Imagining The Metric System

Mr-Shortcut
Mr Shortcut measuring a board

By The Metric Maven

Bulldog Edition

It has been brought to my attention that the Discovery Channel has a show called Gimme Shelter. It has a person called Mr Short Cut who apparently offers viewers advice on short cut methods for DIY work. In a video: “Mr Short Cut demonstrates the advantages of using the metric system for easy measurements.” Here is what he has to say:

Narrator: Here’s a man who gets eight hours of sleep in five hours. Mr Shortcut.

Mr Shortcut: Hey you remember a few years ago when the big craze the big push was to make everything go metric? Well I gotta tell ya when it comes to carpentry I think they might have been on the right track. Let me show you what I mean. I mean if you have to measure and add some distances with boards for example, just something simple I’ll show ya [Mr Shortcut holds a board and tape measure, he then starts to measure] here’s inches, seven and three-sixteenths and let’s add another distance here. How about eighteen and and an eighth. Ok, so you got your sixteenths you got your eighths you gotta change the denominator leave the numerator add two divide by six carry the one thirty days have September, tipi canoe and Tyler too—and I can’t do it—alright without an abacus and three calculators.

Well, here’s the way to do it, metric—because look here, the tapes you can buy now, come with inches on one side if you gotta do it the old way and centimeters—metric on the other side. So all you have to is put it in like this and you get your nineteen centimeters added to forty six centimeters—that’s easy sixty-five. You can do the math. Metric is cool.

My reaction to this was much like the aftermath I experience following the viewing of an Ed Wood movie—vertigo. Beyond the fact that I don’t recall any big push “a few years ago” for metric, what are the odds that one would always hit integer values when using centimeters for woodworking? I suspect it would be approximately zero. The size of the measured board example appears contrived, and unrealistic. The “metric” example offered by “Mr. Shortcut” has the appearance of how an American, who has never actually used or experienced the metric system, imagines how the metric system might work. Mr. Shortcut (MS), like many U.S. “metric promoters” has not bothered to research the subject.

Mr Shortcut proudly shows that one can purchase a tape measure with both inches and centimeters (aka pseudo-inches). Independent of anything, dual scale instruments are evil. They simply allow the person using them to ignore the metric scale, use the familiar side, and continue to hinder metric adoption. This point is enshrined as Naughtin’s First Law.

When a person actually attempts to use centimeters in construction, they will quickly discover the need to use decimals. This often leads the average US citizen to believe that metric is not necessary and only the introduction of tape measures with decimal inches on them is. The use of decimal centimeters is awkward and leads to unnecessary numerical complication, which in turn leads to errors and scrap. This problem is well-known to the Australian and UK construction industries, and Bangladesh, Cameroon, India, Kenya, Mauritius, Pakistan, South Africa, New Zealand and Zimbabwe, but alas, in the US, we, and Mr Shortcut, are ignorant of their practices and our own U.S. metric construction code. The solution is, of course, to use only millimeters so the numbers measured are all whole numbers and eliminate the decimal point entirely. Decimals are great, they are the next best thing to whole numbers, but one should prefer expressions without decimals if possible. This is Naughtin’s Second Law: Prefer Measures Without Decimals.

Am I being a bit too hard on a person who is trying to promote the metric system? Possibly. His heart is in the right place, just not his tape measure. I spoke with my resident woodworking expert, Pierre, to get his view about the importance of measurement. He reminded me that a number of woodworkers completely eschew measurement of any type and build proportionally by eye. In Pierre’s words:

As we’ve discussed, plenty of woodworkers try not to use any measurement at all if they can help it. They know they can’t read a tape measure, that no two tape measures are identical, and they don’t want to do math, ever. But there’s probably a process here. First I convince them that math can be helpful, then you can show them that math can be easy.

I’m probably not qualified to convince any woodworker to use measures, so I’ll let Pierre work on that. But if they should happen to decide that measurement is useful, I can attempt to guide them away from centimeters and toward millimeters, which will make the math easy. That I do know.

Custom-cabinetry-design.com is a company with a name that describes what it does. They would very much like people to use millimeters and have a page which explains how easy it is. They state:

We know change can be difficult. But, we are confident that if you can count money, then the conversion to the metric system will not only save you time and frustration, it will eliminate costly and time consuming mistakes. Imagine no more fraction math, only dealing with whole numbers and half numbers is much easier than working in fractions.

The assumed unit of measure is the millimeter. They even offer a nice side by side example of how easy using millimeters is compared with inch-fraction descriptions:

Metric-Cabinets
— click to enlarge

It appears to me that there are those who have actually used metric to construct physical items, and those, such as Mr. Shortcut, who imagine what it might be like to use the metric system to build something. It is quite possible to build with centimeters, and carry along decimals. The path of least intellectual resistance for Americans is to use centimeters as a decimalized pseudo-inch. Or, one can use millimeters, measure with a ubiquitous centimeter rule, and constantly move a decimal point in one’s head as I did to obtain millimeters. I engaged in this unnecessary arithmetic complication until enlightened Australians guffawed at my ignorance and sent me millimeter only rulers and tape measures. This bad practice is encouraged because of the ubiquity of centimeter marked rulers and tape measures in the US and the minimal availability of metric only millimeter only scales here. The invisible metric embargo makes it very difficult to find a millimeter only tape measure in the U.S..  The only known product available is for carpenters, and called the True 32 tape measure. It has a length of 5 meters, and is marked in millimeters. Obtain one and use it. After you have, I suspect you would no more go back to decimal centimeters than you would contemplate using Roman numerals.

