² Thompson, Kenneth W., “The Study of International Politics: A Survey of Trends and Developments.” Review of Politics, 14 (10 1952), 433–467 CrossRefGoogle Scholar. See also Waldo, Dwight, Political Science in the United States of America (UNESCO, 1956)Google Scholar.

³ This is not to belittle a normative or policy approach to international relations. Although current work in empirical and quantitative international relations may appear more removed from moral commitments by its abstractness, the values of the researcher are involved no less than in traditional policy-oriented scholarship. If any difference between empirical and quantitative international relations on the one hand and that which has gone before on the other is to be drawn, it is not in a difference in moral commitments. Rather, the difference lies in making assumptions, logic, and data explicit so that others may test any conclusions drawn regardless of their values.

⁴ See, for example, Schuman, Frederick, International Politics (New York: McGraw-Hill, 1933)Google Scholar, and Lasswell, H. D., World Politics and Personal Insecurity (New York: McGraw-Hill, 1935)Google Scholar.

⁵ Harold, and Sprout, Margaret, Foundations of International Politics (New York: D. Van Nostrand, 1962)Google Scholar.

⁶ Wright, Quincy, A Study of War, 2 vols. (Chicago: University of Chicago Press, 1942)Google Scholar.

⁷ Morgenthau, Hans J., Politics Among Nations (New York: Knopf, 1948)Google Scholar.

⁸ Pool, Ithiel de Sola, Symbols of Internationalism (Stanford: Stanford University Press, 1951)Google Scholar; Deutsch, Karl W., Nationalism and Social Communication (New York: Wiley, 1953)Google Scholar; Wright, Quincy, The Study of International Relations (New York: Appleton-Century-Crofts, 1955)Google Scholar.

⁹ Klineberg, O., Tensions Affecting International Understanding (New York: Social Science Research Council, 1950)CrossRefGoogle Scholar; Cantril, H., Tensions That Cause Wars (Urbana: University of Illinois Press, 1951)Google Scholar; Richardson, L. F. Statistics of Deadly Quarrels and Arms and Insecurity (Pittsburgh: Boxwood Press, 1960)Google Scholar; Rapoport, A., Fights, Games, and Debates (Ann Arbor: The University of Michigan Press, 1960)Google Scholar; Guetzkow, H. G., “A Use of Simulation in the Study of Inter-Nation Relations,” Behavioral Science, 4 (1959), 183–191 CrossRefGoogle Scholar; Schelling, Thomas C., The Strategy of Conflict. (Cambridge: Harvard University Press, 1960)Google Scholar.

¹⁰ The river simile can be used to make another point. Quantitative research in international relations does not presume an antithesis between traditional and quantitative scholarship. On the contrary the two are complementary. As the course of a river is determined by the fertile valleys through which it flows, so is quantitative research channeled by traditional insight and knowledge. Together the land and the river produce an abundant harvest and together the precision and reliability of quantitative scholarship combined with the rich comprehensiveness of traditional scholarhip bear new fruit.

¹¹ McClelland, David C., The Achieving Society (New York: D. Van Nostrand, 1961)CrossRefGoogle Scholar.

¹² At this point I will have to increasingly rely on a technical vocabulary to communicate the criteria and evidence. If the more traditionally trained scholar has gamely stayed with me so far, I beg his further indulgence. Technical terms I will use to a minimum, but I must employ such terms if any of the accumulated evidence is to be offered.

¹³ Elsewhere I have published a paper on “Understanding Factor Analysis” Journal of Conflict Resolution, 11 (12, 1967), 444–480 CrossRefGoogle Scholar, which might be helpful auxiliary reading for the remainder of this paper.

¹⁴ In some other papers I have used the term “dimension” rather than “pattern.” The latter term is preferred here because it may communicate better the basic idea than does the more mathematical and abstract notion of dimension.

¹⁵ That economic development and size are patterns of nations will be established subsequently.

¹⁶ Bloc membership refers to western, neutral, or eastern bloc membership.

¹⁷ Sawyer, Jack, “Dimensions of Nations: Size, Wealth, and Politics,” American Journal of Sociology, 73 (09 1967), 145–172 CrossRefGoogle Scholar; Rummel, R. J., “The Dimensionality of Nations Project,” in Merritt, Richard and Rokkan, Stern (eds.), Comparing Nations (New Haven: Yale University Press, 1966), pp. 109–129 Google Scholar; Rummel, R. J., Dimensions of Nations, forthcoming, 1969 Google Scholar.

