In the previous discussion and Volumes, I have tried to make clear that distance vectors between actors empirically reflect their relative, latent attitudes and capabilities, and that attitudes are transformed into interests through the stimulation of associated needs. Attitudes are therefore inactive interests. And by themselves, distances only define potentiality. All this will be discussed further in Section 10.2 regarding the structure of conflict.

However, here and in Figure 8.1, I am concerned with distances in a situation in relation to behavior. A perceived situation stimulates needs; it transforms attitudes into interests, potential capability into actual capability. Therefore, the distances linked to an actor's behavior in a situation will reflect his living interests and relevant capabilities. Of course, not all interests will be weighted in a situation--not all interests will be active. It is the situational weights that measure the transformation of attitudes into interests and the relative weight these interests will have. But between the activation of an actor's interests and the utilization of his relevant capabilities is the his will. The will is an actor's power to actually choose and try to gratify his interests--to bring himself to behave.² But not all behavior requires the will. Some behavior is routine, habitual, automatic, reflexive. The will, however, is engaged in interrelating actions and acts, in intentional behavior. Behavior that comprises practices are routine, and habitual, norm and rule following behavior, and therefore due to reasons; behavior that comprises reflexes is automatic, due to causes. Thus, Figure 8.1 shows the variation in an actor's behavior as divisible into that brought intentionally about by the will, and that due to reasons and causes. Note also that some unique practices may be also a matter of will; they may be individualistic, against the common grain, and thus require the will to maintain.

With this crucial understanding that an actor's will is engaged in common acts and actions, I can now deal more precisely with the equation of interests, capabilities, and wills. In a situation, the variation in behavioral dispositions of an actor towards others will be a function of his common interests and capabilities regarding them and his unique interests and capabilities. In vector terms,

Equation 8.1:

W_gi = _gid_i + Q_gi,

where

W_gi = variation in (vector of) i's behavioral dispositions towards others in situation g;

_gi = the perceived salience in situation g of i's interests and capabilities reflected in the distances along the ^th common component of international space-time;

d_i = i's variation in (vector of) distance vectors³ from other actors;

Q_gi = i's (vector of) unique interests, capabilities, and will in situation g.

Thus, distances and situation tell only part of the behavioral story. As actor's in international relations, we are also individualistic. We have our particular interests and capabilities and our independent, free will. Note that Q measures the unpredictable part of an actor's behavioral disposition, the part not reducible to a function of his situation and distances from others. Thus Equation 8.1 embodies the belief that an actor's behavior is partly patterned, partly unique; partly due to his will influenced by common social forces, partly to his will acting independently of such influences.⁴

Equation 8.1 is the vector equation interrelating the various sources of variation in an actor's common behavior that are shown in Figure 8.1. The specific behavioral disposition of an actor towards a specific other is then,

Equation 8.2:

w_{g,i j} = _gid_,i-j + Q_g,ij,

where

w_{g,i j} = the behavioral disposition of i towards j in situation g;

d_,i-j = i's distance vector from j on the ^th component of international space-time;

Q_g,ij = i's unique interests and capabilities regarding j in situation g.

In words, the specific behavior of an actor towards another is a function of an actor's situational expectations and dispositions, where these dispositions themselves are a function of situational perception and distances. More precisely, for common behavior h, from Equations 6.3 and 8.2,

Equation 8.3:

_h,ij = _ghigw_g,ij,

= _ghig(_gid_,i-j + Q_g,ij).

The vector counterpart of this equation is shown at the bottom of Figure 8.1 [note that the subscript i was accidently omitted from the d term, which is corrected below]. It is

Equation 8.4:

_hi = _ghig(_gid_i + Q_gi).

Equation 8.3 is the basic equation of field theory.⁵ To be sure it is understood, Figure 8.2 conceptually defines its elements.

Now to consider again the international sociocultural space-time. Figure 8.3 pictures this space-time, and the inner, common space-time spanned by the components of Table 7.1, such as wealth and power. As shown, the common behavior of an actor related to his distance vectors is a subspace of this common space-time. In other words, that common behavior of an actor associated with his common interests and relative capabilities is imbedded in sociocultural space-time. From Figure 6.3 and Section 6.4,

Equation 8.5:

_i = W_ii,

where

_i = matrix of i's dyadic behavior towards others;

W_i = matrix of i's situational, dyadic dispositions;

_i = matrix of i's expectations of the outcome of behavior in different situations.

This defines i's region of common behavior space-time, as shown in Figure 6.3. Then for the matrix of i's dispositions,

Equation 8.6:

W_i = D_ii + Q_i,

where

D_i = the matrix of i's distance vectors from other actors on the common components of sociocultural space;

_i = the matrix of i's situational perceptions;

Q_i = the matrix of i's unique dyadic interests, capabilities, and will regarding others in various situations.

And from Equations 8.5 and 8.6.

Equation 8.7:

_i = W_ii

= (D_ii + Q_i)_i

= D_iii + Q_ii

_i - Q_ii = D_iii.

Thus, as with the expectation and disposition equations of Chapters 5 and 6, there are also matrix, vector and scalar versions of the behavioral equations of interests, capabilities, and situation. These are shown in Table 8.1.

Of course, in day-to-day reality, interests, capabilities, wills, and situational expectations and perceptions interact in complex and multifold ways. International behavior in its rich daily variation is neither simple, linear, nor wholly reducible to mathematical functions. Historians have tried to capture this flow of events and activities, this interaction of personalities and situations, and often have become convinced thereby that international relations are idiosyncratic, unique, and irreducible to general forces, principles, or laws. At a more abstract level, many who have tried to analyze international relations statistically or mathematically have also become convinced that simple linear equations cannot fit the complex, interdependencies between national behaviors, forces, and conditions.

Here I do not wish to again join this issue.⁶ The equations of situational expectations, perception, and distances are meant to represent latent interwoven interests, perceptions, and so on, at the most general, manifest level. Distances and situations are latent functions⁷ reflecting patterns in this complex, in the same way the historian or statesman reduces the complex reality of potentials, dispositions, powers, and manifestations to abstract concepts like the "balance of power" or "national interest."

The behavioral equations express relationships, interactions, dependencies. But they are not linked into the process of developing international orders, of conflict. The question is central: how do these equations reflect the conflict helix? Answering this is the burden of the following Chapters, and will require far more discussion and specificity about the elements of the behavioral equations than yet given.