Systemic Learning in the Context of Observation.

By

Michael P. Byron, Ph.D.

Abstract.

The hypothesis that the real world political system constitutes a complex adaptive learning system is evaluated. Relevant parameters of this system are abstracted into a difference equation driven BASIC language computer model of the world system. These difference equations impose global, “top-down” transformation rules upon the system. This transformative process is highly modified by “bottom-up” interactions among the model system’s constituent actor-elements. This interplay between order and chaos allows for the emergence, and subsequent evolution of a complex adaptive learning system.

This model is utilized to generate empirical data for a Singular Predictive Instance (SPI) of systemic learning: warfare frequencies. These data are compared with corresponding real world empirical data for this SPI. A finding that the two sets of data are closely correlated allows for extrapolation of model systemic findings to the real world system.

The real world system’s trajectory through learning space is found to resemble that of typical model systems—with the exception that its attractor-bound trajectory is as yet incomplete. The potential effects of conscious observation of the world system upon its evolutionary learning trajectory are evaluated. A conclusion is reached that the effects of this observation process may, potentially, be significant, with respect to the world system’s subsequent trajectory through learning space.

Keywords: complexity, complex adaptive systems, systemic learning, warfare frequencies, empirical corroboration, computer modeling, attractors.

Section I: Conceptual Foundations of the Learning Model.

This study presents and then evaluates the hypothesis that the modern international political system is a complex adaptive learning system. Subsequently it investigates possible effects of conscious observation upon the world system’s trajectory through learning space.
To evaluate the hypothesis that the world system is a complex adaptive learning system I utilize a singular predictive instance (“SPI”) of systemic behavior: warfare frequencies. Warfare frequencies are selected because empirical data for the 1495-1975 time period (Levy, 1983) are available. These data allow for falsifiable empirical testing of my computer model (Byron, 1996) for crisis-driven systemic learning.
Systemic learning, with respect to warfare frequencies, is hypothesized to have occurred in response to increasingly rapid increases in total systemic power. These power increases cause the adverse consequences of warfare, in general, and great-power warfare, specifically, to evince a corresponding increase. This creates ‘selection pressure’ upon the system to ‘learn’ to avoid this ever-increasing danger to its existence. Conscious intervention arising from research into the nature of this learning process, if possible, is thus desirable, in the context of systemic survival via learning optimization.

My investigative strategy was to utilize MS QUICKBASIC to create a model international system program. The results obtained from running this program are employed to generate data for this SPI. These data are then evaluated in the context of Levy’s data. This allows for falsifiable testing of the study’s complex adaptive learning system hypothesis while validating extrapolation from model system data to real world data. Building upon my findings, I then evaluated the possible effects of conscious observation upon the subsequent evolution of the world system.

