Trying To Outrun Ye Olde English

By The Metric Maven

If you’re studying Geology, which is all facts, as soon as you get out of school you forget it all, but Philosophy you remember just enough to screw you up for the rest of your life.

– Steve Martin

I spent a lot of my youth reading about philosophy. I mostly took classes in, and read books about, the philosophy of science. It has been of great interest, and I tended to agree with Steve Martin. Recently, I realized that it is possible to remember just enough about Ye Olde English units to screw me up for the rest of my life. The problem was inculcated into my psyche in High School. I had a serious Basketball Jones, and was almost addicted to playing the game. My coach was not amused when I was not that excited about track, and might have even thought about opting-out. After some time, I realized I was just good enough to run a leg on a relay team, and participated. The world of the mid 1970s was one where metric was in the news, but track still had the 100 yard dash. The rest of the world ran the 100 meter dash.

The relay I often ran was the 440 yard relay, where each person would run 110 yards and then pass a baton off to another person. There was the 880 yard relay where each person would run 220 yards and pass the baton. The distances generally discussed were 110 yards, 220 yards, 440 yards, 880 yards and the mile. Below are images of two ribbons my team won for the 440 yard and 880 yard relays when I was in High School.

The relay team had to place at the district track meet to move on to divisional. Going to the divisional track meet meant you could travel to a large city, experience something different, and hang out with your fellow athletes. One year, a few of the participants from our school were not able to place in any of their chosen events, and it looked like they would have to stay home.

The coach had an idea that definitely demonstrated just how much these unfortunates wanted to participate at the divisional track meet. The last event, which had still not occurred, was the mile relay. It was a terrible gut race. Each person would have to run one-quarter of a mile. My mind immediately realized that each person would have to run a 440 yard leg. The 440 was an all out gut-race. It is so short that you had to run as fast as possible for the entire length of the race. It was so long, that your body was completely spent and almost convulsing by the time you reached the finish line. The group wanted to go badly enough they did the mile relay, placed, and went to the Divisional Track Meet with the rest of us.

What seemed obvious to me at the time was that a 440 yard relay was also often called a quarter-mile relay. The 880 yard relay was also called a half-mile relay. It implied that someone had thought about our Ye Olde English measurement system, and made it possess a symmetry that made sense. A 440 yard relay, had four 110 yard legs, the 880 yard relay had four 220 yard legs, and of course the mile relay would have four 440 yard legs. The symmetry was great and clearly there were 1660 yards in a mile. It made sense, all the others had dual digits: 110, 220, 440, 880 and 1660 made perfect sense. Why would I question it?—it sounded perfectly right. The problem for me was that this incorrect sequence of numbers was attached to my mind as strongly as a leech with superglue.

When Peter Goodyear read Chapter 4 of Death By 1000 Cuts, he noted:

I’ve just read Chapter 4 of Death By A Thousand Cuts. Some of it was new to me, and quite interesting. I noticed one error.

On page 54 you have a list of factors involved in US measurements and you write:

…when one has to cognitively relate factors like 2, 3, 12, 16, 1660, 5280 and so on.

(Emphasis added by me.) I think 1660 should be 1760, shouldn’t it? The number of miles in a yard.

When I read the sentences, I wanted to angrily stare up into the sky, and with my best William Shatner impression yell: “Khan-n-n-n-n-n-n-n-n-n!” Yes, it should be 1760 yards, I’ve had this pointed out to me multiple times, over multiple decades, and my mind always defaults back to 110, 220, 440, 880, 1660. When you think of 8 plus 8 it’s 16, and there is another eight right next to the other eight so it must be 1660 my feeble brain informs me. It has to be the next number in the sequence—right. It only makes sense. As I said, cognition is important. Well, I always end up jotting it down, and hand adding, or add 880 + 880 in my calculator, and discover that yes the sum is 1760 yards, not 1660 yards! When l wrote the passage in Chapter 4, my mind even thought for a moment about the nice symmetry—that doesn’t exist! When Peter pointed this out, I knew it was right, did a face palm, and thought: “I wonder if anyone has any idea why I would write down 1660 instead of 1760?” Well now I’ve had the chance, and no matter what, I’m still wrong, and I’m convinced that I will do it again someday.

So I decided to lash out, looking for someone—anyone—to blame other than myself for my cognitive impairment. I realized that if my High School had changed to metric in the 1970s, as was all the talk in the papers, I would never have been exposed to this numerical horror. There would have been the 100 meter, 200 meter, 400 meter, 800 meter, and then 1500 meters? What? Why is that? Why not 1600 meters? Well, at least I can convert them from meters to Kilometers with ease: 0.1, 0.2, 0.4, 0.8 and 1.5 Km.

Sometime ago, when I was doing some research, I called my old High School in Montana. I asked if the track distances were now all in metric. I talked with a woman who recalled my tenure there. She said they did. Earlier records had been converted to metric and they no longer used yards. I’m still a bit surprised that my old High School changed over to metric in Track. Nowhere else in their everyday measurement lives has anything changed, but track did, but not football of course!