¹⁸ These are orthogonally (varimax) rotated factors. The initial solution was determined using the principal axes technique with unities in the diagonal of the correlation matrix. Correlations were product moment and were calculated on variables with an average of about seventeen percent missing data. All factors with positive eigenvalues were extracted and rotated and all positive eigenvalues exceeded unity. Further details and results are given in Rummel, Dimensions of Nations.

¹⁹ This analysis comprised the oblique (biquartimin) rotation of the initial fifteen factor solution. Because of the number of variables involved, the rotation was carried out in stages of ten major cycles each until there was no major alteration in loadings from one stage to the next.

²⁰ Because of small correlations between the patterns, the loadings can be loosely interpreted in our oblique rotation as the correlation between variable and pattern.

²¹ Cattell, Raymond B., “The Dimensions of Culture Patterns of Factorization of National Characters,” Journal of Abnormal and Social Psychology, 44 (1949), 443–469 CrossRefGoogle ScholarPubMed; Cattell, Raymond B., Hartman, H. P., and Breul, H., “An Attempt at More Refined Definition of the Cultural Dimension of Syntality in Modern Nations,” American Sociological Review, 17 (1952), 408–421 CrossRefGoogle Scholar; Cattell, Raymond B. and Gorsuch, Richard, “The Definition and Measurement of National Morale and Mortality,” The Journal of Social Psychology, 67 (1965), 77–96 CrossRefGoogle Scholar.

²² Berry, Brian J. L., “An Inductive Approach to the Regionalization of Economic Development,” in Ginsburg, Norton (ed.), Essays on Geography and Economic Development (Chicago: University of Chicago Press, 1960)Google Scholar.

²³ Russett, Bruce M., International Regions and International Integration (Chicago: Rand Mc-Nally, 1967)Google Scholar.

²⁴ The intraclass correlation coefficient measures both profile and magnitude correlation, while the product moment measures only profile correlation. The intraclass is therefore a more stringent measure of reliability than the often employed product moment. See Section 12.3.3 of my Applied Factor Analysis (Evanston: Northwestern University Press, 1969) forthcomingGoogle Scholar.

²⁵ The technique of comparison employed was Ahmavaara's transformation analysis. See Ahmavaara, Yrjo, On the Unified Factor Theory of Mind (Helsinki: Annales Akademiae Scientiarum Fennicae, 1957)Google Scholar. The DON fifteen factors were first rotated to a least squares fit with those of another study. Then, the intraclass correlation was calculated between all the DON loadings and those of the other study.

²⁶ Correlations were computed after the DON fifteen factors were rotated to a least squares fit to those of the other study.

²⁷ I have relabelled, for clarity, Cattell and Gorsuch's op. cit. (1965), factors 3 and 14.

²⁸ If the variables involved in a pattern were not included in the analysis of the other study, then the pattern cannot be compared.

²⁹ Russett, op. cit. I wish to express my appreciation to Russett for communicating these comparisons to me before publication.

³⁰ Robinson, John, “Multidimensional Analysis as a Comparative Framework for Poltical Systems,” (Ann Arbor: University of Michigan, 1965 Google Scholar, unpublished manuscript).

³¹ Berry, op. cit.

³² Gregg, Phillip M. and Banks, Arthur S., “Dimensions of Political Systems: Factor Analysis of A Cross-Polity Survey,” this Review, 59 (1965), 602–614 Google Scholar.

³³ Rummel, R. J., “Dimensions of Error in Cross-National Data,” in Naroll, Raoul and Cohen, Ronald (eds.), Handbook of Method in Cultural Anthropology, forthcoming, 1969 Google Scholar.

³⁴ The technique of comparison was the same as in the previous comparisons.

³⁵ Cattell, op. cit. (1949).

³⁶ Cattell, Hartman, and Breul, op. cit.

³⁷ For the size pattern, a basic indicator might be population times energy consumption. It has a higher loading than population, but it also has a coefficient of determination of .37 with energy consumption per capita. For this reason population is a preferred basic indicator.