The model system consists of ten mutually interacting actor-elements which represent the nation-state constituents of the world political system. This number of actors is sufficient to permit the hypothesized systemic learning processes to be detected, if existent, while still remaining a small enough value to allow for maximal analytical clarity.
In conceptualizing the structure of the world system I envisioned that its several levels of analysis (i.e. individual/decision-maker, nation-state, systemic) were, although analytically distinguishable, integrated together into a coherent whole. Pursuant to this, I incorporate two fundamental individual level cognitive precepts into the computer model: 1) Awareness is limited. It is a zero-sum variable (Simon, 1985, 302, Simon & Kaplan, 1991, 9). 2) Cognitive change occurs discretely. This assumption follows logically from the realization that awareness is limited. Given this attentional constraint, information is stored associatively, probably in a schematic arrangement (Schater, 1991, 692). This allows for rapid associative retrieval of stored information. The human brain is limited to performing no more than about 100 associational steps per second (Rumelhart, 1991, 135). Aggregate schemas for any given subject comprise ‘memes.’ This form of information storage allows for rapid information retrieval, and utilization, within the limited attention, ‘100 step’ constraints imposed by the brain’s architecture. Decisional outputs of state level actors are assumed to conform to these individual level cognitive constraints due to the concentration of inter-state decisional power among relatively few leaders.
Possession of a common meta-meme among individual level actors within a nation-state is represented in the context of the model as comprising that actor’s culture. Culture thus acts as a constraint upon state behavior towards other states. In particular it determines a state’s propensity for reciprocal behavior. Reciprocity is the model’s indicator for democracy. Given the theoretical (Doyle, 1983, 1986) as well as empirical (Levy, 1983) observation that democracies do not wage war upon one another, level of democratization, is hypothesized to be a key variable defining nation-state behavior.
My computer model of crisis-driven learning is predicated upon the hypothesis that systemic level learning occurs principally in response to crisis. Crisis, in this context, is defined as any situation in which the application of previously encoded knowledge fails to resolve some situation in a manner in which harm, or the potential for harm, is averted. Because culture represents a common meta-meme between citizens of a given nation-state, it follows that any change in its configuration is likely to be resisted as it will entail significant changes among a given cultural meme’s associative linkages. Thus, it follows that cultural change will likely occur discontinuously, by discrete increments, which represent replacement of entire memes within the greater cultural meta-meme. This change will most likely occur when ‘forced’, that is, in a crisis situation.

Models can be either ‘top-down’ or ‘bottom-up.’ That is, the model’s global properties can be pre-defined algorithmically, or they can arise from unpredictable interactions between actors executing instructions locally. I have chosen a mixed approach in which certain global properties of the model are algorithmically pre-specified, while local interactions among the system’s actors determine its evolution. Thus, one interesting feature of this model is its interplay between deterministic, top-down, global rules, and non-predictable, bottom-up, actor interaction effects. This effect is consciously designed to mirror the interplay of deterministic and non-deterministic phenomena which underlay actual reality.
The model consists of four global, top-down, difference-equation-driven variables along with another variable which sets an upper limit upon one of these variables. These variables are modified in value via local, bottom-up, interactions among system actors, by operation of a WAR subroutine, and a CRISIS procedure. Figure 1, below presents this model schematically.

*EDITORS NOTE: PLACE FIGURE 1 ABOUT HERE. PLACE CAPTION BENEATH IT.*

*EDITORS NOTE: CAPTION FOR FIGURE 1 APPEARS BELOW*

Figure 1

Information Flows Between Model Variables and Procedures. Note: The ECON module is utilized only in the later version of the model discussed below, and then only for the “economically enabled model system” runs.

The four algorithmically defined variables are: 1) Relation 2) Reciprocity 3) Power and, 4) Coupling. Each is difference equation defined. As such each imparts global, top-down’ properties upon the model international system.

Relation.

Relation, R: This variable has a range of between +1.0 and -1.0, for each of nation i’s relations with other actors comprising the model international system. Equation 1 below defines this variable in the context of the model for any two system actors i and j.

Equation 1 Equation for Relation, “R”.

R^ij_{(t + 1)} = R^ij_(t) + b;

where b = ((.25 * (Rcⁱ * Rc^j)/2)) * (R^ij_(t) - (R^i+j))

(N-1))

The “b” term is subtractive as the model assumes that state actors possess limited quantities of attentional capacity. It incorporates the assumption that change occurs gradually under non-crisis circumstances. By including reciprocity, it assumes that more reciprocal states possess greater adaptability.

Reciprocity.
Reciprocity, Rc: This variable represents level of democratization, as articulated above. It is defined by equation 2 below:

Equation 2a) Equation for Reciprocity, “Rc” for “i” and “j”.

Rc_{(t + 1)}ⁱ = 2 * ( å ⁺Rⁱ_(t) )

å½Rⁱ_(t) ½)

Equation 2b) Equation for Reciprocity, “Rc” for “i” and “j”.

Between any two states i and j:

Rc^ij = Rcⁱ * Rc^j.

