Metric Hosers

Bob-and-Doug-RelaxingBy The Metric Maven

Bulldog Edition

When I decided I would change my engineering lab over to metric, I immediately and unknowingly encountered the limits imposed by the Invisible Metric Embargo. I was mantled in American ignorance about what I needed for tools. Finding them would become an odyssey. “Where could I get a decent “meter stick?” was my first question. Clearly Canada is a metric country. I will get online and purchase rulers from there I thought. I spent a lot of time and found only wooden meter sticks. They were all in centimeters, and within the confines of my blissful ignorance that seemed fine. At that point I was only disappointed with the poor quality of the rulers I obtained. I use a milling machine to create printed circuit boards (PCB) with millimeters and wanted a fairly large sized scale. I measured the board dimensions with the Canadian metric ruler in centimeters, shifted the decimal point in my head and then would check against my millimeter drawing.

About that time I wrote a pro-metric editorial for a local paper, and in response received emails from Pat Naughtin and Mike Joy, both from Australia. Pat congratulated me on the editorial; Mike wanted to provide help. When I described my current work, Mike offered to send me a millimeter only ruler. I did not want him to go to the expense, and I really could not see the need. Mike insisted. He told me that he had used centimeters, and they had caused mistakes. He assured me I would see the light after he sent me “real metric rulers.” When the 300 mm and 600 mm rulers arrived at my door, I was engaged with milling a PCB. I removed the rulers from the shipping container even as the mill was running. When I started to check dimensions, I was truly shocked by the amount of eliminated mental effort produced by this simple change. I immediately planned on banishing my centimeter “yardstick” from Canada to an uncomfortable place in my garage.

Sven counseled me about centimeters a fortnight or so before, and I really didn’t see why they were a problem. I began watching Naughtin’s videos, read his metric epistles and the light went on—centimeters really are a bad idea. I had already purchased a centimeter tape measure and now I really did not want to use it. Naughtin pointed out that Canadians, despite their official metric status, did not adopt metric in their housing construction. I went online and looked for millimeter only metric tape measures in Canada. I looked and looked but all the hardware stores offered mostly inches, centimeters, or combinations thereof.

Not long after this, Mike Joy visited the US and brought along a very nice Australian millimeter-only tape measure. I offered to purchase it from him, but he had a person in Vancouver Canada to whom it was promised. I was really jonesing for the tape measure. This was yet another confirmation that Canada was not the place to find millimeter-only metric tools and is part of the Invisible Metric Embargo.

I wanted to put together some type of metric cookbook, and I figured Canada might have some I could purchase. I contacted a number of persons in Canada who had Canadian cook books for sale. They informed me they all used Ye Olde English measures. One woman was clearly confused why someone from the US would want a cook book in metric. Peter Goodyear (another Australian) later offered useful links to some useful Australian cooking websites.

I have only spent about three hours in Canada, and most of those were in a restaurant. I had come to the conclusion that Canada was not nearly as metric as it would appear. I wondered about England, and based on my Canadian experience began to doubt how metric it might be. Derek Pollard of the UK Metric Association convinced me that the UK is about 80%-90% metric. England is not Canada, It is very close to being a completely metric country.

I began to see both Canada and the UK as inverse metric m&m’s. Canada has a thin outer metric coating and looks metric on first glance, but hidden inside its slim shell is an unappetizing center of Ye Olde English/Imperial usage. England’s m&m outer shell makes it look like an Imperial nation. Roadways have miles, pints are sold in pubs, metric martyrs are in the news, but when you get past the outer shell, the interior of the English m&m is all metric.

Lufkin-Vertical-mm-Tapemeasure

Courtesy of Peter Goodyear

In Early February of 2016 a small engineering company in Ohio contacted me. They found the Metric Maven website and wanted to know if there was any place, other than Australia, where they could purchase millimeter only tape measures. I told them that the Fastcap 32 was the only one I knew of available in the US, and it is not nearly as high a quality as my Australian ones. The Fastcap 32 was not good enough for this engineering company’s needs. I finally directed them to a number of Australian sites. They had the same concern I did when I first ordered some from Australia, that the tapes which arrived would be in centimeters and not millimeters. I had to tell them that I’d never found a millimeter only tape measure in Canada (not even an inch/mm tape) and there would be little hope other than Australia to purchase one.

Less than a week later an email arrived from a recently retired woodworker in Canada. He had been thinking about switching to metric in his work, and it came to him that a millimeter only measuring tape would be a very simple way to dimension his work all in integers. He stated that he had come to this conclusion independently and then did a web search to see if a mm only tape measure existed and where he could obtain one. The search directed him to this US based website, where he found images of millimeter only tape measures. The woodworker was quite surprised to find that an Invisible Metric Embargo exists in both the US and Canada. He could not find a mm only tape measure in Canada, nor in the US.

