Search Loci: Convergence:
I was just going to say, when I was interrupted, that one of the many ways of classifying minds is under the heads of arithmetical and algebraical intellects. All economical and practical wisdom is an extension of the following arithmetical formula: 2 + 2 = 4. Every philosophical proposition has the more general character of the expression a + b = c. We are mere operatives, empirics, and egotists until we learn to think in letters instead of figures.
The Autocrat of the Breakfast Table.
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Measuring America: How an Untamed Wilderness Shaped the United States and Fulfilled the Promise of Democracy, Andro Linklater, 2002. 310 pp. $26.00 hardbound. ISBN 0-8027-1396-3. New York: Walker Publishing Co. www.walkerbooks.com
The history of mathematics comes in many guises. Andro Linklater has chosen to reveal it in the telling of this story of how the United States chose to establish its systems and methods for commodity and land measures. With the founding of the United States, a system of property ownership was established, particularly the ownership of land. This opportunity or right was denied to most peoples of the world at this time. The lure of land ownership became a driving force in the settlement of the new country but, for the system to work, the land had to be divided in the fairest and most efficient manner. Accurate boundaries had to be established.
Thomas Jefferson decided that a geometric square would provide the easiest framework around which land ownership could be obtained and democracy established. Furthermore, the square’s four equal sides reflected a measure of reliance on four-ness that had been in existence since Queen Elizabeth I standardized the measure of a “finger” as the length of four grains of barley from which four fingers made a hand, four hands a foot, etc. Both the square and “four-ness” would determine the social/legal mathematics of American life. The device which most assisted in the physical layout of land boundaries was the Gunter surveying chain whose 22 yards were divided into 100 links. A quarter section of 440 yards X 440 yards comprise a 40 acre lot which became an average homestead. The region was easily paced-off by settlers.. This story of measurement evolves to include the standardization of U.S. weights and measures in general, Jefferson’s efforts for “decimalization” and the failed efforts at metrication.
This book is an enjoyable and informative read. The web of connections between measurement, mathematics, legal jurisdictions, social justice and the rise of democracy is expertly constructed. Highlighted by illustrations and supported by a good bibliography and set of footnotes, this book provides an excellent reference on the development of our modern systems of measurement. I highly recommend this book for personal reading and library acquisition.
Frank Swetz, Professor Emeritus, The Pennsylvania State University