Don’t imagine the metric system—use it!

Related essay:

Building a Metric Shed


If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page and contribute. Also purchase his books about the metric system:

The first book is titled: Our Crumbling Invisible Infrastructure. It is a succinct set of essays  that explain why the absence of the metric system in the US is detrimental to our personal heath and our economy. These essays are separately available for free on my website,  but the book has them all in one place in print. The book may be purchased from Amazon here.


The second book is titled The Dimensions of the Cosmos. It takes the metric prefixes from yotta to Yocto and uses each metric prefix to describe a metric world. The book has a considerable number of color images to compliment the prose. It has been receiving good reviews. I think would be a great reference for US science teachers. It has a considerable number of scientific factoids and anecdotes that I believe would be of considerable educational use. It is available from Amazon here.


The third book is called Death By A Thousand Cuts, A Secret History of the Metric System in The United States. This monograph explains how we have been unable to legally deal with weights and measures in the United States from George Washington, to our current day. This book is also available on Amazon here.

Parts is Parts

CO Detector Panel

By The Metric Maven

One Autumn night I was awoken at 2:00 AM by the shrill report of the carbon monoxide (CO) detector in my bedroom.  I was slightly concerned, but mostly annoyed. This CO detector (and another identical unit) had been prone to setting off their alarm even when I suspected nothing was wrong. When I had a new water heater installed a few years back, the company gave me a new CO detector for my basement. I gladly replaced the CO detector that cried wolf with the new unit. So far it has never sounded an alarm. What I dislike about both units is they have no units displayed. They either shriek or don’t shriek. I determined that, if possible, I was going to purchase a new CO detector which provides measurement information. I found a new CO detector, and it indicated that it has a readout, in parts per million (PPM).

The instructions indicated that a low level of CO is 0 to 50 PPM, a mid level of CO is 50 to 100 PPM, and a high level of  CO is above 100 PPM. The detector alarm sounds above 100 PPM. These are all nicely defined values, but I’ve never been sure about parts per million as a “unit.” I assume parts per million of carbon monoxide is the number of parts of CO in a million parts of other stuff. It seems like it’s telling me something, but not quite. I recall a late friend who was a political cartoonist expressed great concern to me that a toxic substance had been found in biscuit mix in parts per billion. I wasn’t sure what to think, a billion is a very big number (1 000 000 000), I wondered if this was even something of concern without any investigation, but with a simple estimate. If the  Earth’s diameter (12.75 Mm) is divided by a billion, one could drop it into the cap of some ball point pens (12.75 mm). I  wondered out loud if sea snake venom, or plutonium in this dilution would be deadly. It seemed like parts per trillion would be almost vanishing in their concentration.

The deadliest snake in the world is said to be the Inland Taipan which is found in Australia. When it delivers a bite (often repeatedly) it injects between 44 and 110 milligrams of venom. The median lethal dose in mice is 25 micrograms/Kg. Below is a comparison of the lethality of a sample of snakes.  The units typically used are milligrams/Kg, but I used micrograms to produce integer numbers (see Naughtin’s Laws).

Inland Taipan (Australia)                                                                                  25 μg/Kg
Beaded Sea Snake                                                                                       164 μg/Kg
Indian Cobra                                                                                                  565 μg/Kg
Eastern Diamond Back Rattlesnake (North America)                             11 400 μg/Kg

But what is this in parts per million?—I have no idea. Parts per million in air can be the number of grams of a substance for every million grams of mass. This is parts per million by mass. It can also be one milliliter of gas for every million milliliters of air. This is parts per million by volume. A third choice is 1 gram of gas for every million milliliters of air. This is parts per million by mass per volume. I think I feel justified at my confusion. Given the units are mass over mass milligrams/Kilogram is a factor of one million, so the LD50 values appear to be:

Inland Taipan (Australia)                                                                              0.025 PPM
Beaded Sea Snake                                                                                     0.164 PPM
Indian Cobra                                                                                                0.565 PPM
Eastern Diamond Back Rattlesnake (North America)                              11.400 PPM

So if these doses were increased by one thousand, they would be parts per billion, and have the same values as found in the first table.

Inland Taipan (Australia)                                                                                 25 PPB
Beaded Sea Snake                                                                                      164 PPB
Indian Cobra                                                                                                 565 PPB
Eastern Diamond Back Rattlesnake (North America)                            11 400 PPB

It appears that the political cartoonist was right, parts per billion can be a problem, but which parts per billion? In this case it’s parts per billion by mass. In the case of my CO detector it just states parts per million, so which PPM? I’m quite sure that “parts is parts” does not apply. Also there are two different “versions” of the words used for magnitude descriptions, which are called long and short scale.

