27 March 2013

The Rule of 3

Judy G. Russell of the Legal Genealogist, mentioned briefly the "Rule of 3" in a blog post today. She gave a simple example (in my opinion) of the this rule from Wikipedia which I won't reproduce here. The whole blog post resulted from someone mentioning that Abraham Lincoln learned his math as far as the Rule of 3.

Chances are, if your ancestor knew the "Rule of 3," that he did not perform the calculations in the way that they are shown in the image Judy used in her blog post. That's a more modern approach.

Chances are also that your ancestor--if a contemporary of Lincoln--might have known the "Rule of 3" as well. Lawyers weren't the only ones who might have encountered the "Rule of 3." If your ancestor was a property owner, merchant, or had another occupation dealing in the buying and selling of various quantities of goods, he may very well have known the "Rule of 3" as well. It was a ready application of proportions

Two texts from the early 19th century contain examples similar to the ones that Lincoln probably saw.

Published by Jacob B. Moore, Concord,
New Hampshire, 1826;
obtained  in digital format on GoogleBooks (http://books.google.com)
 Page 142 of "Pike's System of Arthimetic" contains a simple  problem of this type--modern readers may think it easier to determine that 1 bushel would cost $.60 and work from there to get the value of 12 bushels. That is true. It is easier. Our ancestors did not have calculators which is one reason why math texts from this time period look confusing to modern eyes.

It's worth remembering that algorithms for solving problems are best initially discussed with easier examples. This is likely why the author started with the cost of 12 bushel problem.
Today we sometimes call this property "means-extremes" and use proportions to actually solve it. It is worth remembering that there were no calculators in 1826 and, generally speaking, division is best avoided until the very last step in problem solving, particularly when intermediate answers may not come out "even" and paper is a limited and valuable commodity.

It is worth remembering that the discussion of these problems was not merely academic. There are practical examples of the "rule of 3" that would be encountered by some nineteenth century Americans during their everyday life. There were no calculators and merchants, planters, and farmers needed to know that they were getting  or paying the correct price.

The "Scholar's Arithmetic" from 1818 contains more examples--including ones with varying units of measurement and money. During this point in time, not every part of the United States was using the decimal system of money we use today. There were also more units of measure in use than there are today as well (perches and roods come to mind rather quickly--and that's "rood" not "rod."). This is part of the reason solving problems of this type was not necessarily "easy" for the average person . The unit conversions presented a problem for some, much as they still do today.

Obtained in digital format on GoogleBooks (http://books.google.com)

Looking at a few problems from the text makes it clear why planters, farmers, small businessmen, merchants, and others trading in various goods would encounter problems of this type in the daily course of business. 

p. 118 from "Scholar's Arithmetic"

 Lawyers settling estates, clerks, and others may have had to occasionally "cipher" during their normal course of business.
p. 118 from "Scholar's Arithmetic"

Of course, it is necessary to know how many pence in a shilling, how many shilling in a pound of currency, etc. Those conversions are a part of these computations.

Your ancestor who was a common day laborer probably didn't have any idea how to do these computations.  I'm betting my ancestor Ira Sargent who worked as a laborer and eventually a small tenant farmer in the late 19th century, probably was unable to perform these computations. While I have no proof, I would venture a guess that my ancestor, John Tinsley, who owned over 600 acres of property, produced and sold fairly large amounts of tobacco and lived in Virginia in the early 18th century probably did. Am I certain? No. But Tinsley would have been well served to be aware of such computations in the normal course of doing business.

In a future blog post, we'll go through these examples in more detail.

What were your ancestor's math skills? 
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