Many who work in the human sciences reject completely the idea of trying to measure any human attributes at all. They regard all human attributes as too complicated to be subjected to the insulting process of reductionism to mere numbers. Numbers can be used in descriptions of objects, but they may not be used in relation to subjects. Of course, most
psychometricians do not share such qualms. Psychometricians have spent more than a century trying to quantify a whole range of somewhat intangible human traits. However, they often regard the precise objective measurement that has been the touchstone of the physical sciences as being far beyond their own meager reach.
At least part of this outlook has come about because human scientists remain quite ignorant as to how physical measures came into being. They remain unaware of how much time, money, and effort still are committed to the construction, calibration, and maintenance of the measurement units we routinely use every day. Moreover, most of us think that physical measures are absolutely precise when they are routinely imprecise. We regard physical measures as error free, when in fact systematic and random errors are acknowledged by those who specialize in their use. Yet, we always double and triple check our measurement of linear dimensions when the fit has to be "just so," but then rely on a "one-shot" achievement test from last year, for example, to place young Mary into a reading group at school. If quantitative researchers in the human sciences see the
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attainment of such quality measures as beyond their grasp, it is perhaps because, on the one hand, we overestimate the quality of our physical measures while, on the other hand, we underestimate the quality of the tools we currently have for constructing and maintaining objective measures in the human sciences.
A brief historical look at the experimental techniques of Galileo will help us to understand how time might have been measured in the era before clocks, whereas the problems of measuring time at the beginning of the 21st century will show that the task still is not yet taken for granted. It also is rather helpful to look at how temperature has been
conceptualized and measured, because much historical information about this relatively recent development in physical science methods is available to inform us about the procedures involved. Although measuring the passage of time is crucially fundamental to many of the physical and human sciences, we tend to forget that most of us see time as measured by the angular distance that a sweep second hand might move around a stopwatch dial.
Galileo's Two New Sciences reported how he substituted rolling balls down an inclined plane for his previous experiments with free-falling objects. This allowed him more control of the experimental situation. In particular, it allowed him the opportunity of making more precise measurements. In the 17th century, however, there were no set standards for the measurement of length, so Galileo resorted to arbitrary units, which he replicated along the rolling track to standardize his estimates of length. To estimate the intervals of time required for the balls to traverse the marked sections of track, he collected the volume of water that spurted through a narrow pipe in the base of a large elevated container. The water collected for any interval then was weighed on a very accurate beam balance. The differences between the weights and the ratios between them allowed for the estimation of the relative time intervals. Of course, the process of weighing also was somewhat indirect: Equality of the weights in opposing pans of the balance beam was inferred from the level beam—the moments of force around the central pivot point were held to be equal when equal weights were suspended from equal arms in the absence of friction. What an interesting set of inferential leaps and scientific theories underlies this attempt to measure equal intervals of the time construct (Sobel, 1999).
The construction of the thermometer was developed in a similar manner. What began as human sensations of "hot" and "cold" eventually evolved into the field of thermometrics (i.e., the measurement of temperature). Early records of attempts to construct temperature scales date back to A.D. 180, with Galen mixing equal quantities of ice and boiling water to establish a "neutral" point for a seven-point scale having three levels of warmth and three levels of coldness. Techniques slowly improved throughout the centuries. Scientists in the 17th century, including Galileo, are credited with the early successful work in this area. Santorio of Padua first reported using a tube of air inverted in a container of water, so that the water level rose and fell with temperature changes. Subse--
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quently, he calibrated the scale by marking the water levels at the temperatures of flame and ice. Necessarily, these instruments ignored the systematic errors caused by changes in the volume of the glass and the liquid that occurred during the instrument's use. Neither could contemporaries explain why different liquids behaved in different ways to produce estimates of temperature.
The famous Celsius and Fahrenheit scales, each named for its originator, merely set two known temperature points (e.g., ice and boiling points) and divided the scale into equal units or degrees (e.g., 100). Robert Hooke of the Royal Institute in London defined a scale in which 1° Fahrenheit was defined as "a change of 1/10,000 in the volume of a given body of mercury" and used one fixed calibration point. Despite the publication of detailed construction and calibration
instructions, Hooke's attempts at temperature measurement had little influence at the time. Although measures of
temperature proliferated, Hooke-based temperature measures often did not match measures based on other models, such as the transfer of heat from one liquid to another, or those based on expansion-of-air models. (This sounds familiar. It seems as though there is still hope for psychometrics.)
In approximately 1850, Lord Kelvin's theoretical structure, known as thermodynamics, was accepted as the standard practice and used for 75 years. His additive model posited that the addition of heat units to a given body would change the temperature of that body by that same number of units. This property held regardless of where on the scale the units of heat were added. This measure of heat was based on hydrogen because it was determined that hydrogen provided the best approximation at that time of his model based on the behavior of an ideal gas.
Twentieth-century work has added to Kelvin's hydrogen expansion thermometer (e.g., platinum resistance thermometers and platinum/rhodium thermocouples; Choppin, 1985) to measure temperature changes outside the precision range of the Kelvin scale. Although we commonly use the approximate estimates of temperature provided by mercury and alcohol thermometers, and although we control refrigerators, air conditioners, and car cooling systems with bimetallic strips, even the best temperature-measurement devices based on the models described here show inconsistencies between the various methods at different temperatures.
What we can learn from the process of thermometer construction is that the construction of a reproducible measurement system is always under revision. There is no one true model, and no model comes without imprecision. Working glass thermometers were useful in medicine long before we figured out why they worked, yet these very same thermometers, on which life-and-death decisions are sometimes made, are next to useless for many other temperature-measurement uses. We even have to know how and where to position the medical glass thermometer for it to be fully useful. Yet working within that imprecision, acknowledging it, and proceeding to construct measures despite im--
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precision, is critical to the advancement of science. Even incorrect models, as long as they are based on the creation of additive structures, are very useful in solving current scientific problems. (This brief coverage relies heavily on the work of Choppin, 1985.)
One of the cover stories in the June 2000 issue of Discover. magazine reports, in layperson's terms, the difficulties that currently beset those who maintain watch over the world's time. Although the passage of time was previously marked by sunrise and sunset, and more recently by pendulum clocks, which also are calibrated against the rotation of the earth, inconsistencies in our planet's shape and movement make it unreliable as a basis for the measurement of time. From 1967, the standard definition of the period of 1 second moved to the atomic scale based on the radiation of the cesium 133 atom. Although the $650,000 cesium clock in Boulder, Colorado, estimates the passing of 1 second with almost unbelievable precision, it does not directly keep time. The keeping of the international time standard is the responsibility of the Paris Observatory. Moreover, it is based on an average. The time estimates of more than 200 atomic clocks from around the world are routinely collected, averaged, and fed back to the originating laboratories so that the computer- generated records on the passage of time at each laboratory can be adjusted regularly for the local clock's deviation from the world average, even if it is somewhat after the fact (Klinkenborg, 2000). We could wonder what such a well-funded and well-coordinated international effort might produce in terms of measuring just one key human attribute.