America’s Fractional Mind

By The Metric Maven

“This is dialectics, it’s very simple dialectics, one through nine, no maybes, no supposes, no fractions. You can’t travel in space, you can’t go out into space, you know, without like you know, with fractions. What are you going to land on?—one-quarter?, three-eights? What are you gonna do when you go to from here to Venus or something?”

Dennis Hopper — Apocalypse Now!

While Dennis Hopper’s character in Apocalypse Now! might have been traveling into space without a spacecraft, those who went to the moon in the 1960s did follow his advise about fractions—thankfully! The navigation computer on Apollo 11 was programmed with decimal numbers—in metric. The data internal to the computer was entirely metric. Only when the desired navigational data had been computed was it converted to the “inch-pound” non-system. The computer had such minimal memory that the conversion was a burden. Those who recall the flights might remember that the distances were all given in nautical miles. In America, a sea going romantic metaphor triumphs over measurement clarity.

Every common US measuring tape or ruler with inches on it has fractional divisions. In the US we are all familiar with 1, 1/2, 1/4, 1/8, 1/16 and 1/32 of an inch.

The very first thing one is taught in school, is that in order to add fractions they must have a common denominator. If one measures 1 3/4″ and wants to subtract that from 2 7/32″ well we have to change 1 3/4″ to 1 24/32″ and then there is more work…..I won’t take you through it, I think I’ve made my point. In decimal inches it would be about 2.22″-1.75″ or 0.47″, but good luck finding an inch ruler with decimal divisions in the US. The other choice is to use an all metric, mm only tape measure, like the Australian construction industry does. As I’ve pointed out in a previous blog, finding millimeter only tape measures in the US is only marginally easier than locating Amelia Earhart. In this case we would have 56 mm – 45 mm = 11 mm. That was easier, now wasn’t it? Ok, for those who want sub millimeter accuracy in everyday life it’s  56.39 mm – 44.45 mm  = 11.94 mm, yes it’s off by almost a millimeter or 1/25 of an inch.

Tape measures in mm only — Good luck finding one in the US. Click on image to enlarge

The proverbial video which illustrates how arithmetic with fractions can cause confusion features the crew of American Choppers in an epic numerical struggle. American rulers have several sets of fractional divisions. Most of the time, two measurements on an American ruler do not have the same denominator. One can almost never directly add two fractions, but with millimeters and decimals, you always can. If you are willing to live with 1/25 of an inch or so of tolerance, then just use integers.

My friend Thern has asserted many times that even Americans who have worked in construction for many years seldom learn how to read fractional tape measures. Not because they are intellectually challenged, but it’s the user unfriendly nature of fractional divisions. This is why Australians have saved about 10-15% on construction costs compared with the United States since the 1970s. Less material gets wasted and time is more efficiently used. Apparently confusing the fractional divisions on a scale is so easy that some manufacturers have four different fractional scales separated out on the same scale:

A scale with separate scales on each of its edges. Click on image to enlarge

It has been asserted that not having the metric system costs each of us $16.00 per day. When one adds up all the small efficiencies encountered every day in the US, it’s not hard to believe. My friend Lapin showed me a situation that illustrates this point. Lapin is an amateur radio enthusiast, and like most of his cohort has an interest in antenna design. He directed me to a website which has a computer program which will compute the design values for basic types of antennas. The RFID frequency in the US is 915 MHz. I put that number into the program as an example; the output is below:

Click on image to enlarge

Notice all the 1/32 fractions it spits out. My mind recoiled at the output, but I quickly realized that in the US, tape measures are all fractional, so the programmer did what he needed to, to output fractions so one could use an American ruler. The computer program itself is available to view, and uses decimal arithmetic as you might expect, to compute the lengths of A, B, C, D and E. Similar to the computer navigation program on the Apollo 11 mission, it has to compute the fractional values for output at the end of the program, so they will correspond with our 17th century rulers. Don’t be afraid of what is shown next. I only put it in for illustration, you don’t need to understand it. The computer code below is used by the antenna design program to sort out what fractions correspond to what decimal values for display:

