1: Introduction [and Summary]
... in the political sciences, we cannot, except rarely, deal with functions but are compelled to operate with functionals, that is functions of functions, and actually of many functions, including time.|
----Robert Strausz-Hupé and Stefan T. Possony, International Relation: In the Age of the Conflict Between Democracy and Dictatorship, 191-92
The mind intuitively or rationally, the culture pragmatically, or science quantitatively imposes order, pattern, regularity, intelligibility, and understanding on these manifestations in terms of the latents common to each similar system. Each manifestation, m, is then seen as a function of these common latents. These common latents are within the perspective of the percipient and comprise part of the transformation of external potentialities, dispositions, and their powers. Each system, such as a woman, is a field of potentialities and a configuration of dispositions, determinables, and powers. Some of these, in reality, are common to different but similar systems, as all we all share the disposition of hunger, or the power of will. The common latents are our perspective on these commonalities as perceived through their manifestations.
Now, the potentialities, dispositions, determinables, and powers composing systems are mutually interrelated and entangled, combining in complex, multifold fashion to generate manifestations. As this potentiality and actuality become patterned into common latents, the latents themselves are enmeshed in these complicated relationships. For example, several manifestations of similar systems may be a function of some latents L1, L2, and L3 such that any one manifestation Xim = f(L1, L2, L3) = L1 + 2L22 + L3. Some other manifestation n of the same system may result from a different combination of common latents, such that any one Xin = f2(L1, L2, L4) = L1L2 - 3L4. Yet other manifestations for similar systems may be generated by both f1(L1, L2, L3) and f2(L1, L2, L4). Thus, for a set of manifestations 1, 2,...,m,n,...,p, we may find that the manifestations for system i depend on common latents as follows.
- Xi1 = 11f1(L1, L2, L3) + Ui1,
- Xi2 = 21f1(L1, L2, L3) + 22f2(L1, L2, L4) + Ui2,
- Xi3 = 32f2(L1, L2, L4) + Ui3,
- Xim = m1f1(L1, L2, L3) + Uim,
- Xin = i2f2(L1, L2, L4) + Uin,
- Xip = p1f1(L1, L2, L3) + p2f2(L1, L2, L4) + Uip,
- where the alpha () coefficients simply mean that each manifestation is a differently weighted function of the latents (L), and U defines the specific (unique) aspects of the manifestations not dependent on the common latents.
Because of the complexity of the relations between common latents underlying the manifestations, we may only intuit or cognitize the functions and not the latents and their complex relations involved in the functions; that is, as we confront reality with our perspective, we drive to transform its multitudinous actuality and potentialities into simpler, more orderly, and comprehensible relationships. Accordingly, we often apprehend the functions themselves as the latents. We then simply perceive the latents underlying the manifestations of Equation 10.1 as f1( ) and f2( ), such that
- Xi1 = 11f1 ( ) + Ui1,
- Xi2 = 21f1 ( ) + 22f2( ) + Ui2,
- Xi3 = 32f2( ) + Ui3,
- Xim = m1f1( ) + Uim,
- Xin = i2f2( ) + Uin,
- Xip = p1f1( ) + p2f2( ) + Uip.
The parentheses of the functions are left blank to indicate that we do not perceive the latents contributing to each function. Each of these functions is perceived, however, as a unity generating the manifestations; they comprise state functions, defining for us the state of system i in terms of its manifestations. However, consistent with the previous discussion, I will call these latent functions. They are generally the latencies our understanding comprehends in imposing order on nature's welter of ephemeral manifestations. These latencies--latent functions--are the invariant potentialities, dispositions, determinables, and powers we perceive or cognitize in moving through life.
Some will note that the manifestations are linearly dependent on the common latent functions. This is not the place to consider the passionate, almost theological, linear-nonlinear controversy. Clearly, equations 10.1 and 10.2 are linear in the functions of the functions, although the functions themselves may be nonlinear, and are completely general. They could represent our quantitative scientific knowledge in science (the underlying latents can be defined by differential or integral operators--the basic equations in quantum physics, for example, are similar to equations 10.1-2)1 or our qualitative distinctions in other areas (which would not be the case if differential equations, say, were employed).2 Indeed, any perceptual-cognitive distinction that can be made about a system is reducible to equations like 10.2.3 The equations are thus a universal perspective for perceiving and understanding manifestations of systems.4
Xij = 1f1( ) + 2f2( ),
where f1( ) is the number of miles north or south and f2( ) is the number of miles east or west, and 1 = 2 = 1.0. In a similar way, the location of any phenomenon in local Euclidean space is a function of the three dimensions (x, y, z) of physical space.