³⁸ Data were transformed to increase the normality of the distributions and to remove extreme values. This reduces the effect on the results of a few high behavior dyads, such as UK→USA and USA→UK.

³⁹ Russett, op. cit. Cattell, Raymond B., “The Principal Culture Patterns Discoverable in the Syntal Dimensions of Existing Nations,” The Journal of Social Psychology, 32 (1950), 215–253 CrossRefGoogle Scholar.

⁴⁰ The same factor analysis and rotation procedures were used as for the attribute analysis. See footnotes 18 and 19.

⁴¹ This sample has the most interesting dyads and raw data patterns. Moreover, indicators selected from the analysis of this sample will be simpler to interpret and employ.

⁴² The same factor comparison method was used as employed for the comparisons of Figure 3.

⁴³ The patterns of each of the three samples were rotated to a least squares fit to those of the raw selected sample. This maximized the linear correspondence of the results and washed out irrelevant effects on the oblique rotations which were done independently for each sample.

⁴⁴ The Euclidean distance, d_{A, B}, between two nations, A and B, in the space of p orthogonal factors (uncorrelated patterns)

S₁, S₂, …, S₁,…, S_p is

where S _Al and S _Bl are the factor scores of nations A and B on the 1th factor.

⁴⁵ The issue patterns were internationalism, admission of new members, self determination, semantic (determined largely by one roll call as to whether the word “man” should be replaced by “human being” in the covenant of human rights), feminine rights, petitioning (Ethiopia), and self-government (Togo).

⁴⁶ Rummel, R. J., “Some Attribute and Behavioral Patterns of Nations,” Journal of Peace Research, 2 (1967), 196–206 CrossRefGoogle Scholar.

⁴⁷ They were violent acts, planned violent acts, incidences of violence, discrete military acts or clashes, days of violence, negative acts, diplomatic rebuffs, negative communications, written negative communications, oral negative communications, written or oral negative communications, unclassified negative communications, accusations, representations or protests, warnings, and anti-foreign demonstrations.

⁴⁸ In the terminology of linear algebra, the patterns (as factor dimensions) can be considered as bases of nation attribute and behavioral spaces.

⁴⁹ For all following examples, the data are assumed to be standardized.

⁵⁰ These and subsequent linear combinations (regressions) are derived from the orthogonal factor results of the 236 variable attribute and 40 variable (raw selected sample) behavioral analyses (Rummel, Dimensions of Nations, op. cit.). The values for the constants in the equations are the loadings of the dependent variable on the factor patterns indexed by the basic indicators.

⁵¹ The reason for dividing international relations into these two spaces is to mathematically resolve the problem of linking the characteristics of nations to their international behavior, or to use more fashionable language, to mathematically couple national subsystems to the international system. The representation of national attributes as a mathematical (Euclidean) space enables us to define nations as points in this space. Then we can define a distance vector between any two nation-points on each coordinate, say economic development, of space. Such distance vectors for all the coordinants of the space will measure the differences and similarities of nations across all their attributes.

Now, in the space of behavior we can locate pairs of nations—dyads—as points according to the behavior of the actor nation to the object nation. If we draw a line from the origin of this space to each dyad and add an arrowhead at the point where the line makes contact with the dyad, we then have a vector representation of each dyad's location in behavior space. The basic linkage between attribute space (nation attributes) and behavior space (nation behavior) is made through the distance vector. The magnitude and direction of a dyad vector in behavior space is a mathematical function of the distance vectors between the two nations in attribute space. That is

where = the vector describing the location of the dyad, A→B, in behavior space,

Thus, international behavior is made a function of the similarities and differences between nations. The mathematical notions are fully integrated into one model, are operationalizable and the linkage is testable. The purpose of this paper, however, was not to present this linkage but rather a set of indicators (which locate each nation on the coordinants of these spaces). Describing this theory in detail would take us far afield from our original purpose. However, those wishing to read more on this theory, which I call a social field theory, are referred to my “A Field Theory of Social Action with Application to Conflict Within Nations,” General Systems Yearbook, 10 (1965), 183–211 Google Scholar; “A Social Field Theory of Foreign Conflict Behavior,” Peace Research Society: Papers, IV, Cracow Conference, 1965, pp. 131–150 Google Scholar; Dimensions of Nations, op. cit., Chapter 16.