Close Enough for American Work

Rose-Quartz

By The Metric Maven

Metric Day Edition

Recently my Significant Other (SO) requested that I take her to a rock and mineral shop. She had driven past it many times, but never stopped. There were all manner of minerals and small fossils. The displays were all very interesting and it seemed I would be destined to look, but not to make a purchase. Then, I noticed the tools section. There was a common inch ruler with a centimeter scale on its opposite edge. Yet another sad testament to metric “practice” in the US. Nothing unexpected there. To my surprise there was also a small dual-scale caliper with þe olde English and metric, but it had fractional inches on one side and millimeters on the other. I was quite surprised and for $7.50 I could not resist purchasing it. Here is a photo:

Rock_Caliper
Inexpensive Calipers (click to enlarge)

My SO, who had requested we visit, did not make a purchase, but I did. When I arrived at the cash register, an older man with a beard was waiting. I commented on the millimeter scale on the calipers and that it did not have centimeters. The man did not miss a beat and said “We have to have them, all the precious stones are measured in millimeters.”

I looked at the calipers with more care and noticed a lower scale.

Then I said: “Oh my goodness, look at this, it has a vernier scale on the metric side.”

The cashier had no idea what a vernier scale is. I did my best to explain it from memory. I also told him that in my opinion, the creation of the vernier scale was a very important development in the history of engineering and science. I recalled that I had learned to use a vernier scale when using a micrometer during my time working as an offset pressman. It was in Daniel J. Boorstein’s book The Discoverers (pg 400) that I first ran into a historical discussion of the vernier scale. The scale was created by French Mathematician Pierre Vernier (1580–1637) and bears his name.

A U.S. Quarter Dollar coin has a diameter of 24.26 millimeters. I placed a current 25 cent coin into the calipers to measure it. The scale is shown below:

Vernier_Scale_Quarter
Vernier measurement of a US quarter Dollar (click to enlarge)

The first line of the vernier scale indicates the measured length is between 24 and 25 millimeters. We next look for the vernier line that matches up best with the upper scale. The three is probably the closest to the best alignment and so we could estimate that the diameter is about 24.3 mm. This deviation is only 0.04 mm (40 um) from the design value. This is a very close estimate for such a roughly fabricated device.

Let’s look at upper inch scale. Oh, my, there is no vernier scale. It would appear that because it is graduated in fractions, a vernier scale was not added. The smallest fractional division appears to be in sixteenths of an inch or 0.0625 inch. When converted to a useful metric unit, 1/16″ is 1.588 mm. It also appears that it would be rather easy to confuse the smallest division with 1/8″ rather than 1/16″ and this would complicate the inch measurement considerably. The mark half-way between zero and 1/2 has about the same downward length as 1/8. This is not the “standard” way that U.S. rulers are marked. Below is an example with the first inch divided down to 1/32″ and the second inch down to 1/16″.

Fractional-Divisions

If you want to know why the divisions are different for the first inch, I invite you to read my blog The Design of Everyday Rulers. This odd set of graduations caused me to wonder if the calipers had been manufactured in a metric country by a person who is not familiar with our complex þe olde English practices. That the word meter is employed, with an er rather than an re, makes one suspicious that an American was behind this muddled design. Clearly the calipers makes measurements in millimeters and not meters. Why use the word meters rather than millimeters or metric?

Assuming we have figured out the inch fractions on the caliper, we see about 15/16″ and “a little more.” How much more is this? Well, because we do not have a vernier scale, we have to estimate the value by eye.  It looks like it maybe about 1/10th of a 1/16″ space if I have to guess—which I do. So what is 1/10th of 1/16″ to divide fractions we invert and multiply as I was told as a youth. We end up with 10/16 — that can’t be right. Oh wait we need to divide 1/16 into 10 parts or 1/16 divided by 10/1. When we invert and multiply now we get 1/160. Now we need a common denominator to add the fractions and obtain a final value. We multiply the top and bottom of 15/16″ by 10 and have 150/160. We now can add 150/160 + 1/160 to get 151/160 inches. Now we can make this fraction a decimal and get 0.94375 inches or, when converted to millimeters, it becomes 23.97 mm which we can compare with the vernier value of 24.3 mm directly. Even after all of that work and estimating, the vernier scale with millimeters is more accurate, and DEFINITELY simpler to read.

Today we have mechanical dial calipers, and also calipers with electronic readouts; but a vernier scale with millimeters is still an accurate and simple way to measure length. This example also illustrates the inaccurate and complicated way we in the US measure with fractional inches. We have not even bothered to decimalize the inch on our common everyday rulers. I have a proposal, let’s just switch-over to the metric system directly, and skip a kludge like decimal inches for the streamlined system that uses millimeters.


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.