if (temp3 <= .03125) fract = “1/32”
else if ((temp3 > .03125) && (temp3 <=.0625)) fract= “1/16”
else if ((temp3 > .0625) && (temp3 <=.09375)) fract = “3/32”
else if ((temp3 > .09375) && (temp3 <=.125)) fract= “1/8”
else if ((temp3 > .125) && (temp3 <=.15625)) fract= “5/32”
else if ((temp3 > .15625) && (temp3 <=.1875)) fract= “3/16”
else if ((temp3 > .1875) && (temp3 <=.21875)) fract= “7/32”
else if ((temp3 > .21875) && (temp3 <=.25)) fract=”1/4″
else if ((temp3 > .25) && (temp3 <=.28125)) fract=”9/32″
else if ((temp3 > .28125) && (temp3 <=.3125)) fract=”5/16″
else if ((temp3 > .3125) && (temp3 <=.34375)) fract=”11/32″
else if ((temp3 > .34375) && (temp3 <=.375)) fract=”3/8″
else if ((temp3 > .375) && (temp3 <=.40625)) fract=”13/32″
else if ((temp3 > .40625) && (temp3 <=.4375)) fract=”7/16″
else if ((temp3 > .4375) && (temp3 <=.46875)) fract=”15/32″
else if ((temp3 > .46875) && (temp3 <=.5)) fract=”1/2″
else if ((temp3 > .5) && (temp3 <=.53125)) fract=”17/32″
else if ((temp3 > .53125) && (temp3 <=.5625)) fract=”9/16″
else if ((temp3 > .5625) && (temp3 <=.59375)) fract=”19/32″
else if ((temp3 > .59375) && (temp3 <=.625)) fract=”5/8″
else if ((temp3 > .625) && (temp3 <=.65625)) fract=”21/32″
else if ((temp3 > .65625) && (temp3 <=.6875)) fract=”11/16″
else if ((temp3 > .6875) && (temp3 <=.71875)) fract=”23/32″
else if ((temp3 > .71875) && (temp3 <=.75)) fract=”3/4″
else if ((temp3 > .75) && (temp3 <=.78125)) fract=”25/32″
else if ((temp3 > .78125) && (temp3 <=.8125)) fract=”13/16″
else if ((temp3 > .8125) && (temp3 <=.84375)) fract=”27/32″
else if ((temp3 > .84375) && (temp3 <=.875)) fract=”7/8″
else if ((temp3 > .875) && (temp3 <=.90625)) fract=”29/32″
else if ((temp3 > .90625) && (temp3 <=.9375)) fract=”15/16″
else if (temp3 > .9375) fract=”31/32″;

If we had the metric system in this country, writing code like this would be eliminated. Clearly creating and writing this sorting section of computer code took a long time to accomplish.  Had we become metric in the 1970s, like Australia did,  this computer code would never have been written, there would be no need.

The word fraction comes from the latin word fractio which means to break. I cannot think of a more appropriate rubric. It’s long past time to break with the past, and embrace the decimal metric system, so we can live in the future, rather than living in the past.

Related essays:

Stickin’ it to Yardsticks

The American “Metric Ruler”

The Design of Everyday Rulers

Postscript:

My friend Pierre was asked to fill out a form which provides information for a medical report. The form asked for his height, and defaulted to centimeters (tsk…tsk millimeters please!) Below is the first image:

We won’t go into the fact that it is in centimeters, but requests a person’s height to tenths of millimeters. Straight millimeters would have been just fine, which is a single unit, and may be expressed without a decimal point. Pierre is a proud user of Ye Olde English units and attempted to set the software to feet and inches. You can see in the screenshot below his what his choices are:

Indeed the software designer did not use USC, Ye Olde English, Imperial, WOMBAT, “royal measurements” or whatever, to describe the choice, but something perhaps even more appropriate: archaic. The final screen after the selection is shown below:

Now the programmer needs to also embrace the international date format. Thanks to Pierre for letting me share this.


