A Scientific Patina for Everything under the SunApril 6, 2011
Philip J. Davis
Quantify! A Crash Course in Smart Thinking. By Göran Grimvall, Johns Hopkins University Press, Baltimore, 2011, 232 pages, $25.00.
Let no item escape your eye.
---With a nod to Tom Lehrer
Having attended a discussion group on K–12 mathematical education, and having heard complaints about the weak instruction given teachers on imparting a sense of numerosity, I returned to find Quantify! in my mail slot.
Numbers are omnipresent in today's world. As I write, I have on my desk a jar of dry roasted peanuts on which I counted about a dozen numbers. If I were to take into consideration the "Nutrition Facts" on the label, the number would exceed fifty. Just open the daily paper and count how many numbers are present on the front page. And while you're at it, identify the different purposes those numbers serve.
There are the cardinals that answer "how much?" There are the ordinals that answer "how far along a sequence?" Then there are identification tags, such as a car's license plate, that answer "which of many?" But numbers, of course, can also carry multiple semantic and semiotic meanings, as when a single digit on the license plate of a car indicates a superior social or political status.
We are curious to know "how much of this or that?" Perhaps this reflects our basic acquisitive natures. A fuzzy answer, such as "just a bit" or "a pinch of," would lack the seeming authenticity, the objectivity, the unambiguosity, or the preciseness of a number. Driving along a back road, we might see a sign: "Cucumbertown Pop. 672," a number of which the inhabitants are very proud. We are impressed by its exactness, and it is irrelevant whether John and Mary Doe moved to NYC two weeks after the sign was put up.
Quantification is the process of attaching a number, exact or approximate, to something as a measure of its bulk, significance, or some other characteristic. Göran Grimvall, a professor emeritus of physics at the Royal Institute of Technology, Stockholm, has given us a book on quantification that is chock full of lively, often familiar examples that occasionally brought smiles to me as I read along.
Grimvall's book should appeal to and amuse a wide audience, extending from professional scientists, teachers, school kids, newspaper columnists to the so-called average citizen---provided that the inhabitant of any of these human categories doesn't shrink at the sight of a few simple algebraic symbols.
Open the book to page 102 and you will find a discussion of the time needed to roast a turkey. The text is complete with graphs, recommendations from the United States Department of Agriculture, and a culinary precept that ought to make it into Rachel Ray's official website:
"The cooking time varies as the square of a typical length characterizing the object that is cooked."
Turn to page 71 for a discussion of whether listening to music can make you deaf. The National Institute for Occupational Safety and Health has arrived at maximum safe exposure times for a variety of decibel levels, dB(A). This warning is amplified by a table that gives typical noise levels experienced in a range of settings: breathing (10 dB(A)), a pigpen at feeding time (100–110 dB(A)), a jet taking off 25 meters away (140 dB(A)). If Grimvall is contemplating an enlarged and improved edition of his book, I suggest that he include the dB(A) of the music emanating from the boom box of a car that passes frequently, windows open, along the street in front of my office.
Grimvall disabuses us of certain of our plausible, but incorrect, views, explaining why
"riding a bicycle has nothing to do with gyroscopic effects, a thickened church window nothing to do with the flow of glass under gravity, and the bathtub vortex nothing to do with the rotation of the earth."
Go to page 117 and you will find a trenchant discussion of the famous curve drawn by economist Arthur Laffer in 1974. An upside-down parabola (sheared a bit, perhaps), the curve plots income tax rate (0%–100%) against total tax collected. "The implication," Grimvall tells us, "is that to the right of the maximum in the curve, a reduced rate will increase the incentive for people to work and therefore increase the total collected tax."
Advocates of the Laffer curve have been debunked, and its debunkers have been debunked. But Grimvall, ever the pragmatist, has not rushed off to the U.S. House of Representatives Subcommittee on Taxation waving the Laffer curve about. His intention was merely to "illustrate a mode of thinking that is highly relevant far outside the field of economics." I would call this mode of thinking "quasi-qualitative/quantitative."
Are you interested in Olympic racing records? If so, you will be informed and illuminated by the explanation (page 79) of "why you might have a shorter time in the 100-m dash with manual timing."
Lord Kelvin wrote:
"When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge of it is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced it to the stage of science."
James Clerk Maxwell agreed: "Numbers and Measures are key elements in scientific literacy."
These days the process is often rotated 180º so as to provide a scientific patina for whatever topic is being discussed. Indices have been created for everything under the sun: for national corruption, social health, economic opportunity, the hotness of pepper (Tabasco: 30k–50k Scoville units). There is the Rudolf Flesch index of readability. There is probably (or I shall soon introduce) an index of amorousness, setting a light peck on the cheek at 10 units.
In an epilogue, Grimvall lists his Seven Principles of Scientific Literacy. Here they are, very slightly modified: It is not a global world. Man is not the measure of all things. Data can be uncertain. A model is only a model. There are limits to growth. Knowledge is provisional. Humans are only human.
There are, I've read, remote tribes that have no numbers, not even one, two, many. We are lucky---we can compare the livability of Cucumbertown with that of Parsnipburg, expressing the comparison in precise and objective numbers.
Philip J. Davis, professor emeritus of applied mathematics at Brown University, is an independent writer, scholar, and lecturer. He lives in Providence, Rhode Island, and can be reached at email@example.com.