This equation assumes that positive values of relation contribute to increasing power, for a given nation “i”, with respect to negative relational values.

Power.
Power, P: This variable represents total power which a given state, “i”, possesses at any time t. Equation 3, below defines this variable:

Equation 3a) Equation for Power, “P”.

P^i’_{(t + 1)} = Pⁱ_(t) + a,

where a = ½{(å⁺Rⁱ_(t))}½ + ½[.01 * {(å ⁺R_(t))}]½

½{(å Rⁱ_(t))} ½ ½ {(å R_(t))} ½

Equation 3b) Equation for Renormalization of Power, “P”.

Pⁱ_{(t + 1)} = P^i’_{(t + 1)}

P _{(t + 1)}

The power equation assumes that propensity towards reciprocal behavior is conducive to increasing power.

Culture.

Culture is represented by a variable, “K”. K has a potential range of 0.00 to 1.00. Initial values of K are arbitrarily assigned. (Five nations are placed into a “high bound” culture with values of .75, while the remaining five are assigned to a “low bound” culture with K values of .25) Subsequently, these values may be modified by application of the CRISIS procedure, as detailed below. K simply sets an upper limit for the potential range of state i’s Rc values. Rc values are free to vary within the upper bound set by this limit. K varies by discrete increments of .05 because cognitive, or behavioral, change is assumed to occur discretely. Coupling.
Finally, the model incorporates a coupling parameter, CF. CF provides a measure of how closely coupled any two nations i and j are at any time t. In effect, it determines the extent to which any nation i may interact with, and thus algorithmically influence, the behavior of a given other nation, j. Evaluated for the system as a whole (by computing its mean value) it provides a measure of the degree of “openness” of the system. Equation 4 assumes that perfect coupling can be closely approached, but never actually reached.
CF is calculated in one of three ways. These are given below in equation 4:

Equation 4a) Equation (a) for Coupling Parameter “CF”.

If Rcⁱ < MRc: CFⁱ = MRc - ((Rcⁱ - MRc)/2)

Equation 4b) Equation (b) for Coupling Parameter “CF”.

If Rcⁱ > MRc: CFⁱ = MRc + ((Rcⁱ - MRc)/2)

Equation 4c) Equation (c) for Coupling Parameter “CF”.

If Rcⁱ = MRc: CFⁱ = MRc Where MRc = Rc^total /( N-1)

WAR Subroutine.

The model’s WAR subroutine is triggered when the following criteria are met: IF Rc^ij_(t) * ((CFⁱ + CF^j) / 2) £ .25 AND R^ij_(t) £ 0 THEN GOSUB WAR.

Each of the ten model system nations compares itself with each of the other nine, sequentially to determine whether the WAR criteria are met. Thus wars occur dyadically in the model.

When the model’s WAR subroutine is triggered, the power renormalization process is reversed, or ‘denormalized’, for each of the participating nations. This means that if two nations i and j trigger the WAR subroutine, their total, raw, power is calculated. This allows for the effects of increasing power upon warfare to be modeled.

ECON Subroutine.

Like the WAR subroutine, the ECON subroutine checks sequentially for the presence of dyads which meet the ECON selection criteria. The models ECON subroutine is triggered when the following conditions are met:

IF Rc^ij_(t) * ((CFⁱ + CF^j) / 2) £ .35 THEN GOSUB ECON.

Economic interactions are enabled only beginning at moderately high values of Rc because the model assumes that systemically meaningful levels of trade require the absence of outright systemic anarchy to take hold and flourish. As the system becomes more reciprocal, conditions for trade improve. The model does allow for asymmetric trading gains when power is highly unequal and reciprocity is relatively low between members of a given dyad. However under high reciprocity conditions, it is possible for “smaller” (less powerful) nations to actually benefit disproportionately from a given trade interaction. Unlike the WAR subroutine, nations which attempt and fail to establish a trade agreement, BOTH undergo the CRISIS procedure. The reasoning behind this is that both are aware of having forfeited potential gains. This allows crisis‑driven learning to continue even at levels of reciprocity to great to permit war. However, such occurrences (trade failures) are substantially less frequent than war, ceteris paribus.

