functioning properly, but also that the system is in a state of dynamic equilibrium or balance with its external environment.

It became quite clear from the panel discussions that each discipline has its own standards or vital signs for measuring its health and that these metrics, like those for assessing the well-being of different organisms, must be relative and not absolute. Moreover, even within a single discipline, the metrics and their interpretation will vary depending on who is doing the assessment and for what purpose.

In this regard, the Commission agreed with the Mathematics Assessment Panel, which rejected the notion that the health of a discipline can be measured based solely on numerical indicators. Statistical data can provide us with quantitative measures of some aspects of the state of a field, and while these measures can be used singly or in the aggregate as indicators, they do not provide direct measurements of its “health.”

For example, statistics can tell us the number of Ph.D. mathematicians produced each year, the level of federal funding and its distribution among areas of the mathematical sciences, or the number of graduate students supported as research or teaching assistants. These are measurements of some aspects of the pipeline and support—two areas important to the health of a field. These same statistics, however, are insufficient to determine the adequacy or appropriate balance of the funding or of the personnel levels. Different groups of discipline experts will reach different conclusions on what rate of Ph.D. production is desired, or on what is the optimum balance of support among the different areas of, for example, the mathematical sciences.

The discussion that follows lists potentially useful indicators of a discipline's state, suggests possible supporting data, and summarizes several significant issues regarding their application. It is important to emphasize that these indicators are not all of equal importance or effectiveness and that their applicability depends on the discipline being assessed and the purpose of the assessment.

Human Resources

Information on human resources—the people involved in the research activities of a particular discipline —is fundamental to determining the discipline's overall status. By far the most voluminous and widely available statistics for all disciplines are data on human resources, which provide us with information about various characteristics of the scientific work force.

Human resources data have been used extensively by government and academia to track the student population from grade school through graduate school and to monitor a variety of characteristics of the professional work force. Such data are collected regularly by several organizations, including the National Science Foundation (NSF), the Department of Education's National Center for Education Statistics, the Department of Labor's Bureau of Labor Statistics, the Commerce Department's Census Bureau, the NRC's Office of Scientific and Engineering Personnel, and the scientific professional societies. In addition, specialized surveys are conducted periodically by various research institutions and universities for certain segments of the student and professional populations. Taken together, these existing data sources provide a reasonably comprehensive and accurate portrayal of past demographic trends in distinct areas of scientific research.

In particular, many of these data can be used to characterize specific aspects of a discipline's supporting human infrastructure over time, as initially suggested by the Commission. The assessment panels divided the Commission's proposed “demo-



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