This example should clarify somewhat my cryptic reference to the cultural matrix within which we perceive reality as containing, in part, Kant-like a prioris. The above common latents positioning things in space (and a comparable example could be given for space-time) are part of our cultural schema enabling us to make sense of perceptibles.
As a second example, note the many quantitative determinables of a human body, such-as weight, cranial size, finger length, height, toenail width, ad nauseum. Besides qualitative properties, such as color, posture, build, these quantitative aspects are transformed into the physical whole we perceive as a person. Underlying these physical manifestations are, in essence, two common latent functions: height and girth.5 Let Xij refer to person i's neck length j. Then, this manifestation can be represented by the equation
Xij = 1f1( ) + 2f2( ) + Uij,
where f1( ) is i's girth, f2( ) is our height, and Uij defines the unique sources of this manifestation (such as heredity). Of course, height and girth in turn have many interdependent bio-environmental dispositions and powers underlying their values. However, the mind generally ignores or cannot encompass them, and perceives instead height and girth in making the physical manifestations intelligible. Need I mention our cultural emphasis on fat versus thin and tall versus short, and how we employ these common latent functions as an everyday perspective for perceiving, thinking, or talking about others?
Not to slight my own field and to show the function of latents in social phenomena, two final examples will be taken from politics and government. One fast illustration concerns voting for candidates in elections. Clearly, through the perspective of political science, we perceive voting (manifestations) as dependent on a number of common latent functions, such as religion, age, socioeconomic status, region, and party membership.
A second, less known example deserving more detail has to do with national political systems. In their manifestations, such systems vary considerably, a variety which reflects the causal and interactive relationships among a number of underlying dispositions and powers associated with identifying issues, articulating and channeling interests, mobilizing support, deciding issues, and so on. There is a simplifying perspective through which these interrelated dispositions and powers may be transformed6 into essentially three common latent functions, three aspects that in combination give us the variety of common political manifestations. These are Western pluralistic democracy, communism, and monarchy.7 A manifestation, say censorship, of Uganda's political system, then, can be perceived as mainly a function of the degree to which (1) its political system is pluralistic in a Western sense, (2) it is of communist character, and (3) it is monarchical.
Before pushing on further, a brief summary may help. Underlying the manifestations we perceive are latents. These transform the haze of reality to invariant patterns and, within a particular perspective, make reality orderly and predictable. Latents may be considered properties, essences, or forms of things, but, in any case, they reflect the complex interrelationship between potentialities, dispositions, determinables, and powers. Moreover, and most important, latents may also comprise the cultural perspective, the schema, and meanings-values that are added to the perceptibles reality imposes on us. Percepts, themselves, are a seamless mixture of such latents and their manifestations.
Finally, although manifestations and latents are interrelated in complex ways, these relationships reduce to those between manifestations and common latent functions (or state functions): manifestations are a function of these latent functions. Specifically, an intuitive awareness or knowledge of these latent functions enables the probabilistic (it is likely that .... it seems that . . . , it is probable that ... ) content of manifests to be perceived or known.
To be sure that I am understood up to this point, let me use another language more appropriate for some contemporary philosophers of science or system theorists, but in form the same as what I am saying above. The haze of reality is transformed through our perceptual perspective into interdependent configurations, into systems. These systems link a variety of constructs connected to phenomena by rules of correspondence and which carry empirical properties (observables), some of which are latent observables (like the x, y, z, t coordinate axes of our space-time systems). These latent observables are state functions defining the state of a particular system and investing observables of that system with probable content.
For our purposes here, the point is that functions of latent functions presuppose a space delimited by the common latent functions. These functions will be called the components of the space. Henceforth, when the term components is used, it will mean common latent functions.7a To see what is meant by components, consider Figure 10.1 which displays the political system space. In the figure the components define a three-dimensional space, such as a corner of a room. The three components are at mutual right angles,8 with the vertical one defining, say, the height of an object in a room, and the other two lines fixing objects parallel to each wall. These three lines enable any object in the room to be located uniquely, or in general terms, the three components enable any point in the space to be fixed uniquely. Because the three components, Communism, Pluralism, and Monarchy, define the space of political systems, any manifest, such as X1, X2, X3, and X4, would have a specific location in the space. In other words, the figure shows what is meant by a common latent function underlying manifestations.