Crisis Procedure.
Nations which lose at WAR, or fail at trade, (ECON module) experience two outcomes, the first, a reduction in their power, was mentioned above. The second is that they undergo the CRISIS procedure. Here, their K values are randomly raised, or lowered, by an increment of .05. The probabilities for each outcome are equal. This discrete value is selected in conformity with the models assumption that cultural change occurs adaptively, by discrete intervals, corresponding to memetic replacement, in response to crisis.
In essence, via operation of the model’s WAR subroutine, and its CRISIS procedure, each nation compares itself dyadically, with all other nations. This comparison determines whether the two nations will engage in war, and if so, which one will initiate it. The effects of this process include substantial adjustments in power and, for losers at war, culture, and hence reciprocity. It is this local, interactive process, which allow for the system’s adaptive learning behavior to emerge locally within the context of its difference equation specified global structure. Analysis.
The model system program was run 200 times to produce a sufficient N of cases for analysis of key analytical parameters. Figure 2, below displays this information.

*EDITORS NOTE: PLACE FIGURE 2 ABOUT HERE. PLACE CAPTION BENEATH IT.*

*EDITORS NOTE: CAPTION FOR FIGURE 2 APPEARS BELOW*

Figure 2

Number of Program Iterations Required for Attainment of Systemic No‑War Equilibrium.

Figure 2 represents the distribution of learning times required for a model system to find a no-war equilibrium solution. At this point two additional systemic variables need to be introduced: The first of these is termed “C”. C varies uniquely for each system. It has a maximum value of approximately 1.0, and a minimum value of 0.0. It provides an indicator of the model system’s trajectory within the learning space matrix. The second is designated as “PI.” PI represents the value of the ratio of instant systemic power to initial systemic power. It provides an indicator of the model system’s depth within the learning space matrix.
Given an initial mean Rc value of .5, and a mean systemic no-war threshold Rc value of .775, as determined by observation during the 200 model runs, each nation must learn through, on average, 6 .05 K increments to reach the no‑war threshold. As the probability of a positive increment learning result is equal to the corresponding probability of a negative increment learning outcome, this yields a mean of 12 .05 Rc increments. As there are 10 nations involved, each of which may influence the Rc values of the others, the total mean volume of learning space must comprise 12¹⁰ discreet K points, assuming normal distribution. Each of these points is located .05 K from all other points. These points are configured as a 10‑dimensional array. Each time the program is initiated a unique model system is created de novo and positioned in an arbitrary location in this space, consistent with a moderately low initial level of learning.
Direction in the learning space matrix is provided by recalling that each of the 10 dimensions is, in actuality, a range of discrete values. Motion along this range towards a no-war equilibrium solution (that is towards an attractor which represents a discrete solution to the problem of attaining this condition) corresponds to motion along the C‑axis towards its end-point, 0. Thus, lower C values, and correspondingly, higher amounts of learning, (a closer approach to a no-war equilibrium problem attractor solution) equate to motion “deeper” into the learning array.
This visualization also allows for the geometry of the learning array to be comprehended: As the end-point, or vertex, for C is common to all 10 nations, and C contours the learning space of these nations, then C’s common vertex is the common vertex of learning space. All 10 dimensions therefore posses a common vertex. At this unique point, and only at this point, they coincide. As I visualize it, the learning space manifold, when mapped to conventional 3‑D space, looks something like an inverted 10-sided step polygon, which steps ‘downwards’ towards this singularity in increments of .05 K. These 10 sides, or dimensions, correspond to the 10 nations which comprise the model system. Topographically, the model’s learning space, which lies within the interior volume of this 10‑sided inverted step polygon, is contorted away from exactly resembling a rectilinear grid by the presence of attractors, which represent unique solutions to a system’s no-war equilibrium search. PI may be visualized as providing a measure of the ‘steepness’ of a system’s trajectory through this learning space, measured with respect to its vertex.