Popped Secret

By The Metric Maven

Bulldog Edition

Popcorn is a very New World food. It is amazing that in ideal conditions the kernels of unpopped popcorn can be stored almost indefinitely. Corn was first domesticated in Mexico about 9000 years ago. As a young boy, I recall a friend showing me a popcorn pan with a hand-crank on the lid. We were watching an old movie and he wanted to make something special. My friend placed oil into the pan and heated it, he then tossed in a measured amount of popping corn. Normally, at that point one would  immediately put the lid on to keep from being splashed if it started popping immediately. He next tossed in some sugar. The handle was part of a wire sweeper that could push the corn around. This was done until the popcorn had finished popping, and for the first time I had popcorn with a sugar coating. At that age it seemed exotic. At that point in my life I gave no thought to how much extra energy was imparted by the introduction of sugar. The agitator was a nice addition. Generally when popping popcorn in a pan one would need to continuously shake the pan forward and backward to keep the popcorn from burning. Popping popcorn at home was an acquired skill. Popcorn balls (generally colored in some fashion) were often handed out at Halloween in my small town as a treat. The largest documented popcorn ball is 2.4 meters in diameter, 7.5 meters in circumference, with a mass of 1549 Kilograms (well over a Megagram). Popcorn was also strung on thread to decorate Christmas trees during the winter holiday season.

In China and Korea a sealed cast-iron canister with popcorn inside is used like a rotisserie  over a fire.  When a pressure gauge on the container reaches a threshold value, the canister is taken from the flame, a canvas sack placed over the top and the seal broken. With a large boom, the popcorn explodes all at once. It is then poured into the canvas bag.

The first popcorn was popped by hand (sometimes over an open fire), and  was later automated with steam powered mechanisms designed in the late 19th century. This new popcorn popper was introduced at the 1893 Colombian Exposition. When I was a boy we purchased sealed plastic bags of popcorn kernels with Jolly Time printed onto the transparent film. The big change in popcorn preparation came when General Mills obtained the first patent for bagged microwave popcorn in 1981. This made popping popcorn much more convenient and a surge in popcorn consumption followed. People also ceased to see popcorn kernels any longer as they now come in an opaque bag.

Microwave popcorn allows one to eat popcorn with a very consistent serving size in terms of mass and volume. This consistency would be great for those who are trying to monitor their food energy intake. When I first attempted to determine the energy content of popcorn I was very surprised at the low value. The serving size per bag is about 3 and the serving size is 1 cup popped or three cups. This works out to 90 Calories (377 KJ). My significant other (SO) immediately doubted this value. It had to be higher. In recent years it has been emphasized that we should go back to Olde English only nutrition labels. One can see this from the nutrition labels that Ye Olde English is still Kyng. Here is the nutrition label for Pop Secret’s Homestyle Microwave Popcorn:

Pop-Secret-Label-1

So if the servings per bag is about three, and the serving size is two tablespoons unpopped, then it would be a total of 3*150 Calories or 450 Calories (1884 KJ). The fact that the serving size is given as 2 tablespoons unpopped and 1 cup popped seems to indicate an equivalence. So which is it? Ninety Calories per bag or 450 Calories per bag? This difference is a factor of five! The range given on the web for a single bag of Pop Secret Homestyle was from around 400-500 Calories or so. When I looked at the bag after popping, and used my 100 mm wide hand to measure it, the bag appeared to be somewhere around two liters in volume, but I had no idea how many cups that might be. I could immediately estimate the value in metric, but could not do the same with Ye Olde English.  My SO and myself then conducted an experiment, we popped a bag and measured it with a one cup measure. It turned out to be somewhere from about 10-12 cups of popped popcorn. It would seem that each bag contains about 6 tablespoons of unpopped popcorn, and 15 cups when popped, but the nutrition label does not say that.

When converted to metric the clarity has not increased much:

Nutrition Facts
Serving Size  15 mL unpopped  237 mL popped

Amount            15 mL     237 mL
Per Serving      Unpopped   Popped

Calories           150        30

So 15 mL of popcorn becomes about half of a 500 mL bottle of soda or water. Does that make sense or not? I was able to estimate the volume of a popped bag at about two liters or 2000 mL.  Given about 200 mL per serving 2 liters would be about ten servings or 300 Calories. Clearly the value would not be 90 Calories.

In my view this label has been designed to confuse. Who eats unpopped popcorn? Who even sees the unpopped popcorn in a sealed opaque paper bag? How would you estimate the unpopped amount when you can’t even see it! One would immediately look  at the label assume 3 cups per bag at 30 Calories per cup and compute 90 Calories total. There have been moves to go back to Ye Olde English from metric for US nutrition labels to make them more “understandable.” The Pop Secret label is unclear in metric and even more inaccessible in Ye Olde English. It could have been written:

Nutrition Facts

Calories per bag: 450

Servings per bag: 3

Calories per serving 150.

Calories per cup 30

Volume of bag: approximately 2500 mL

The nutrition label as it is originally formatted appears to be designed to mislead consumers into believing that microwave popcorn contains far less calories than it does. This in turn causes the person to consume more calories and hence more product while blowing their estimated food energy intake.

Profiting from measurement confusion and misinterpretation is often thought to be a thing of the past. It is clearly not—and never has been. I have a measuring scoop provided inside my laundry detergent box which has a volume twice that recommended for each wash. It has a line halfway up its side which is the recommended volume. People don’t notice the transparent line, or read the tiny instructions, and generally fill the scoop up to the top, using twice the recommended amount of soap. People who see the importance of implementing the metric system, and the teaching of basic numeracy as fringe issues in the United States, are but ignorant marks for our modern industrialized hucksters.


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.