What can we do?

Stephen Stigler
Book Review With Commentary

Stigler is a gifted historian of mathematics, especially in the sense of his dedication to thoroughness and objectivity. His insightful readings of obscure authors alone are worth reading in their own right. He has gone to great lengths to recount thinking as it evolved toward the modern sub-discipline of mathematics now known as statistics.

Statistics is an archane field and has rightly earned its place as the butt of many jokes. Our favorite is:

"Statistics Don't Lie; Statisticians do!" Another version goes: "There are three kinds of lies: lies, damned lies and Statistics." Author or authors not identifiable without probable error.

For the serious researchers, for those who care about history or have a serious need to know about how to evaluate social behavior with the least possible error, this is the book to be read carefully. It is not a how-to book; rather, it is a collection of essays on a number of statistical concepts, how they developed, and who was really who in the history of this key branch of mathematics. Every essay carries a "moral" of substance that requires little or no math to grasp.

Aside from the need for retrieving data, inferential statistical analyses enables new technologies to arise from new or old science, and to keep those technologies in control. Such analyses have two fundamental uses. The first is to define experimental scatter for use in assigning proper levels of significance to results or expected correlations. The second is even more important. In this case, one can systematically search for effects and interactions not self-evident from the data. Experimental designs can be quite efficient when amenable to statistical techniques. Although this second application may raise more questions than it answers, that is the essence of science and the requisite of progress. Public health is probably the most important technology to most people, yet few of us realize what may or may not lie behind a label on foods or medicines alike. In a very real way, statistics underlies modern societies. We cannot know too much, but we can know too little.

Stigler traces the evolution of thought from intuitive hunches, through qualitative conclusions to semi-quantitative statements, always with the margin of error in mind. The margin of error separates the statistical approach from all other analytical techniques. Those who employ statistics on all available information in their decision making, will be right rather more often than their counterparts proceeding on hunches, biases or intuition. The value of this tool is literally immeasurable. Neverthless, it can also be misused, and Stigler is perhaps at his best in describing how that has happened so often inadvertantly, even by statisticians themselves!

For those who have not yet connected observed variations with their mathematic counterpart, variances, Stigler explains simply what it is that each of his historic characters was about in trying to extend the frontiers of the known into unknown waters. He analyzes their thinking without regard to the renown earned in their day. The essence of each concept lies in his words; so those put off by notation and strange symbols, can still get his points. Most of us think math is all about hard proofs. Stigler shows otherwise; math benefits from intuition as much as any other branch of science.

More than all that, Stigler breathes life into the human beings that made the subject what it is today by illustrating their humanity and foibles, always respectful of their personhood. It is easy to enjoy the interplay of talents and personalities that motivated these pioneers in their individual quests as well as in their means of interacting with and supporting one another.

At once Stigler has written a book that is scholarly, poetic, and an easy read -- especially for the non-mathematician who can skip the symbolism without losing the essence.

For those who seriously want to change the world, this book is a "must-read." Stigler demonstrates vividly how difficult it is to find one's bearings in darkness. But once on track, the margin of error can be minimized as the march goes forward. Keep in mind:

By providing margins of error, statistics can be a very helpful guide in the quest for peace. By the same token, statistics alone do not provide absolute proof of cause and effect. Only science based on consistent predictiveness within the margin of error can do that.

Now for the ratings:

• Five stars: for scientific methods on how to grope in the dark and make progress against the radical elements of our times be they social, fiscal or theological. From this book one can better appreciate the mathematical tools now available for illuminating pathways to peace. The tools are not perfect, but they do estimate accurately the direction, magnitude, and error bar an effect will have on a given desired result.
• Five stars also: for history buffs wondering about the Technology of history and idea development.
• Four stars: for open minded folk looking for enlightenment.
Two or three stars: for most of us.
• One star: for those whose world begins and ends in dogma of whatever origin. This book is counter to such belief systems. Belief systems have a place, but this book only goes as far as intuition allows; it does not support any belief based on faith alone, and certainly does not support any one faith in particular. In that sense it is anti-Authoritarian

This strange listing is an experiment in itself. For example, Fundamentalists might view parts of this book as being atheistic. Others might see it as supporting both logos and mythos for Stigler repeatedly pays homage to the intuition that sets humanity apart from the animals. Remarkably, he even "demonstrates" how an early experimenter discovered the existence of intuition ("unconscious thinking") by using a careful experimental design and probability theory!

Counter to all that, it is possible that intuition is in fact a genetic remnant that expresses itself as a unconscious result of early learning in the manner of a Hang-up that happens to have life-long benefits.

Reviewed by: Harry Rosenberg