Findings.
How do the model generated data compare with those of the real world system with respect to this SPI? Levy’s real world findings may be succinctly summarized by his observation that:

The results are not perfectly congruent across all of these indicators, but some overall patterns emerge. In general, interstate war involving the Great-powers has been diminishing over time. There has been a strong decline in the frequency of war, particularly in the frequency of Great-power war. (Levy, 1983, 135).

Thus, the real world system appears to be learning how to deal with the crisis, caused by warfare, in the context of rapidly increasing systemic power, which threatens its continued existence, by increasingly seeking out non-warfare solutions to inter-state conflicts. In effect, it appears to evince a trajectory through its learning space manifold towards a no-war equilibrium attractor, driven by selection pressure arising from this endogenously generated crisis.
Overall, Levy’s war frequencies data were found to correlate very closely with equivalent model system generated data. Figures 3 and 4, below, illustrate this correspondence. Figure 3 depicts Levy’s data for all great-power wars, measured at 20 year increments. Figure 4 represents data generated by one of the model system runs, (termed “model system 1”) for all wars, per program iteration.

*EDITORS NOTE: PLACE FIGURE 3 ABOUT HERE. PLACE CAPTION BENEATH IT.*

*EDITORS NOTE: CAPTION FOR FIGURE 3 APPEARS BELOW*

Figure 3.

Real World: Aggregate Warfare at 20 Year Resolution.

Note for internet version: Click on each of the figures (figures 4 – 12) presented below to view them.

Figure 4.

Model System 1: All Wars.

Figure 5.

Model System 1: C.

Model system 1 evinced fairly typical systemic parameters. It reached its no-war equilibrium after 116 cycles. This is less than 1 standard deviation from the mean value calculated above in figure 2. Model system 1 has a PI of 1,260. A glance at figure 5 which graphs C, depicts model system 1’s trajectory through learning space. At cycle 13, the system ‘identifies’ a deep attractor, representing a stable solution to its war-end boundary conditions. Its subsequent trajectory is towards this attractor. Other, less deep attractors are also encountered en route to this deep attractor‑solution at cycle 31, cycle 43, cycle 62, and cycle 65.
The topology of model system 1’s learning space matrix is better evinced by figure 6. Figure 7 clearly portrays its trajectory. One caveat is that as the learning space matrix decreases in area towards 0 in increments of .05, while the diagrams portray it as possessing equal area for all values of C, deeper attractors are depicted multiply. Thus in figure 7 what appears to be two deep attractors are in actuality, a single point attractor.

Figure 6

Topology of Model System 1.

Figure 7

Trajectory of Model System 1 in Learning Space.

Extrapolation from figures 5, 6, and 7, above, to the real world system, implies that we are presently “locked on” to and approaching, although along a non‑deterministic trajectory, a corresponding point attractor somewhere in our own endogenously generated learning space. The deep issue is whether, or not, the length of our future systemic trajectory is sufficiently short as to allow us to arrive at our no-war equilibrium attractor‑solution prior to the crash of our world system. More specifically, the issue is what effect(s), if any, our apprehension of our position, and movement through the topography of learning space, can have on this process.

It is important to note that since the world system’s topology is endogenously generated, it follows that any substantive restructuring of that system will likely cause a concomitant shift in its learning space topology. Thus, if for some reason, perhaps a life-or-death systemic crisis, a global process of memetic replacement, leading to a fundamental replacement of one global meta-meme by another were to occur, then, the world system would, necessarily, find itself following some other trajectory, through a learning space imbued with some other metric. Presumably it would be seeking some other deep attractor‑solution.

It follows from this that conscious intervention into the learning process of the system, arising from research into this process, does possess the potential to substantially affect the trajectory of the world system. If this intervention is accepted by political decision‑makers, then this potential can be actualized.