Pardon The Decimal Dust

by The Metric Maven

Early in my time as an undergraduate at a Midwestern university, I discovered that having “too many decimal places” on my homework was a terrible and ignorant trespass on rationality and technical competence. I was told that the decimal values in my calculation, that were only a few places past the decimal marker, were meaningless. As a graduate student, my TA had the “experience” to understand this problem, and the importance of properly rounding numbers. What I’ve generally settled on these days, is to use three places past a decimal point so that I can easily change a metric number to an integer expression, should I want to change the chosen metric prefix. I also have enough years behind me to realize that whatever number of places were chosen by my TA, they were not the product of an error analysis, they were the product of personal preference.

I’ve heard critics of “too many decimal places” call values they believe are insignificant “decimal dust.” There is no clear definition of this rubric. It has been defined as:


DECIMAL DUST: An inconsequential numerical amount.

What I’ve come to realize, is that a sort of meaningless bifurcated “intellectual” tug-of-war occurs between those who are concerned about “the excessive use of decimals,” and those who see “too much precision.” Historians have noticed that Newton would compute answers out to an excessively unnecessary number of decimal places. Their conclusion is that “he just liked doing the calculation.” This is very probably true. Quite possibly the best engineer I’ve ever shared an office with was Michel. He was able to take the abstract equations of electromagnetism and turn them into useful computer code. We were, of course, banned from presenting any results that interfaced with the Aerospace world in metric, but inside of every computer was, to my knowledge, metric computations hidden away in ones and zeros, so as not to offend delicate Olde English sensibilities.

I was fascinated with understanding the details of how Michel implemented his computer code and verified it. What I noticed immediately was that Michel would hand compute each line of code, and compare it with the computer code’s output at each line. I was surprised that he was carrying the hand calculation out to perhaps ten decimal places! I had always harbored a secret desire to compute out to that many places. It gave me some strange reassurance that my code was right when I did, despite the admonishment I’d received at my University against creating and propagating meaningless “garbage numbers.”

One day I could clearly see that something was bothering Michel, and I just had to know what it was, as what he worked on was usually very interesting. He had some computer code he had not written, that had been used in-house for sometime. He was told to use it to predict the outcome of a measurement. Michel had derived a formula that should have been equivalent to what was implemented in the computer code, but about four or five decimal places out, the values were different. Michel showed me the hand calculation (he checked it three times) and the computer output. In his French accent he said “They should be the same, should they not?” I agreed. We checked the value of physical constants, such as the speed of light. They were all the same. Finally Michel saw the problem, and it was in the code. At certain extremes it would introduce a considerable error into the computation. That was the day I began to always check my hand and computer code computations to at least 5-6 places, minimum. I would learn that one man’s decimal dust is another man’s gold dust.

Indeed, decimal dust can be a source of new scientific knowledge. In the 1960s, Edward Lorenz (1917-2008) had noticed a very interesting output from a non-linear mathematical computer model he was using. He wanted to repeat the computation and input the initial conditions by hand as a short-cut. Lorenz rounded the original input value of 0.506127 to 0.506, a number of decimal places expected to be insignificant, and plenty accurate. When he ran it again, the computation output was nothing like the previous computation after a short period. Changing the input value at the level of “decimal dust” was expected to have no effect on the computation, clearly for the mostly non-linear world we live in, this is not the case. It was Lorenz that coined the now ubiquitous term “the butterfly effect” for sensitivity to initial conditions, and ushered along the science of chaos theory into what it is today. The tiny pressure changes caused from a butterfly flapping its wings in Africa, has the potential to be the seed for a hurricane in the Atlantic ocean. There are cases where non-linear deterministic equations need an infinite number of decimal places for a computation to repeat over all time.

In the early 1980s, British scientists using ground-based measurements reported a large ozone hole had appeared above Antarctica. This was quite surprising as satellite data had not noted the same problem. The computer code for the satellite had “data quality control algorithms” that rejected such values as “unreasonable.” Assumptions about what values are important, and those that are not, are assumptions, and should be understood as such. Another example is “filtered viruses.” It was assumed viruses had to be smaller than a certain dimension, so all other microbes above that size were removed with filter paper. It took decades for researchers to realize that monster size viruses exist. I’ve written about this in my essay Don’t Assume What You Don’t Know.

The a priori assumption of what is important is used as a rhetorical cudgel to suppress “excessive” information. When I’ve argued that human height should be represented in meters or millimeters (preferably millimeters), there is a vast outcry that only the traditional atavistic pseudo-inch known as the centimeter should be used. To use millimeters is, harrumph!, “too much precision.” It is also a possible lost opportunity for researchers as information has been suppressed from the introduction of a capricious assumption. One can always round the offending values down, but obtaining better precision after-the-fact is not an option. In my view, those who use the term decimal dust in a manner other than as a metaphor for tiny, are lazy in their criticisms, and assume they know how many decimal places matter without any familiarity with subject and the values involved.

When long and thoughtful effort is expended, one can introduce the astonishing simplification of using integers, which eschew decimal points entirely. As has been pointed out ad nausium in this blog, using millimeters for housing construction is a measurement environment that is partitioned in a way that allows for this incredible simplification. Pat Naughtin noted that integer values in grams should be used for measuring babies. This produces an intuitive understanding of the amount of weight that a baby gains or loses compared with Kilograms. Grams, millimeters and milliliters are efficient for everyday use. Integer values are the most instinctual numerals for comparison tables. The metric system is beautiful in its ability to provide the most intuitive ways of expressing the values of nature. It is up to us to use it wisely and thoughtfully, instead of dogmatically. In my view, this measurement introspection is sorely lacking in our modern society, and definitely in the community of science writers and researchers.

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