In physics and other sciences, researchers must sometimes make approximations in the calculations they perform. Aaron Santos, a post-doctoral researcher in engineering at the University of Michigan, has applied this idea to a number of quirky questions for the general public in his new book How Many Licks? The title of Santos's small paperback volume is, of course, based on the old TV commercial about getting to the center of a Tootsie Pop. (In the interest of full disclosure, Santos's publisher contacted me with the offer of a free copy to review and I accepted.)
After an introductory overview chapter on approximation in science, Santos provides 70 brief chapters (each 2-3 pages), tackling different enumeration questions. The problems in roughly the first half of the book (we're into estimates, right?) involve magnitude. Examples of such questions include "How many miles does a person walk in a lifetime?" and "How many times can you outline the continental United States in shoelaces [from all the shoes owned by Americans]?" For each problem, Santos outlines for the reader (but doesn't immediately give away) the component quantities needed to solve the problem, plus how to construct the (approximate) solution via formula.
In the latter half of the book, Santos goes beyond simple magnitude-focused problems to ones invoking substantive concepts in physics. For example, the question "[Over] how much area would you need to have solar panels [to power] the entire United States?" requires the concept of electrical efficiency for its solution.
How Many Licks? would seem to be a fun way to get young (or maybe even not-so-young) people interested in math and science. Reflecting on my own education, I think the book would probably be most appropriate at the high-school level or above. However, really bright students may be able to profit academically from the book at younger ages. Approximately speaking, that is...