Many readers may see the above spatial representation as an attempt to belabor the obvious. Or others may wonder why I do not say it in plain English without the "physicalism." It is essential to grasp the nature of what is being done here. Many social scientists (for example, Lewin, Coutu, Heider, Bentley, Dodd, Sorokin, Parsons) have fallen down precisely where they did not appreciate the extent to which their models, philosophies, or theories presupposed a particular spatial perspective. Accordingly, they could not exploit the considerable analytic power that would otherwise have been at their disposal. At any rate, as far as the story here is concerned, I can now uncork the genie in the bottle: the dynamic field.
* Scanned from Chapter in R.J. Rummel, The Dynamic Psychological Field, 1975. For full reference to the book and the list of its contents in hypertext, click book. Typographical errors have been corrected, clarifications added, and style updated.
1. See Henry Margenau, The Nature of Physical Reality (New York: McGraw-Hill, 1950), which mainly concerns the pervasive and central role of latent or state functions in scientific perception.
2. This is a fundamental mistake of some general systems theorists. Bertalanffy, for example, argues that differential equations are the proper expression of system dependencies (Ludwig von Bertalanffy, General Systems Theory, New York: George Braziller, 1968). By doing so he limits "systems" mainly to those in physics and engineering, and to those quantitative manifestations comprising interval or ratio-scaled data. In contrast, if he had incorporated such differential equations as functions and treated manifestations as functions of such functions, as in equations 10.1 and 10.2, then he would have had a completely general expression of system relationships applicable not only to certain kinds of systems, but to social, cultural, aesthetic, linguistic, and in short, an systems.
3. I am well aware that most social scientists will see this as passing beyond the permissible bounds of an author's expected exuberance for his own views, but consider. Any distinction can be treated a dichotomy and then as binary numbers. For example, whether a person is a Catholic or not is a dichotomy which can be denoted as 1 = Catholic, 0 = non-Catholic. A collection of such dichotomous distinctions--manifestations--is then always reducible or transformable to equation 10.2. In more technical terms, every finite dimensional matrix of binary numbers has a basis, consisting of a set of linearly independent dimensions (functions). On measurement of qualitative manifestations, see my Applied Factor Analysis (Evanston: Northwestern University Press, 1970), sec. 9.1.3. On the relation between such measurements and latent functions, see ibid., part 2.
4. As the quote heading this Chapter shows, some students of international relations have begun to think in terms of the manifest-latent distinctions (although in different terms) and function of functions as discussed here (although not so specific). In Ernest Haas (Beyond the Nation State, Stanford: Stanford University Press, 1964) for example, we find: "Throughout this discussion, the kind of 'system' to which we shall address ourselves is the network or relationships among relationships; not merely the relations among nations, but the relations among the abstractions that can be used to summarize the relations among nations . . ." (p. 53).
5. See Harry Harman's Modern Factor Analysis (Chicago: University of Chicago Press, 1960) index for "eight physical variables."
6. All latent functions are given their particular importance through a specific perspective transformation. For example, if the latent functions are the dimensions of a space of potentialities, dispositions, and so forth, then the dimensions are subject to rotation and when differently rotated, they still generate the same manifestations. And different perspectives produce different rotations. In other words, there are many different but interdependent latent functions that can be perceived as the source of manifestations, and those particular latent functions actualized by our perspective (as for the point of view--the station--of the observer in Einstein's relativity) are the ones we perceive.
7. See my Applied Factor Analysis (op. cit.) index for "political characteristics."
7a. Throughout Volumes 1-4 of Understanding Conflict and War, I have adhered to this definition that a component equals a common latent function. However, because of a need to occasionally distinguish the component of component analysis from that of common factor analysis (see "Understanding Factor Analysis"), I sometimes have referred to the latter components as "common components." Moreover, if in context it was useful to stress that a component was a common underlying latent function, I have described it as a common component. In all cases, nothing new is added to the definition here.
8. This is done only for illustrative reasons. There is no necessity that components be so.