Given that the effects of fundamental systemic change upon the system’s learning space matrix topology are unknowable, with respect to its resultant, changed, configuration, in advance, due to the stochastic nature of the systems bottom‑up interactions discussed above, it follows that such intervention would only be reasonable if it could be shown to be beneficial in all, or nearly all, possible cases. Is this possible?

Section II: Extension of the Model

To answer this question, I next set out to evaluate the possible effects of economic interactions, that is of trade, upon the development of my model world systems. This entailed the addition of a trade subroutine to the model’s underlying BASIC program. As discussed in greater detail above, this subroutine operates very similarly to that of the WAR subroutine. Recall that the principle differences are that it is triggered by a higher threshold value (Rc^ij * ((CFⁱ + CF^j) / 2) £ .35 as opposed to the WAR subroutines threshold criteria of (Rc^ij * ((CFⁱ + CF^j) / 2) £ .25). Also, if failure to reach a trade agreement occurs BOTH actors undergo the CRISIS procedure, as opposed to only the loser doing so in the in WAR subroutine.

My reasoning is that if crisis is modeled to be the primary driver of systemic learning, then any class of conditions, the failure of which would likely be perceived by system actors as creating harm to their well-being, ought to be a generator of crisis. As trade is unlikely to flourish in a war-prone, anarchic systemic environment, I have a-priori set a higher triggering threshold level for it than I have for inter-state war.

The effects of this change are hypothesized to be an increase in the overall rate of learning for the model system. My assumption is that such an increase is desirable. As I envision it such a process is equivalent, in the simplified context of my model, to Ernst Hass’ (1990) concept of epistemic communities.

What are the consequences of my economic assumptions upon systemic evolution, evaluated with respect to a “standard” power-dominated model system (e.g. Gilpin, 1981) which does not incorporate these economic effects? What is the relationship between international trade and international warfare, in the context of the model? Does this difference, if existent, provide an answer to the question of the desirability of consciously altering the trajectory of the world system?

To find out, I ran each type of model system 80 times so as to establish a sufficiently large N for meaningful determination of mean values of systemic variables. To determine the potential effects upon war-instigated systemic collapse, I also incorporated a ‘collapse module’ into the program. Basically, for each iteration of system time, there is a very small possibility of collapse. This possibility increases as net systemic power increases. As the collapse probabilities are identical for each type of model system they provide a standard metric against which the performance of the two types of systems can be evaluated. Due to the continuing presence of small, but persistent differences in these two resultant values, I used a higher N of 240 to allow for statistically significant comparison of these apparent differences, as we shall see below.

These two later variants of my basic model, being developed following much testing and analysis of the initial model incorporate several refinements over it. Principally these are: 1) A systemic collapse module is added. This provides a small probability of collapse for any war prone model system. This probability increases as systemic power increases. 2) The initial model’s power difference equation utilized a fixed value (.01) in determining the quantity of power by which the following program cycle of the model would be incremented. This represents an unrealistic simplification. The later version permits the model system to self‑regulate this value utilizing an incremental value derived algorithmically from the mean systemic value of Rc for that program iteration . Thus, the below values cannot be directly compared to those obtained above. The above analysis represents proof of concept, while the below findings build upon their foundation.

Table 1

Economic Interaction Enabled Model System Runs.

Variable N Missing Mean Std. Deviation*

Cycles 80 0 60.400 34.230

PI 80 0 103400.238 449154.836

C 80 0 0.244 0.130

MeanCF 80 0 0.871 0.353

MeanRc 80 0 0.826 0.330

Collapse 240 0 0.287 0.454

Table 2

Power-Dominated Model System Runs.

Variable N Missing Mean Std. Deviation*

Cycles 80 0 93.412 49.863

PI 80 0 90449.663 433517.532

C 80 0 0.237 0.109

MeanCF 80 0 0.813 0.249

MeanRc 80 0 0.771