This is a good book. Not because it is a comprehensive history of statistics - it is not and it does not claim to be. Not because it is a particularly easy read. Notwithstanding its elegant rendering into English by Camille Naish, it still has a Gallic essence - a kind of stylistic profundity - that can make it hard going. In parts it is repetitious, sometimes coming over as a collection of essays rather than as a single text that logically and sequentially develops a theme. Most important, however, it is demanding because its intellectual breadth and depth requires a sustained commitment.
The strength of Alain Desrosières's account lies in the rich and insightful way he has analysed his subject - statistical reasoning. Take one example. As a fan of William of Ockham, I was pleased to see him restored to his rightful position as a developer of concepts that laid the foundations for the development of science - not just as a historical figure but as a thinker whose ideas are still relevant. In the index Ockham has as many entries as Boole and as Gauss.
For centuries it has been held that medieval philosophy is dead. Like Scrooge or Marley, many would say as dead as a doornail. But, as with Marley, its ghost will not go away. Neither should it. Debates still go on about realism and nominalism - that is whether classes have an essence or whether they are groupings linked only by a name.
Desrosières's description of Ockham's major role as a nominalist is a nice one. The statistical importance of this is that before one can count the things that exist in the real world, and long before one can manipulate the results and act on them, it is necessary to define the objects to be enumerated. To do this accurately and in a way that satisfies everyone is one of the most difficult tasks imaginable. Its problematic nature is consistently underestimated. Disraeli understood it, though, in his "lies, damned lies, and statistics". So did Darwin. In his On the Origin of Species he defined the main object in his title thus: "In determining whether a form should be ranked as a species or a variety, the opinion of naturalists having sound judgement and wide experience seems the only guide to follow."
This illustrates the problem. It is all very well for the taxonomy and systematics of things like biological species to be left to experts and their tacit knowledge. Hardly anybody cares, for example, whether British wild roses - a problem discussed by Darwin - belong to a single species or should be classified as a group of many different ones. But politicians and ordinary folk care deeply about categories like the unemployed or the poor, and they care with equal strength about health and illness and social class. Modern states have a deep interest in these things, and statistical considerations play a central part in the development, application and evaluation of public policy about them. So all these entities are too important to be left just to experts to codify and debate. Desrosières devotes a very important chapter of his book to discussing their classifying and encoding. He illuminates the links that our need and desire to quantify make between such seemingly unrelated subjects as Linnaeus's taxonomies of living things, the Poor Law, the definition of a German civil servant, and the role of bacteria in the causation of disease. Perhaps inevitably in an account of this breadth it is easy to criticise the author's choice of secondary sources in fields not his own. Whatever Michel Foucault's merits, his analysis of the history of biological classification is not the one I would chose.
Anyone interested in the history of science and economics and, particularly, applied mathematics, will be stimulated by this book. Its breadth is its strength - and, to a degree, its weakness. It is true to its national origins. So read it as a collection of impressionistic essays, not as a handbuch.
Hugh Pennington is professor of bacteriology, University of Aberdeen.
The Politics of Large Numbers: A History of Statistical Reasoning
Author - Alain Desrosières
ISBN - 0 674 68932 1
Publisher - Harvard University Press
Price - £.95
Pages - 368