as less internationalized than either astronomy and astrophysics or the mathematical sciences. Moreover, the atomic and molecular sciences were combined with optics only recently, which raises some problems of definition in their collective assessment.

The structural and methodological differences in the research activities of these three different disciplines therefore provided a diverse set of elements to measure. The panels were asked to obtain and review the available data regarding their respective disciplines, and to assess the utility of those data in determining their discipline 's health or status. This report summarizes the results of these three pilot assessment projects and also incorporates the principal findings of a workshop that was held to critique and help integrate the results of the panels' work.

PURPOSE AND SCOPE OF DISCIPLINE ASSESSMENTS

The purpose of the NRC's discipline assessments is to establish new research goals and priorities, to detect incipient problems that need to be addressed, and to compare progress with previously established goals and priorities. The rationale for periodically assessing a discipline is both internal and external to the discipline. From an internal viewpoint, it is important for the community to have a better understanding of its overall situation in order to identify significant issues in its research activities that require some corrective action and response. An introspective analysis can address issues that are perhaps unique to the conduct of research in a particular discipline and that are best resolved by the community itself.

An external perspective places a discipline in the larger research and development (R&D) context and in the nation's broader social, economic, and political milieu. Such a perspective must determine the impact of externally generated pressures, such as those currently being caused by the U.S. budget deficit and military contraction, as well as the role of a field such as mathematics in supporting the nation's R&D and other socioeconomic and political goals. These linkages have become increasingly important to identify and understand at a time when government policymakers and the R&D establishment are seeking to improve our nation's return on public and private investments in both basic and applied research.

If one accepts the validity of an organic or ecological model in describing and analyzing the status of a particular discipline, it becomes conceptually difficult to focus on any given aspect without considering the whole. Scientific research is a highly interactive system; dissecting it into its many components inevitably leads to isolating them artificially. It is necessary to look not only at a discipline and the interaction of all its intrinsic elements, but also at the relationship of the discipline to its immediate environment, to other disciplines, and to the larger society. The scope of a discipline assessment thus potentially embraces a very broad set of issues and activities, greatly complicating a consistent application of quantitative methods for all areas of research.

A major task at the outset of a discipline assessment is to properly define the boundaries of the discipline and appropriately categorize the activities being assessed. Similarly, it is desirable to precisely and unambiguously define all terms and categories of research activities. Although determining the scope of an assessment is to some extent arbitrary, it is an essential precondition for any subsequent comparisons of data sets, which often use different discipline boundaries and definitions.

Stipulating appropriate boundaries and definitions is more easily done in well-established and relatively small disciplines, such as astronomy, where standard tax-



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QUANTITATIVE ASSESSMENTS OF THE PHYSICAL AND MATHEMATICAL SCIENCES: A Summary of Lessons Learned as less internationalized than either astronomy and astrophysics or the mathematical sciences. Moreover, the atomic and molecular sciences were combined with optics only recently, which raises some problems of definition in their collective assessment. The structural and methodological differences in the research activities of these three different disciplines therefore provided a diverse set of elements to measure. The panels were asked to obtain and review the available data regarding their respective disciplines, and to assess the utility of those data in determining their discipline 's health or status. This report summarizes the results of these three pilot assessment projects and also incorporates the principal findings of a workshop that was held to critique and help integrate the results of the panels' work. PURPOSE AND SCOPE OF DISCIPLINE ASSESSMENTS The purpose of the NRC's discipline assessments is to establish new research goals and priorities, to detect incipient problems that need to be addressed, and to compare progress with previously established goals and priorities. The rationale for periodically assessing a discipline is both internal and external to the discipline. From an internal viewpoint, it is important for the community to have a better understanding of its overall situation in order to identify significant issues in its research activities that require some corrective action and response. An introspective analysis can address issues that are perhaps unique to the conduct of research in a particular discipline and that are best resolved by the community itself. An external perspective places a discipline in the larger research and development (R&D) context and in the nation's broader social, economic, and political milieu. Such a perspective must determine the impact of externally generated pressures, such as those currently being caused by the U.S. budget deficit and military contraction, as well as the role of a field such as mathematics in supporting the nation's R&D and other socioeconomic and political goals. These linkages have become increasingly important to identify and understand at a time when government policymakers and the R&D establishment are seeking to improve our nation's return on public and private investments in both basic and applied research. If one accepts the validity of an organic or ecological model in describing and analyzing the status of a particular discipline, it becomes conceptually difficult to focus on any given aspect without considering the whole. Scientific research is a highly interactive system; dissecting it into its many components inevitably leads to isolating them artificially. It is necessary to look not only at a discipline and the interaction of all its intrinsic elements, but also at the relationship of the discipline to its immediate environment, to other disciplines, and to the larger society. The scope of a discipline assessment thus potentially embraces a very broad set of issues and activities, greatly complicating a consistent application of quantitative methods for all areas of research. A major task at the outset of a discipline assessment is to properly define the boundaries of the discipline and appropriately categorize the activities being assessed. Similarly, it is desirable to precisely and unambiguously define all terms and categories of research activities. Although determining the scope of an assessment is to some extent arbitrary, it is an essential precondition for any subsequent comparisons of data sets, which often use different discipline boundaries and definitions. Stipulating appropriate boundaries and definitions is more easily done in well-established and relatively small disciplines, such as astronomy, where standard tax-