possible confusion when my GPS reset itself to Ye Olde English—and I grew up in this country.

Unfortunately our provincial culture does not seem to allow us to understand the potential confusion our jumble of units could cause a visitor from another country. The few who do try to accommodate visitors find it tough going. In 1982 the state of Florida decided to add metric units to its highway signs. The rationale behind this change was that over five million tourists visited Florida and many of them were unfamiliar with Olde English units. They also believed it would encourage Americans to become more familiar with metric units. Florida was going to use its own funds to implement this change. There was only one thing they needed, the approval of the Federal Highway Administration (FHWA).

It came as a surprise, when, despite the 1866 federal law which does not allow the prohibition of metric units in the US, the FHWA refused to allow the signs. They argued that Congress had passed a law which prohibited the installation of solely metric highway signs using Federal funds, unless Congress approved. The installation of these signs would violate neither of those conditions. The FHWA would later reverse itself without providing rational reasons for the attempted ban, or why it changed its stand. Like most tales of metric in the US, a later Florida Governor would refuse to allow the signs to be installed.

After my experience losing metric in my GPS, I can truly say to visitors to this country who must drive our roads, I feel your pain.

* Yes I’m using capital K deliberately.

The Incorporeal Ruler

By The Metric Maven

It has been noted that on Star Trek (TOS) that one never sees a ruler. Measurements are made, but only using a tricorder or some other device it appears. Rulers had somehow been banished to the past. Technological change has apparently rendered rulers obsolete in the 22nd Century.

One evening I was watching an episode of World’s Toughest Fixes. Sean Riley, the host and participator in the fixes was involved in dealing with a problem where the clearance of a roof, inside of a giant building, which was many, many meters high needed to be known to within 125 mm or so. This accuracy and precision over such a large distance was causing great heartburn. Riley reached into his complement of tools and produced one which could be placed on the floor and would measure the distance to the roof with millimeter accuracy. It uses a laser. I was dumbfounded. This was such a cool measuring device I wanted one, but could not really justify it in my line of work. After the measurement was performed, the crew was now confident they had enough clearance, even though none of them could have possibly used a tape measure to directly determine the unknown distance. The customary use of a graduated rule was essentially out of the question. This lead me to think about the origins of the common everyday ruler.

The earliest known graduated measuring rod dates from 2650 BC, and comes from ancient Sumer. It is very crude and has six graduated lines across its length. It’s not much to look at and is reproduced below.

Copper Alloy Sumer Cubit Bar (click to enlarge) -- Wikimedia Commons

One can see considerable scale refinement in a surviving cubit rod from Ancient Egypt. The rod has a number of equal divisions along its length. This base division has separate divisions of the base length division, into 1/2, 1/3, 1/4, 1/5 … to 1/16. This device is beginning to look remotely like a modern measurement scale, but still has a long way to evolve.

Cubit Rod from the Turin Museum (click to enlarge) -- Wikimedia Commons

Rectangular/square bars with fixed graduations continued in use with more precise markings and of more stable materials into the 19th Century.  A British Parliament fire in 1834 destroyed their length standards and new ones were commissioned to replace those lost. The British fabricated one inch square rods which are 38 inches in length. The rods are constructed using Baily’s metal No. 4 consisting of 16 parts copper, 2 1/2 parts tin, and 1 part zinc. A pair of markings on gold plugs, which are recessed into the bar, defined the length of one yard at 62° F. The plugs are recessed into the bar so they would be co-located with the axis of symmetry. This is known as the “neutral plane” where length error due to the sag of the bar under its own weight is minimum. Two protective plugs were used to preserve the defining lines. Despite the fact that the standard provided by the British was not sanctioned as an official version by parliament, only the first five copies were, the English Bronze Yard No. 11 was the official standard of the US until 1893, when the metric system was adopted.

The Official-Unofficial Yard Bar No. 11

The change to metric standards for length definition in the US occurred because the yard and its copies were shrinking at a rate of one part per million every twenty years. This shrinking was due to the relaxation of internal strain which had been introduced in the fabrication process. It was also noted that the pound provided by Britain was also “unfit for use.” By the time these problems were understood, it appears that the technical community in the UK saw the future was with metric and joined in the international collaboration. The best technical minds available were all focused on the best and most stable measurement artifact possible, which did not use a prohibitively large amount of platinum. The book The Evolution of Weights and Measures and the Metric System (1906) has an illustration of the candidate cross-sections which were studied for a meter length standard. The idea was to produce a very rigid bar which would create a very stable “neutral axis” in the center of the bar.

The use of an X cross-section was finally settled upon. Below is what was finally adopted.

There were two versions, one version with a pair of lines, and another which the length of a meter was defined by the ends of the bar. Below is a meter bar with engraved lines.

Meter Bar

This was the first adoption of a non-rectangular cross section measurement artifact for use as a calibration standard. The original meter bar was rectangular (figure 1). This change to a X design illustrates that the metric system continued to evolve, and the English standards atrophied and became neglected. T.C. Mendenhall (1841-1924), superintendent of the U.S. Coast and Geodetic Survey, realized that if the US wished to maintain accurate metrology when compared with the rest of the world, metric standards would have to be used. There was no alternative. Fortunately, the US had signed the Treaty of the Meter and a set of US metric standards existed and were available. Congressional inaction required Mendenhall to make a decision to use the existing metric standards, instead of the British ones, despite the fact that there was no legislation which sanctioned such a change. Mother nature does not succumb to the will of legislative bodies, and so Mendenhall now defined all lengths in the US in terms of the meter so that American metrology would not be left behind.

The neglected British measurement standards no longer kept up with improvements in metrology; they were now technologically dead. All new metrology improvements were only to be found within the metric system. Technical improvement continued to evolve until finally the meter artifact itself became obsolete and  was replaced with a length based on the counting of a number of wavelengths of light (pioneered by Americans). From this point forward, an artifact ruler was no longer the basis for a length standard, but was instead derived using a standard which was tied to a repeatable scientific phenomenon, which meant it could be reproduced anywhere on the planet–or even off the planet. Length definition had outgrown the primitive measuring stick used by our ancestors.

The laser measurement device used in World’s Toughest Fixes points to a possible future when rulers might become less ubiquitous (it is hard to imagine them actually disappearing from use). Unfortunately, we in the US continue to pretend there has been no improvement in measurement and its usage since the days when barleycorns were used to define length, and fractions were the state of the art for tape measures, rather than the use of decimals. It is an embarrassment for the US that our measurement usage has more in common with an ancient hand-carved cubit rod, than a precision laser.