Measure for Measure: The Story of Imperial, Metric, and Other Units

When Bill Berlinghoff and I were working on Math through the Ages, we felt it was important to include a chapter on the history of units, and especially of metric units. After all, this topic is part of the school mathematics curriculum. But we found it difficult to find good references. The best we could find was John Roche's The Mathematics of Measurement: A Critical History, which is useful but too heavy, technical, and expensive for our intended audience. Alex Hebra's Measure for Measure: The Story of Imperial, Metric, and Other Units is an attempt to fill that gap.

In short chapters, Hebra takes us through a plethora of units for all sorts of quantities: length, time, angles, mass and force, temperature, luminosity, etc. He tells us about attempts to create units based on natural phenomena and about ways of formulating natural laws in terms of dimensionless quantities. One of the last chapters takes the reader through an interesting exercise: suppose an alien race, communicating over intergalactic distances, asked us how to build a dam; could we give them directions despite the fact that we have no idea what sort of units of measurement they use?

Despite the subtitle, there is very little history here. Hebra does include lots of stories, but he doesn't really attempt to trace in detail the evolution of the various systems and units of measurement. The organization by kind of unit (a chapter for length, a chapter for time,...) makes it hard to get a sense of historical flow, and the transition from isolated units to systems of units does not get the emphasis it deserves. There are occasional lapses; for example, in the chapter on measuring angles, the radian is defined but no explanation is given as to why one would want to use a unit of measurement that resulted in such strange numbers. (There is also a problem with a graphic in that section: π has come out as p.) Finally, both the discussion of whether the United States should "go metric" and the jokes based on unit conversions (e.g.,"28 to 29 grams of prevention are worth 0.454 kilograms of cure") get old fairly quickly.

Nevertheless, this is a useful book for anyone wanting to know more about units of measurement and their role in science (especially physics). Many of the examples would make for excellent assignments for students, and the many illustrations are very helpful. So: not exactly the book I wanted it to be, but I'll take it.

 Fernando Q. Gouvêa is the co-author, with William P. Berlinghoff, of Math through the Ages: A Gentle History for Teachers and Others.