“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.
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:
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:
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.
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: