Exactly Right

There is something seductive about the sharp edge of precision. Time sliced into nanoseconds or soap that is 99.44% pure; satellite navigation systems that can pin down position to a few square yards or sound systems that sing in clean digital tones; precision cars, razor blades, haircuts, paint colors, personality profiles. Whether it’s IQ scores, TV ratings or the skill of Olympic ice skaters, we attach a precise number and, presto, we think we hear the clear ring of truth.

Precision validates our senses, adding trust, a sense of surety. “Precision is everything that ambiguity, uncertainty, messiness, and unreliability are not,� writes M. Norton Wise, editor of “The Values of Precision,� a collection of essays exploring the “explosion of everyday precision� that defines the modern world. “How did numbers come to represent the cutting edge of modernity?� asks Wise. “It was not always so. . . .�

Exact measurements are relatively recent inventions that emerged in the late 18th century, largely in the physical sciences. But above all, they emerged from culture. The history of precision is not about numbers or instruments or machines so much as it is about people and the societies they build. It is about what people value, how they value it and how they agree on values.

Consider: Just why would anyone want or need to know precisely how many people live in a nation’s borders, how much money they earn or what they do with it? How far is it from here to there? How much has the climate changed over the last 100 years? How smart is someone or how beautiful? How much a hunk of something weighs or how much liquid fits in a bottle? What’s the probability that someone will die at a given age? How much is something or someone worth? What’s the size of a brain or the length of a meter? The fact that we bother to count tells us that these are the kinds of things we care about.

At root, the search for precision is an intensely human enterprise and as such can’t ever be, well, precise. It reminds us, over and over, that “numerical values attach to things that are valued,� in Wise’s words. It’s a disturbing (if imprecise) thought: If we haven’t yet attached a precise number to something, we probably don’t value it much.

Luckily, this volume rejoices in the many levels of ambiguity present in the history and practice of precision. “We intend to open topics rather than to close them,� writes Wise in his preface. Based on a series of papers and discussions that took place in 1991 and 1992 under the auspices of the Princeton Workshop in the History of Science, the collection presents historical case studies by a variety of authors, including Theodore M. Porter of UCLA and Kathryn M. Olesko of Georgetown University.

Curiously, precision is not an objective enterprise. It requires consensus among people, an often tortuously negotiated social contract. Consider, for example, what it means to make a precise measurement of someone’s height. What makes the measurement exact?

First, of course, the measuring tape needs to be of standard specifications calibrated correctly down to the desired level of detail: let’s say, 1 millimeter. Then it has to be anchored in the right place, and the resulting measurement has to be read without error. Another person making the same measurement should get exactly the same result.

The result of the measurement is a number. What does it mean? That’s very hard to say. In the first place, measuring anyone’s height to a millimeter is meaningless because most people shrink an inch each day (and gain back the inch at night) simply because of the pull of gravity. So it makes about as much sense to measure height to the millimeter as it does to measure the distance from New York to L.A. in inches. While you’re making the measurement, the ground can shift.

But there’s more: The temperature of the room (and therefore the length of the tape) can change. The person being measured can shift or slump. The person doing the measurement can get distracted, slip, tremble or lie.

Moving from home to the laboratory, the same kinds of caveats apply. Precision within the laboratory requires “an extensive set of agreements about materials, instruments, methods and values that reach out into the larger culture,� writes Wise, “[R]eliability is never a matter simply of a reliable instrument. It is also a matter of people judged to be reliable using methods that display their reliability.�

Wise makes an important distinction between precision and accuracy. Precision means that a measurement shows little spread: You get the same measurement time after time, always within a narrow margin of error. However, precision tells us nothing at all about accuracy. Accuracy implies that the measurement represents the true value of something. You can weigh yourself on a scale that is extremely precise, but if you set the zero mark at minus-10, the reading won’t be accurate. In the same way, though you might be able to give an extremely precise accounting of the dollar value of the chemical elements in a human body, that wouldn’t necessarily be a very accurate reflection of the person’s worth. You could stick a ruler in someone’s mouth to take their temperature and no doubt get a number, but that number is unlikely to tell you whether the person is sick.

Measures of intelligence, trustworthiness, beauty and other human qualities are notoriously imprecise; they depend a great deal on who is doing the measuring and when. But the bigger question is: Even if they could be made precise, would they be accurate? Could they ever convey anything important about the thing being measured?

Despite the difficulty of pinning down precision, however, it has been a goal of governments since people first hovered around communal fires and created societies. Indeed, “The Values of Precision� makes a good argument that the main value of precision has been the building and enhancing of institutions--from nation-states to armies to businesses. A government can’t exist without information about who and what it controls. Bureaucracies run on numbers: numbers of people, dollars, goods, weapons, trees, acres, hospitals, schools, tons of gold, barrels of oil, miles of coastline. A government can’t tax its citizenry if it doesn’t know what it is or where to find it.

To get these numbers, a government must impose uniform standards: one currency, one measure of time and weight and length, one way to calculate income or taxes. Precise measurements of these quantities require control over them. It also makes controlling easier. “The generalized drive for precision has regularly been linked to attempts to extend uniform order and control over larger territories,� writes Wise.

In the same way, precise measurements put businesses in control of their people and products. Manufacturers need instruments that can measure quantities of matter, temperature, magnetism, time, electrical conductivity, light. They need precise navigation systems to locate ships and time clocks to keep track of workers’ hours. They need telephones and telegraphs to communicate over long distances and standard weights, measures and currency to conduct long-distance trade.

Although the essays in “The Value of Precision� deal specifically with historical interludes like the calculation of insurance tables in Victorian England, the themes are surprisingly modern, and the lessons shed light on many issues of current importance. For example, the essay by Andrea Rusnock of the Rensselaer Polytechnic Institute on determinations of population in 18th century France echoes uncannily with the ongoing debate between Democrats and Republicans in 20th century America over how to conduct a census of the population.

But though Republicans even today insist that counting heads is the only way to get an accurate measure of the population, the 18th century French demographer Antoine Auget, baron de Montyon, made an argument that sounds exactly like those used today by mathematicians and census workers who say that counting noses is both impossible and inherently inaccurate. “A head-by-head enumeration of the inhabitants of a realm would not make known exactly the number, the less because it cannot be done at the same time in all places,� he wrote. “Further the moment when the census is complete, it is no longer true, and the unexpected birth or disappearance of some individuals changes the state of things.�

Indeed, already well aware of the fallacy of thinking that counting is the best way to find out how many people there are, the natural philosopher Pierre-Simon de Laplace proposed as far back as the late 1700s that governments use sampling methods, relying on the mathematics of probability. Laplace’s sampling scenario is similar to the method proposed by the U.S. Census Bureau today. (The bureau may need an alternative for its 2000 census if the Supreme Court upholds last week’s federal appeals court ruling that sampling violates federal laws about the census.)

Scientists and philosophers of the 18th century were also grappling with the difficulty of inflicting the metric system on an unreceptive population--a goal that still eludes their counterparts in this country today. “Putting meter sticks in the hands of ordinary citizens was easier said than done,� writes Ken Adler of Northwestern University.

There’s more at stake here than the always unpleasant task of unlearning the old and assimilating the new. There’s the question: Just what is a “natural� measure? In France, at the time, measurement was a mess, with 700 to 800 different units used to count quantities of grain, wine, oil, hay, wood, etc. Yet they all made some sense, in a common-sense way. They were derived from the stuff being measured itself, just as a “foot� measured, more or less, the length of a foot.

Today, we base our international measures of length on meters, not feet. And rather than the distance from heel to toe, the definition of a meter is more precise: The distance traveled by light in a vacuum over 1/299,792,458 of a second. Which is the more “natural,� appropriate way to measure distance? Is the rotation of the Earth a better or worse measure of time than the tick of a cesium atom?

The price of precision, as the use of a cesium atom or the speed of light illustrates, is the severing of measurement from human experience. “Indeed, the whole thirst of the metric reform,� writes Adler, “was to replace an economic system based on value, with one in which everything--human labor, as well as its artifacts--was translated into the single, paramount variable of price.�

Scientists in the 19th century, similarly, began to come to terms with the role of morality in precision. The qualities of the measurer were as important as the quality of the measurement itself, and a scrupulous scientist must be as finicky about pinning down what is not known as what is known. Every possible source of error must be precisely cataloged and quantified. Precision about error, then, becomes the real measure of truth.

All this is presented in “The Value of Precision� with far more detail than perhaps most people care to know, both about the history and the science. Still, the essays teach important lessons about the often inappropriate uses of precision; how we rely on numbers instead of sense, substituting formulas for compassion or real knowledge.

In our age of health care by formula, teaching by number and evaluation by score, it’s wise to remember that quantification takes us only so far. Or as contributor Theodore M. Porter puts it: “[T]he abandonment of judgment in favor of mechanical precision� ultimately reflects weakness, not strength. “Precision instruments are packaged trust,� concludes Wise. “Where trust is weak, the chain is weak.