Preface · پیش‌گفتار

Before the first page

The book is dedicated to Fran, Salsburg’s wife of 42 years. She kept urging him to turn his stories about the people behind the statistical revolution into a book without mathematics. Because she had no mathematical training, she read every revision and pointed out where his explanations were not clear. He credits the clearest parts of the book to her persistence. That is a good lesson for anyone who teaches statistics.

Two epigraphs follow, and they pull in opposite directions. The poet W. H. Auden, in a playful list of “thou shalt not” commandments, tells us not to answer questionnaires, not to take tests, and not to sit with statisticians. Florence Nightingale says the opposite:

“To understand God’s thoughts, we must study statistics, for these are the measure of his purpose.”

Act I: the clockwork universe

Science entered the nineteenth century with a confident picture that has been called the clockwork universe. A few exact mathematical laws, such as Newton’s laws of motion and Boyle’s law for gases, together with measurements taken with enough precision, were thought to describe reality and predict every future event.

Pierre-Simon Laplace had written a monumental book showing how to compute the future positions of planets and comets from a few observations made on Earth. The story goes that Napoléon told him:

“I find no mention of God in your treatise, M. Laplace.”

And Laplace replied:

“I had no need for that hypothesis.”

Many people were horrified by a godless universe running forever without divine intervention. Salsburg suggests that the Romantic movement was partly a reaction against this cold, exact reasoning. Then, in the 1840s, Newton’s laws predicted an unseen planet, and Neptune was found where the laws said it would be. Almost all resistance crumbled.

Act II: the error that wouldn’t shrink

Laplace did not need God, but he did need an error function. Observations never matched predictions exactly. The differences were blamed on disturbances in the atmosphere or on human error, and Laplace collected all of them into one extra term. The expectation was that this term would fade away as instruments improved. This was the age of philosophical determinism.

It did the opposite. By the end of the nineteenth century, the more precisely scientists measured, the more error turned up, and the clockwork universe “lay in shambles”. The search for exact laws in biology and sociology had failed, and in physics and chemistry the laws of Newton and Laplace turned out to be only rough approximations. A new paradigm took over, the statistical model of reality. By the end of the twentieth century almost all of science had moved to statistical models.

Salsburg argues that popular culture has not caught up. Words like “correlation”, “odds” and “risk” are part of everyday speech, but few people outside science understand the deep change in philosophy behind them.

Act III: three ideas

Randomness. For most people “random” just means unpredictable. Salsburg quotes the Talmud:

“One should not go hunting for buried treasure, because buried treasure is found at random, and, by definition, one cannot go searching for something which is found at random.”

For the modern scientist, random events are not simply wild and unexpected. They have a structure that can be described mathematically, and probability distributions give us a limited ability to predict them.

Probability. This is an ancient idea. Aristotle wrote:

“It is the nature of probability that improbable things will happen.”

In the seventeenth and eighteenth centuries the Bernoullis, Fermat, de Moivre and Pascal built a mathematical theory of probability, starting from games of chance. De Moivre brought in calculus, and the Bernoullis found the “laws of large numbers”. Yet by 1900 probability was still a collection of sophisticated tricks without a solid theoretical foundation.

Statistics. Statistics applies probability to real scientific questions through distributions. Salsburg’s example is a 1971 Harvard study in The Lancet that asked whether coffee drinking was linked to cancer of the lower urinary tract. About 25% of patients with this cancer drank four or more cups a day, compared with 10% of patients without it. From these data the authors built a probability distribution function, which is like Laplace’s error function but far more complicated.

The first question to ask is: what else differs between the two groups? Later research pointed to smoking, which goes with heavy coffee drinking and also with bladder cancer, as a major confounder.

The promise of the book

Salsburg says plainly that this is not a book about probability theory, and that readers will not learn to analyse data from it, because that takes several years of graduate study. The book tells the story of the people who made the statistical revolution and gives a sense of how each discovery fits the larger picture. Probability “drifts in and out” of the chapters, used where it is needed and ignored where it is not.

The preface ends like this:

“So, where does the nonmathematician go to understand this revolution in science? I think that a good place to start is with a lady tasting tea…”

Next episode: Chapter 1, an afternoon tea in Cambridge in the late 1920s.

Which idea in statistics changed how you see the world?

Reference. Salsburg, D. (2001). The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century. New York: W. H. Freeman.