American Scientist

The Triumph of Numbers: How Counting Shaped Modern Life. I. Bernard Cohen. 199 pp. W. W. Norton, 2005. $24.95.

I treasure the memory of a cartoon showing a barbarian encampment with a group of barbarians surrounding a seated, sulking warrior. The caption reads "Aw, come on Genghis, we only need one more to make a horde."

In the 18th century, nations decided they needed a far clearer picture of their resources for war. How many men could the state place under arms? How many horses could it provide? How could it feed the armies it raised? Even in peacetime, governments had to collect taxes. What were the taxable resources of the nation? It was natural for the rise of the modern nation-state to be associated with a rise in statistical record keeping, and it was natural that France, the most modern of all, should be in the forefront.

One of the many claims of the modern state was that it had a monopoly on justice. But the nationwide administration of justice called for money and organization, and money and organization require numerical records. In the 19th century, when first André-Michel Guerry and then Adolphe Quetelet examined French records of crimes, they made a most remarkable discovery. Quetelet wrote that

[We] pass from one year to another with the sad perspective of seeing the same crimes reproduced [in the same numbers] and calling down the same punishments in the same proportions. . . . [We] can enumerate in advance how many individuals will stain their hands in the blood of their fellows, how many will be forgers, how many will be poisoners. . . .

Thus in the years 1826, 1827, 1828 and 1829 there were recorded 241, 234, 227 and 231 manslaughters respectively. Of these, 47, 52, 54 and 54 were committed with rifles.

The first purpose of this book is to remind us how extraordinary these figures are. There are few uses of free will more dreadful than killing a human being, yet although we can predict neither killer nor victim, the number of killers and victims hardly varies from year to year.

The second purpose of the book is to explain why, unless we pause and think, these figures no longer shock us. Our first impulse might be to mutter something about "central limit theorems," but this is mere evasion. "Second moments," "Fourier transforms," "infinitely divisible distributions" and suchlike mathematical paraphernalia can have no relevance to the sudden moment of passion or the misfortune of a drunken brawl.

The reason why the figures above have lost their power to shock must be sought in the history of what we might call social statistics, and The Triumph of Numbers is a contribution to that history. Because it is a popular book, the author, the late I. Bernard Cohen, chose to tell the story through individual cases. Because he was a fine historian, these are well chosen and described with insight. If, like me, you were unaware of the nature of "David's sin" and didn't know why Britons in the 1750s feared the consequences of a national census, this book will inform and enlighten you. A chapter on two of the "Founding Fathers" indicates the importance of social statistics in their thought and reminds us that Benjamin Franklin was more complex, and Thomas Jefferson was more dangerous, than patriotic hagiography allows.

Again, because Cohen was a fine historian, he included some of the numerous dead ends that swallowed up so many of those who pursued social goals through mathematics. I would have liked yet more of these, because the history of a failure is often more illuminating than the history of a success.

This book paints a vivid picture of the rise of social statistics. However, it was Cohen's last work, completed under great difficulties, and as is the case for many last pictures, the general plan and many of the details show the master hand of the artist, but some details are supplied by others or remain incomplete. On the one hand, we can enjoy moments of offhand erudition such as the following:

One of [Philippe] Pinel's American students was a Boston physician, Dr. George Parkman (1799–1849). Dr. Parkman later gained notoriety in the annals of crime as being the only person to have been murdered by a Harvard professor. Dr. John White Webster, a professor of chemistry, cut up Parkman's corpse and fed the pieces into a furnace in his chemistry laboratory. . . . But Dr. Parkman's teeth, found in Dr. Webster's furnace, were enough to convict Webster.

On the other hand, there are paragraphs that read like the notes of a dutiful student of a rather dull course on mathematics and civilization.

The next-to-last chapter is on Charles Dickens and Thomas Carlyle as opponents of the new social statistics, and the last is on Florence Nightingale as a proponent. I found the chapter on Dickens and Carlyle slightly unsatisfying. That heart is to be preferred to head is a conventional piety of English literature going back to Henry Fielding and before. There is little evidence that it has any effect on readers, either in the great matter of making them kinder or in the minor matter of making them more averse to statistics than they were before.

More interesting is Cohen's example of one of the things that angered Dickens—a letter to The Times using the yearly average temperature in the Crimea to minimize the suffering of the British Army in the Crimean winter. I would have liked to see reference to some of the writings of economists on the Irish famine—commentary that now strikes us as truly wicked and which may well have exercised a malign influence on the course of events.

There are still many people who, like me, consider Florence Nightingale to be a sort of secular saint. (Remember that sainthood does not require an easy personality.) They will be pleased by Cohen's insightful account of how her life intertwined with the rise of social statistics. Nightingale became an instant Victorian celebrity by her devoted nursing of the troops in the disastrously conducted Crimean War and was immortalized as "the Lady with the Lamp" in Henry Wadsworth Longfellow's poem "Santa Filomela":

Lo! in that house of misery
A lady with a lamp I see
Pass through the glimmering gloom
And flit from room to room.

But she is better viewed as the lady with the scrubbing brush and statistical abstract. It was not selfless devotion but sanitation that saved lives. During the first seven months of the campaign, hospitalized troops experienced a mortality rate from disease alone (60 percent a year) greater than that seen in London during the Great Plague. After the creation of a new "Sanitary Commission" armed with real powers and clear goals, including the cleaning of latrines and flushing of sewers, hospital deaths among troops at the front dropped to two-thirds of those among troops at home.

On returning to England, Nightingale devoted her enormous prestige to the cause of improving the health of her beloved soldiers. She forced the appointment of royal commissions, collected and analyzed their statistics and, to a great extent, wrote their reports. Her work produced staggering results—for example, the death rate among soldiers serving in India was cut by a factor of three. It is appropriate that Cohen's survey should finish with such a great and effective champion of statistics.

However, the triumph that Cohen describes is of a particularly nuanced kind. Numbers have entered our vision of society. They are a common currency of newspaper articles and political speeches. But we do not use them (and perhaps we cannot use them) in the way that the innovators hoped. Cohen reports that when Florence Nightingale wrote to Francis Galton on the purpose of social statistics, she concluded

You remember what Quetelet wrote . . . "Put down what you expect from such and such legislation; after        years, see where it has given you what you expected, and where it has failed. But you [politicians] change your laws, your administering of them, so fast, and without inquiry after results past or present, that it is all experiment, see-saw, doctrinaire, a shuttlecock between two battledores."

How shall we judge our politicians and, with them, ourselves against Miss Nightingale's standard?