Editorial: Calculating History

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Younger surveyors can’t imagine a time before computers and calculators. But as the article in this issue by Carlton Brown shows, calculations weren’t always an easy button push away. This year marks the 400th anniversary of an invention that made surveying calculations possible.

According to an article in Science News, "…back in those days, when the Scientific Revolution was just revving up, doing math was tedious and frustrating. Measurements of features of the Earth, navigational problems, astronomical phenomena, all demanded high-level calculational prowess from the practitioners of those disciplines. But when the numbers involved were large, manipulating them was messy. Even the best math wizards made almost as many mistakes as baseball umpires do today."

"Then in 1614 John Napier, a Scottish landowner and theologian with some mathematical training, published Mirifici logarithmorum canonis descriptio, or A Description of the Admirable Table of Logarithms. It introduced a new method for quickly performing complicated calculations. It was a godsend. As one logarithm user noted much later, logarithms effectively doubled a mathematician’s useful lifetime."

Because multiplication and division are more difficult than addition and subtraction, the cool thing about logarithms is that to multiply you simply have to add two numbers, and to divide, all you have to do is subtract one number from another. And these numbers (logs and anti-logs) can easily be found in published log tables.

Logarithms made possible the slide rule, which has an interesting history of its own. Not suitable for survey calcs, slide rules were suitable for sending men to the Moon, and indeed, were part of the basic onboard equipment for the Apollo missions. For my high school electronics class, my parents bought me the nice bamboo slide rule shown here. Slide rules could also perform trig calcs, but again, not at a precision or accuracy suitable for our work.

In my own career I used logs as an Army surveyor to perform coordinate calcs. We had pre-printed forms for our traverses, zone transformations, and astro, all based on log tables. In true government fashion, our survey parties had 7-8 people, and two of these people were responsible for calcs. Calcs were done in the field on the hood of a Jeep, it was always a race to see who could finish first, and if our answers didn’t agree, we started over. As I recall, who bought the beer was based on winning the race, or at the least, who made a calculation mistake.

After I returned to the US, I worked with party chiefs who used Monroe hand cranks to do our survey calcs in a motel room, and one of my calculations mentors, Marilyn Brooks, spent many an hour cranking away on what she called the Pepper Grinder, a Curta. At one point we even had a motorized Monroe.

Also in this issue is a new series by Jason Foose, the Mohave Country Arizona County Surveyor, about programming the HP 35s calculator. The last license exam I took was in the 80s, and although I was aware that NCEES had banned some programmable calculators from the exam, I was unaware that the 35s is on the approved list. Jason says he has enough material for more than a dozen installments, so you younger surveyors who want to take a licensing exam can benefit and never have to deal with logarithms or mechanical devices.

Marc Cheves is editor of the magazine.