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A Failure to Communicate

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Shoes

"Without agreed upon units of measure it is sometimes very difficult to communicate. I was traveling to the United States from my home in Great Britain. The security people at the airport noticed that the heel on my right shoe was somewhat thicker than the one on the left shoe, an adjustment I have to make to compensate for a slight difference in leg length."

Bernd Eggen
SEED Alumnus

The security staff found this highly suspicious and inspected my shoes so thoroughly that they needed to have new heels made.

Upon arriving in Louisville, Kentucky I went to a local shoemaker and explained to him that my right heel needed to be 1.5cm thicker than the left one. The shoemaker was an elderly gentleman who had lived all his life in the United States, and had not been exposed to the metric system. I grew up in Germany and now live in England, where I have had little occasion to measure in inches. The shoemaker had no idea what 1.5cm looked like. Now some rulers sold in the US have inches along one edge and centimeters along the other, but the shoemaker’s rulers were only in inches.

ruler

A ruler with inches along the top edge and centimeters on the bottom. We found two things wrong with this ruler. What do you notice?
Click on the ruler to see what we found.

So I pulled out my trusty Unix conversion program and found that 1.5cm = 0.6 inches. This didn’t help. My attempt to metricise the inch left the shoemaker still confused since inches are not customarily divided in tenths, but rather into halves, fourths, eights, sixteenths, etc.

Looking at the shoemaker’s ruler I figured that computing to the nearest eighth of an inch was accurate enough and did this calculation:

formula

where X is the number of eighths of an inch that will equal 0.6 inches.

formula  
formula  

Rounding this to the nearest eight of an inch, the shoemaker made my right heel fractionof an inch thicker than the left heel.

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