On 2016-03-05 a carpenter from Western Australia had an “ask me anything” thread on Reddit. Here was a bit of the exchange:

Mr Gupples: always wondered about stud placement in metric countries. maybe you guys dont use the metric system, i dont know. do you do 16 on center there? are plywood sheets 4 x 8?

Australian Carpenter:  Stud placement is typically 600 center to center. That’s basically 2 foot. It gets tighter in cyclone prone areas. 450 centers. That’s 1 and a half foot. All measurements in millimeters.

We still use feet and inches but not for anything precise. Some older blokes will still call a sheet of ply an 8 by 4 rather than a two four by twelve.

Samz0rpt1: weird. canada uses 16 oc and 4 by 8 sheets. so do you guys have metric tape measures or do you use metric imperial ones like what you would get in home depot (hardware store)

Australian Carpenter: Meteic [Metric] both sides.

The use of millimeters is seen by Samz0rpt1 as “weird.” He wants to know how on Earth millimeter tape measures can be obtained. I’m assuming he is probably Canadian and is as surprised as the retired Canadian woodworker about the Invisible Metric Embargo. I see this shock on the faces of US engineers every time I tell them about metric construction. Provincial, thy name is American.

I won’t chastise Canada too much for their non-metric ways in housing construction. They clearly know better, but they have the overwhelming negative influence of an ill-tempered Olde English bully to their south with which to contend. This antique non-metric country to Canada’s south still constructs all their houses in inches, with all other compliment of irrational Ye Olde English measures for plumbing and such. The best way to help make the US more metric might be if Canada would take the lead with metric construction, because I see no way the Frozen Republic in the US will ever mandate metric. Canadians, please try to muster up as much outrage as was found when the beaver was to be taken off the nickel, and implement millimeter metric construction in Canada. It only took the Australians about 18 months to complete. Perhaps this will help the backward neighbor to your south to finally see the advantages of metric they currently cannot even contemplate.

When John Shafroth was introducing metric legislation in the US at the end of the 19th century, Canada was on board. Here is an article from the December 30, 1900 issue of The Times of Washington:

Washington-Times-1900-12-30-Metric-CanadaCanada began its metrication 70 years later, but has stalled out with a metric system implementation that is but a veneer. It’s been 115 years, it’s time to ignore the US and complete your metrication. If you did, this American would thank you for it.

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The Metric Maven has published a new book titled The Dimensions of The Cosmos. It examines the basic quantities of the world from yocto to Yotta with a mixture of scientific anecdotes and may be purchased here.

Insignificance

Insignificance2By The Metric Maven

Bulldog Edition

Some years back I became involved in evaluating the results of an experiment that clearly had scientific issues. I assisted two other volunteers, and was mostly there to critique the experimental methods. Early on I asked if the answer was as simple as the data had been cooked. One of the volunteers was a graduate student in mathematics. He looked at me and said “no, it’s fine, I already looked at the data.” I was a bit puzzled and wanted to know why he had such confidence that the data had not been altered. The mathematician said “the data is consistent with Benford’s Law.” I had no idea what that was, and surprised to hear that generally the first significant digit of numerical data is not random. The distribution of 1’s, 2’s, 3’s and so on up to 9 is not uniform. The probability of a one is higher than a two and they all follow a statistical pattern.

My mind had a very difficult time accepting this statement. The mathematician told me to “go look it up” which I did.

The story goes that Frank Benford (1883-1948), while working as an electrical engineer at General Electric, had obtained a well-used copy of a book of logarithms. He noticed that the beginning pages were the most soiled and worn. The idea that people would most often look up logarithms of numbers that begin with number one, and then those with two, and so on up to nine was surprising. Benford wrote up his observation, which is often called Benford’s Law. However Simon Newcomb (1835-1909) had earlier published the same observation in 1881.

I had a hard time accepting this because it meant that the first significant digit of a number is not statistically independent. The mathematical analysis to derive Benford’s law is beyond my expertise.[1] Sven pointed out that Warren Weaver (1874-1978) in his book Lady Luck has a reasonably intuitive explanation of how Benford’s Law comes to be. The relevant section is called The Distribution of Significant Digits, and does not mention Benford directly. Weaver makes this statement: “Although it remained unsuspected or at least unidentified for centuries, this distribution law for first integers is a built-in characteristic of our number system.”

Here is a nice graph from Wikipedia showing the distribution of the first significant digit for numerical data:

Benford-2Thirty percent of the time, the first significant digit of commonly used physical constants found in an elementary physics textbook is one. Census populations follow Benford’s Law, as do income tax data, one-day returns on the Dow-Jones industrial average and Standard and Poors indexes. Benford’s law is often used in forensic accounting to screen for fraud.

At this point, I want you to note something about this plot of Benford’s Law: what is the probability of zero for the first significant digit? Well, there isn’t one. If you add up all the probabilities you end up with 100%, so no probability is assigned to zero for the first significant digit, or should it be called the first insignificant digit?

I had given thought to discussing significant digits in the past, but there are differing views about how to go about determining significant figures in calculations, and so I tended to shy away from any discussion of the topic. Not until a reader took me to task over a statement I made in a blog about the 100th anniversary of the USMA did I decide it was worth some examination:

Also, the Maven writes: “The world record eyebrow hair is touted as 9 centimeters (90 millimeters for those with a refined measurement sense).”
In this case, since the measurement apparently was not to the nearest 0.1 cm, writing it as 90 millimeters would be false precision. (Of course if it were given as, say 9.2 cm, then 92 mm would be better.)
Thus, centimeters should be considered in such circumstances to avoid any indication of false precision; otherwise, centi-, and deci-, deka, and hecto-, should be considered as sort of “informal prefixes”…

While there is a lot of disagreement about how to determine significant digits, the one statement about them which is generally accepted is that adding zeros on the right side of a whole number does not constitute adding significant digits.

Here is a statement from Learn How To Determine Significant Figures:

If no decimal point is present, the rightmost non-zero digit is the least significant figure. In the number 5800, the least significant figure is ‘8’.

Another university website has:

Trailing zeros in a whole number with no decimal shown are NOT significant. Writing just “540” indicates that the zero is NOT significant, and there are only TWO significant figures in this value.

Wikipedia has this to say:

The significant figures of a number are digits that carry meaning contributing to its measurement resolution. This includes all digits except:[1]

Wikipedia in its rules for identifying significant figures states:

In a number without a decimal point, trailing zeros may or may not be significant. More information through additional graphical symbols or explicit information on errors is needed to clarify the significance of trailing zeros.

If a whole number is encountered without any context, the trailing zeros should be assumed as insignificant unless the text specifies otherwise.  Clearly when I pointed out that 9 cm would be better written as 90 mm, I did not conjure up an extra significant digit and imply more measurement resolution. The commentator made an unwarranted assumption about the 9 cm value: “since the measurement apparently was not to the nearest 0.1 cm, writing it as 90 millimeters would be false precision.”  He is acting as a psychic and divining what precision was implied by the person who measured the value and offered it as 9 cm. What was offered up by the commentator is actually an example of false precision. There is no reason to assume the measurement was or was not to the nearest 0.1 cm or 0.05 cm or 0.025 cm. Only a single integer with a single significant figure of 9 is offered. Adding a zero on the end and expressing it in millimeters without providing any additional information altered that fact not one bit.

In this situation the zero is just a final place holder, therefore when an extra zero is added to the end, it does not introduce any increase in implied precision or become a significant figure. The first significant digit is still nine for 90 mm as it was for 9 cm.

“Trapped zeros” are considered significant. In the case of 402, the zero between the 4 and the 2 is significant, but a trailing zero such as that found on 420 is not. Adding an infinite number of trailing zeros to an integer number does not increase the number of significant digits. When I pointed out that Metric Today should change centimeter values to exclusively millimeter values, I only changed 9 cm to 90 mm. I can equivalently write 9 cm as 90 mm, or 90 000 µm or 90 000 000 nm without introducing any extra “implied precision.” Unless I tell you that 90 mm is a value with two significant figures, you should assume the zero is not significant. The centimeter is a coarse enough measurement length, that when implemented for everyday measure, any useful value will have a decimal point, and is more appropriately written in millimeters.

The “implied precision” argument against using millimeters exclusively in everyday life is one that has an appearance of technical relevance, but is no more than an ad hoc truthiness statement. Everyday it is empirically demonstrated as vacuous by those who construct metric buildings in Australia, Bangladesh, Botswana, Cameroon, India, Kenya, Mauritius, New Zealand, Pakistan, South Africa, United Kingdom, and Zimbabwe. It is also theoretically superficial when examined carefully. Adopting knee-jerk contrarianism mantled in truthiness does not contribute to human understanding, it only attempts to squelch it.

Why is this question worthy of an entire blog? Because we probably get more flak on the millimeter vs centimeter question than any other. And the flak comes from metric advocates. Occasionally, it comes from a metric advocate whom we admire. And yet, the argument for keeping the centimeter hanging around like an albatross is always based on a misunderstanding of precision: the notion that that extra zero has some meaning beyond establishing scale.  It doesn’t. Scientists, engineers, and mathematicians are all in accord that it doesn’t.  It really isn’t even a metric question, but it’s only metric advocates that aren’t on the same page here. Odd, that.

[1] Hill, Theodore P., “A Statistical Derivation of the Significant-Digit Law” 1996-03-20 Georgia Institute of Technology