In the case of gasses, it makes sense to have a standard temperature and pressure, and express values with metric units. This is often done with mass over a given volume which is a density. It is possible to convert 50 PPM CO to an equivalent value of 58 milligrams per cubic meter. One hundred parts per million is about 115 milligrams per cubic meter. These values are close enough that the CO levels of concern could be 0 to 50 mg/m³ for low levels, 50 to 100 mg/m³ for mid levels, and 100 mg/m³ and above for high levels of CO. I can imagine a milligram spread over a cubic meter, but an alternative could clearly be a version of grams per liter. In both cases one can visualize the quantities involved more intuitively. Milligrams are a common dosage mass for aspirin and other over the counter products.

Carbon dioxide (CO2) is a greenhouse gas, and its concentration has been measured since the late 1950s at Mauna Loa, Hawaii. The value is generally given in parts per million, which has very little meaning for me. Here is a current graph of the Keeling Curve:

Mauna_Loa_Carbon_Dioxide

The values would make a lot more sense to my intuition if the graph were in mass per cubic meter. Assuming the analysis presented here is correct, we can re-plot the monthly data (I could not find the seasonally corrected data) in terms of milligrams per cubic meter, assuming 380 ppmv is 684 mg/m³:

Measured at Mauna Loa, Hawaii

I can immediately estimate that the amount of CO2 per cubic meter has increased by about 100 milligrams per cubic meter since 1982 (http://spacemath.gsfc.nasa.gov/data/KeelingData.xls). The upper graph has a value of about 315 ppmv in 1960, which is approximately 567 milligrams per cubic meter. So just since measurements have been kept, the amount of CO2 in the air has increased by about 130 mg/m³. I have some intuitive understanding of this increase, and it seems like a lot!

Sulfur Dioxide (SO2) is another common pollutant. A blogger named Rei has been measuring the amount of sulfur dioxide with pollutant meters located around the Baroabunga volcano in Iceland. His blog Barobunga: “Like Being In An Enclosed Space With A Diesel Engine.” first describes human safety limits, and context levels in micrograms per cubic meter from 20 micrograms per cubic meter to the highest recorded concentration, 1000 µg/m³, taken next to Russian smelters. He observed this graph on 2014-09-10:

Sulfer Dioxide Measurement

Rei had the reaction I would have: “could that be right?” Perhaps the equipment calibration was off?—or some other problem had occurred. After checking the equipment, it was determined that these measurements are accurate. The measured levels peaked at almost 2600 µg/m³. This plume descended on a nearby town and began to produce respiratory distress. (tip of the hat to Helen for posting a link to this article) I’ve always been doubtful about the use of parts per million, billion, trillion and so on as providing any understandable quantitative information. This article by Rei re-ignited my interest in this question.

The Wikipedia page on sulfur dioxide shows that the amount of the substance released into the air has decreased from 28.3 Megagrams in 1970 to 17.1 Mg in 1999 (the last year data is provided). Knowing the 24 hour safety limit for the World Heath Organization is 20  µg/m³ one can see that 17 Megagrams released in the the air above the US is a significant amount of pollution. One aim of this blog is to examine the clearest expression of numerical magnitudes possible to convey information in the most accessible way possible. It seems that it might be best to go with expressions which contain metric units over those which are in terms of normalized values (i.e. PPM). Determining the best method of expression in the case of CO and SO2 is not just an academic exercise, peoples lives can be lost from misinterpretation. Mass of pollutant per cubic meter of air looks like a good way to express these values, but this is a serious enough question that it should be the subject of rigorous study.

EU NOx Pollution Limits
click to enlarge

In September of 2015 Volkswagen admitted that it had rigged car emissions tests using software. This fraudulent activity affected about 11 million cars. New Scientist in a 2015-10-03 article entitled The Curious Case of NOx Pollution stated: “If this practice is widespread, it could help explain why NOx emissions in many European countries continue to overshoot targets.” The figure to the left is from the article. The limits are in micrograms per cubic meter. Perhaps the world is beginning to change and use this more accessible way of numerical expression. Unfortunately the U.S. has not embraced the metric system and abandoned its medieval units in the 21st century. If it did, we all might breath a little easier.


If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page and contribute. Also purchase his books about the metric system:

The first book is titled: Our Crumbling Invisible Infrastructure. It is a succinct set of essays  that explain why the absence of the metric system in the US is detrimental to our personal heath and our economy. These essays are separately available for free on my website,  but the book has them all in one place in print. The book may be purchased from Amazon here.


The second book is titled The Dimensions of the Cosmos. It takes the metric prefixes from yotta to Yocto and uses each metric prefix to describe a metric world. The book has a considerable number of color images to compliment the prose. It has been receiving good reviews. I think would be a great reference for US science teachers. It has a considerable number of scientific factoids and anecdotes that I believe would be of considerable educational use. It is available from Amazon here.


The third book is called Death By A Thousand Cuts, A Secret History of the Metric System in The United States. This monograph explains how we have been unable to legally deal with weights and measures in the United States from George Washington, to our current day. This book is also available on Amazon here.