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 not of direct importance to metric education. It 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.

Mad Man Muntz & Metric

Earl Mad Man Muntz (1914-1987)

By The Metric Maven

It was as a young boy in Minnesota that I was first exposed to an independent television station.  The channel, which offered a new movie each night, (as well as Star Trek reruns)  was WTCN 11 in Minneapolis. The Movie Matinee host was the incomparable Mel Jass, a pitchman of considerable enthusiasm, who on many nights would endorse the technical innovations  and quality design of Muntz Televisions. Mel’s movies and personality helped inspire the Cohen Brothers to a career in film.

Years later when I worked at my first job as an Engineer in Southern California, an older Engineer made a joke about Mad Man Muntz. He looked over at me and said “you’ve probably never heard of Mad Man Muntz.” He was surprised I had and that I had heard of Muntz Televisions. He laughingly went to a whiteboard and said  “Here, let me draw you a schematic of a Muntz TV.” He drew a 117 volt power cord and connected it directly to a cathode ray tube. A TV like this would not work of course, but it was simple—and cheap. His fellow engineers told stories about what would happen as Muntz televisions aged, and colors would become “interesting.” No one was angry at Muntz, they found it all to be great memories of a kind of lovable huckster.

In mid-career I ended up working at one of the last television manufacturers in the US. It was there that I was first introduced to Muntzing. We were working on a new consumer electronics offering when Lapin said “Well, we better design it as best we can now, because it’s nothing but Muntzing from here on out.” Muntzing refers to what Mad Man Muntz did to his engineers as they were designing products. Muntz would prowl Engineering labs with a pair of side-cutters in his hand and behind his back. He would look at a circuit which was being designed, and use his side cutters to clip out a random part. If the circuit continued to work, he would tell the Engineers they had to remove the part, as he could not see it did anything other than cost money. Muntz did not want to produce optimal products, he wanted to product that were just “good enough” for the public to accept, and no more.

The engineering graveyard of products which entombs those that were superior in operation, but defeated by Muntzed versions overflows with corpses. The “just good enough” survived and the high quality products suffered extinction. There are well known examples such as Beta versus VHS, the RPN calculator versus Algebraic calculators, the QWERTY keyboard versus DVORAK and many, many which are not so well known.

One day at lunch, a decade or so back, Mr Landi, studied a specification sheet for a $1200 VHS player. I was stunned, why on earth would he want that and be willing to pay so much? Mr Landi is an Engineer who loves quality design, and tries never to compromise if possible. Mr Landi talked about how the syncing of the picture was done by a VHS recorder. It went over my head at first, but Lapin generously explained. An NTSC television picture is drawn with 483 lines. One can have a circuit that optimally decodes each line, or one that averages the decoding of each frame (set of lines) and produces a lower quality image. When I understood what was under discussion I blurted out “but what could the difference in circuitry cost!?–20 cents?” I knew this was a silly statement before my words finished echoing about the room. It had been decided by those who decide such things that this was too much money to put into a television. Most people would not notice, so it would be “just good enough.” One of our competitors televisions had a single resistor in place of a circuit that color corrected the picture over the age of a picture tube. It took a lot of convincing to keep “those who decide” from doing the same thing. The argument was that if the color changed slowly enough, no one would notice.

My friend Dr. Sunshine asked me about taking a hike in a nearby woods one day. The discussion turned to the dangers of rattlesnakes and ended up at bears.

Dr. Sunshine said “oh, I’m not worried about bears.”

“You’re not! I said with surprise.

Dr. Sunshine said “No, I’m not afraid of bears when I’m with you, because I’ll just run. I don’t have to be faster than the bear, only faster than you.”

Dr. Sunshine had a point. He had run the 100 meters in college, and was very competitive. My high school 100 meter time could be measured in Megaseconds. I could only hope a bear would not find me palatable.

The more serious question is “what’s good enough?”  When the Romans invaded Britain, the natives had only wood and stone type weapons. When fighting other tribes in Britain, they had never needed anything better. Until then “that had been good enough” there was no need to do anything else. The Romans had metal, and by comparison advanced military technology. The Romans “good enough” was more “good enough” than early Britain’s “good enough.”

Which brings me to the metric system. There appear to be people who embrace the mistaken believe that a consumer market produces more and more optimum solutions, and relentlessly marches toward perfection. My experience has been that it does not. It produces the absolute minimum we as consumers will accept, and nothing more.

A contractor can build a deck onto the side of my house in Olde English, and waste more materials than if we had the metric system, but from his perspective, the way he built it is “just good enough.” There is no need to do more. He also has nothing to compare it with as he’s never used metric. The cost of non-metrication is passed on to me, and becomes just an externality. One which is invisible to the majority of US citizens. The extra cost is masked inside of the US, because we, like the Roman Britons, only see local methods and competition in most cases.  Indeed the  Ye Olde English/“Standard” non-system is “just good enough” to produce an acceptable quality deck—even if metric would produce a higher quality one. A casual overview of the US set of unrelated fasteners and drill sizes shows that we are a “hammer to fit, paint to match” society.

But what business persons, who wish to maximize profits, conceive of as “just good enough” for a consumer is often disconnected from the needs of a nation and the general welfare of its citizens. Any cost beyond their view of “just good enough” is considered anathema. In the 19th century the job of railroad brakeman was incredibly dangerous. Many were killed and often their body was just left along side the railroad tracks. When George Westinghouse invented the air-brake, it was seen as an unnecessary cost of doing business, despite the fact that it would save countless lives.

Quentin R. Skrabec Jr. in his book George Westinghouse Gentle Genius described it this way:

…brakes to many railroad executives were a safety issue, not a profit issue. In fact, Westinghouse’ success struck fear in many because of the cost of potentially converting all existing trains. One estimate was that $40 million would have been needed in 1875 to convert the industry (more like a billion in today’s money).”

And you can be sure the estimate was as realistic as the “out of thin air” estimates of metric conversion costs offered over the years in front of Congress.

The memory of the push-back against the Westinghouse air brake by the railroads was still fresh, when the 1921 metric hearings occurred. A transition period of 10 years was proposed for switching to the metric system. David A. Molitor C.E. (Civil and Consulting Engineer) stated:

It is a great mistake to agitate in favor of a long transition period [for metric]. This would mean a long period of watchful waiting, with the outcome that nobody would do anything toward adopting the new system until the time fixed had expired. Such a law would be forgotten before it ever became operative. The United States Government had this experience when the railroads were ordered to equip all freight cars with automatic couplers and continuous brakes. The railroads did nothing toward complying with the law until the allotted five years had expired. The time was then extended two years and seven months, during the last year of which most cars were equipped.

Market Darwinism cannot be relied upon to be the guardian of the public good. It will also not provide metrication in the United States. Only when the United States Government passes a law which states that it no longer allows the use of the “just good enough” to barely work Ye Olde English measurements, will metrication occur. The legislation must provide a plan, an oversight board, funding, penalties for non-compliance and enforcement. Only then, will the metric system become the “as good as it gets for now” replacement for the absolutely “not good enough” Olde English kludge of measures under which we are pilloried, and from which the rest of the world freed itself decades ago.

Postscript:

Ganda Suthivarkom who writes for The Sweet Home contacted me about how to determine the accuracy of measuring cups. He has published his review of the best measuring cups to purchase appropriately called: The Best Measuring Cups. The article is very pro-metric and has an interesting section at the end about the origins of the cup in American cooking and why we in the US (unlike others) began using volume measuring rather than doing it by mass. Here is a short quotation from the beginning of the article:

….If you’re a serious baker or you care about precision, get a food scale. But until we can convince American recipe writers to abandon the archaic, imprecise convention of the cup, these picks will do.

I didn’t start the research with this opinion; I came around to it after learning how wacky the world of inch-pound measurement in the U.S. is and how much variability there can be in the definition of a cup’s volume.


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 not of direct importance to metric education. It 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.