Inches in a Mile

By The Metric Maven

Isaac Asimov Edition

Those who have read my essays realize that I see Isaac Asimov as the greatest science writer that ever lived. I still purchase hardcover copies of his books to augment the paperbacks I own, and then re-read the essays. Isaac was an unwavering promoter of implementing the metric system in the United States throughout his life. Asimov claimed what allowed for his prolific writing was that he was a “speed learner.” I thought about this when I read his essay: “How Many Inches in a Mile?” 1

The good doctor points out that in most ordinary situations this question would never come up, but then shifts to an every day question:

Suppose you have a rectangular living room that is 12 feet 6 inches in one direction and 18 feet 4 inches in the other. You are going to carpet that from side to side and fore to aft, and would like to get some sort of an idea what it will cost. The carpeting is sold at a price which is so much per square yard. Therefore, you have to know the area of the of the room in square yards.

You are welcome to work this out for yourself right now. The necessary information you may need is that there are 12 inches to the foot and 3 feet to the yard. It may also be useful to know that there are 144 square inches to the square foot and 9 square feet to the square yard. Or perhaps you prefer to make use of the fact that there are 36 inches to the yard and 1,296 square inches to the square yard.

This essay was written in 1971, in an age where electronic calculators were an expensive novelty, and most computations were done by hand. Many times in my father’s print shop I would see boxes of paper with numbers and calculations scrawled on them. It is something which has completely vanished in modern times. Isaac points out that it took him about four times, using different conversion methods to determine the value consistently. He then interjects “(Actually, the area of the room is almost 25 1/2 square yards: 25.46 to be a little more exact.)”

He then goes on to observe:

But why is it so hard to do such a problem? After all, to work out the area of a rectangle we need only multiply the lengths of adjacent sides. A rectangle that is 12 feet by 18 feet is 12 x 18 or 216 square feet in area.

The trouble seems to be that what is easy where only feet are involved becomes difficult when inches and yards are dragged in as well, because one unit goes into another an inconvenient number of times. Why are there 3 feet to the yard? Why not 2, or 4? Why 12 inches to the foot? Why 5280 feet to the mile.

Asimov then examines the obscure origins of the farrago of units that some call US Customary, and I call Ye Olde English, or medieval units as they pre-date the British Imperial System of units, and originated in medieval times. When thinking of the confused list of US units, my mind goes back to a conversation in the movie Apocalypse Now! where Willard is sent up river to terminate Coronel Kurtz’s command, and states that part of the reason for this, was that his methods were deemed unsound. Kurtz asks if now that he was there, if his methods appeared unsound, Willard replies “I don’t see any method—at all.”

After an interlude with Roman miles, furrows, fluid ounces, gills, pints quarts, gallons, firkins, hogseheads, gallons, pecks, bushels, Imperial gallons (gas sold in Canada at the time), ounces, pounds (Troy and Avoirdupois)….and you get the idea, he finally settles down to discussing the metric system, and his original problem:

Suppose, for instance, you have a rectangular room which is 32 decimeters, 4 centimeters long and 49 decimeters 6 centimeters wide, and you want to carpet it completely at a price of so much a square meter. That sounds like the earlier problem in yards, feet, and inches, but—-

Anyone using the metric system sees at once that 32 decimeters 4 centimeters is equal to 32.4 decimeters or 3.24 meters; and that 49 decimeters 6 centimeters is equal to 49.6 decimeters or 4.96 meters. The area is 3.24 x 4.96, or just about 16.07 square meters. You have that one nasty multiplication to make and no divisions.
All the rest is taking care of the decimal point.

Oh, my, this is an example of forcing pre-metric thinking on the metric system. Decimeters are treated like tiny feet, and centimeters are virtual inches. There is no reason to use two units to describe a single distance! As I’ve pointed out ad nausum here, metric construction uses millimeters only! It is still true that to this day you will find feet and inches with fractions on a US tape measure; on a proper metric tape measure, you have only a single unit, millimeters. In the case of Isaac’s example, we would have measured 3240 mm and 4960 mm in each direction. Clearly the unit we want is square meters, so, using the idea that metric is better by 1000, we see this is 3.240 meters by 4.960 meters, and we multiply those together without involving any mixed units at all!

But remember, this essay was published in 1971. English speaking nations viewed metric conversion as something in their future, and still used Olde English Units or Imperial everyday. New Zealand and Australia had only begun metrication in 1969 and 1970. Canada began two years later in 1973, and is still not complete. There was very little experience with using metric at the time, or any examination of its best usage.

By the 1980s, enough experience had been achieved by nations such as Australia, New Zealand, South Africa, and others to see the rational for using only millimeters in housing construction, milliliters for volume, and grams for mass. Isaac, the speed learner, wrote the book The Measure of The Universe in 1983, and by then had come around to realizing that centimeters were a hindrance, and millimeters produced smooth metric usage. He dropped the idea of multiple units, and entered more modern metric usage. The United States on the other hand is a no learner, and not even a slow learner when it comes to metric, despite the passing of more than three decades since Asimov’s updated work was published.

Dr Asimov saw a number of problems associated with lack of the metric system in the US:

For one thing, only American children will waste incredible numbers of hours trying to ram into their heads an unlearnable system, when they might be learning something useful instead. Only American children will have this additional reason for learning to hate school. All other school children, including Russians and Chinese, dismiss the measurement system in a day of explanation and a week of practice.

What else? All scientists everywhere, even in the United States, use the metric system exclusively in their scientific labors. Everywhere else, scientists use the metric system in daily life and learn it as children. In the United States, scientists learn the metric system only late in life and have to keep on using the common system also. It means that American scientists are never quite as much at home with their basic language of measurement as are all other scientists.

The lack of the metric system in everyday use, also isolates the US public from science, at a time when most serious problems we face require scientific understanding to address them.

What else? Only American industry makes use of the inches and pounds. The rest of the world is on the metric system. A double standard must therefore be used in international trade, with ourselves on the losing side.

The United States must accept the metric system sooner or later, then. It is not too late now. Would that it had been done long ago in the infancy of the republic, but better now than later.

The political powers that be in the US have chosen an indefinite later, to our disadvantage as a nation.

1 Asimov, Isaac, Today Tomorrow and …… Doubleday & Company, Inc. Garden City, New York 1973 pg 147.

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Fisherman Jeremy Wade was in Sydney Australia looking for an extinct fish which might still exist. He began his research by visiting a fish market there. I could not help but note the clearance sign at the market, and the units it used:

Now if they would only use lower case mm, as others in Australia do.

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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