The Globalization of the World Systems

with Sequences of their Power Structures

David Wilkinson

Department of Political Science, UCLA

Los Angeles, CA 90024-1472

Presentation to a

Specialist Workshop on


Globalization in the World-System:

Mapping Change over Time


Institute for Research on World-Systems

University of California, Riverside

February 7-8, 2004


     My responsibility for this workshop is to prepare a short

paper on a substantive topic that invites (a) visualization by

technical methods of mapping temporal evolution, and/or (b) time-

series analysis.


     I propose to do this by showing the group some data which I

have collected, presented and analyzed in fairly straightforward

ways, but which seem to me to beg for more sophisticated methods

than I am ready, willing and able to apply, since my commitments

for the near future lie more in the making of new data than in the

exploitation of what has already been collected.


     I have for some years been working on developing data and, to

a much lesser extent, testing theory concerning the political

structures, the power configurations, of civilizations or "world

systems," exploring typologies for such structures, locating the

sequences of such configurations over very long durations,

developing and testing hypotheses about the expected succession of

such sequences.


     I have elected two topics for this workshop: the globalization

of the world systems, and the sequences of their power structures.

Both topics have associated datasets.  The data on first topic--the

spatial and temporal paths which the several autonomous

civilizations or world systems of the past took as they grew,

collided, and fused to become the single world system of today's

global civilization--seems to me to demand better visualization

immediately, but then will need considerably more data before it

invites technical analysis. 


     The data on the second topic--the sequences of power

configurations within the several world systems of the distant

past, and within the single world system of the present and the

recent past--seem to me, on the contrary, to beg technical

analysis, though they too might be usefully re-visualized.


     At this point let me draw your attention to Figure 1.


Figure 1, "The Incorporation of Twelve Civilizations into One"

     Figure 1 dates from 1984 and the era of the typewriter; it is

a software-free time chart which begins at the top of the page.  As

one goes down the page and forward in time, civilizations or world

systems come into existence at various moments in time and points

in space, coexist for some duration, then merge into larger


     While this figure shows with reasonable clarity what is meant

by the merging of many systems into one, it has certain

deficiencies which a superior graphing software could perhaps


     (1)  All column sizes are the same, in some sense suggesting

equal sizes for all systems at all times except the merged Central

system.  This is of course not the case, whether we speak of size

in terms of area, of population, or of city numbers.  This

deficiency can be obviated when and if the changing sizes of

civilizations could be easily graphed by software which would input

a number and turn it into a columnar width. 

     The input might be, e.g., the number of large cities, or the

civilizational area in square miles, or a population estimate for

the whole civilization--more likely logarithmic magnitudes for both

the latter, to hedge against pseudoprecision, or city numbers).

     Preliminary data for such input exist, or could perhaps be

derived via GIS.  A representation of such extant data will be

found in Figure 2, which locates, names and assigns to their

respective civilizations or world systems 75 cities of the year AD





Figure 2, "The Old Oikumene and its Civilizations in A.D. 1500"



     (2)  The columns of Figure 1 are immediately adjacent to one

another, suggesting that systems were so adjacent and in touch

throughout their durations.  This is not the case: the

civilizations grew in space, threw out penumbras of trade nets, and

were increasingly interrelated until they merged.  If some measure

of separation or interrelationship (as for instance distance

between semiperipheral cities, or number of goods-types known to be

traded at a given moment) could be incorporated into a graphic, we

could see these entities approach one another over the interval

before they merged.


     (3)  The chart is two-dimensional, and since time is included

the north-south spatial dimension is simply ignored, and systems

arranged on an east-west dimension, placing say Ireland and Mali as

neighbors.  If time is to be retained, and a north-south separation

included, the graphic will have either to be a hologram or a fairly

sophisticated two-dimensional representation.


     This is the problem, for me, of the visualization of

globalization.  I have looked for software which might solve at

least the first two problems, in what seemed to me the logical

place, namely software for mapping or diagramming river systems,

since river basins commonly show streams of different width and

changing separation merging in space, which is at least analogous

to world systems merging over time.  But I have found no simple

application that does what I think needs doing, and while there may

be complex software that could be put to service, it seems wasteful

to learn to pilot a 747 just to make the trip to the corner 7-11.


     So here's my first challenge to the technical side: can you

find or fabricate graphic software that will allow a superior

diagramming of the growth and merger of world systems, by taking

numerical input representing the sizes of such systems, and the

separations of pairs of such systems at given moments, and

interpolating values between the moments?  Maybe yes, maybe no; it

would be good to know either way.


     My second problem has to do with the representation and

analysis of the power configurations or political structures of

world systems at different moments in their careers.  For a

preliminary look at what I mean, please examine Figure 3, again

from the typewriter era.






     Figure 3 overlays Figure 1 with shadings.  The shaded and

unshaded areas represent values of a nominal variable treated here

as dichotomous, two possible political conditions for a world

system: centralization vs. decentralization; universal empire vs.

systems of independent states.  The variable is an important one

theoretically, concerning which there have existed various

hypotheses, usually expecting increasing centralization over time,

hence a preponderance of circle-shadings toward the top and of

unshaded areas toward the bottom.  This graphic is useful for

showing that this is not at all the case, and that the problem is

more complex.


     Since producing Figure 3, I have been attempting to deal with

the obvious concern that a dichotomous variable--Empire vs. States

System--underrepresents intriguing complexities of power structure.

For the next step in data collection I elected to try a

heptachotomy, a seven-valued nominal power configuration variable,

which included configurations long of interest to political

scientists and world-systems analysts: in addition to empire, I

look for a weaker form of domination, namely hegemony; and among

states-systems, I varied the number of great powers, distinguishing

unipolarity (with one superpower, as in the world today) from

bipolarity (as during the Cold War) from tripolarity (with three

great powers), multipolarity (more than three great powers, as in

the world system during say 1815-1945), and nonpolarity (no great

powers but many small independent states).


     Surveying the world systems on this much more complex variable

is taking a long time, and I'm far from finishing even a first cut,

but I have some results.  I provide a sample of these results as

Figures 4-7.






     As will be obvious, there is some orderliness here, yet no

supreme pattern leaps out at you.  So what will be needed is an

analysis that tests one hypothesis after another, and builds new

ones partly upon the ways and directions in which rejected

hypotheses fail, as demonstrated for instance in L.F. Richardson's

analysis of the complexity of wars.


     Let me state some of the simpler hypotheses which float about

the environment, sometimes compatibly with, sometimes contradicting

one another.


     (1)  Systems increase in centralization as they age.

     (2)  Systems tend to increase in centralization over time, but

there are strong short-duration fluctuations enroute.


     The data graphed in Figures 4-7 are not at all consistent with

either (1) or (2), which reflect the civilizational ideas of

Spengler, Toynbee (original) and Melko.


     (3)  Multipolarity is the norm.

     (4)  Multipolarity is the stablest configuration.


     The notion that multipolarity is the stable norm is

represented in an idealized way in Figure 8.  Although

multipolarism is widely approved by contemporary politicians, it is

fairly consistent with only one graph (Figure 5, SW Asia), and even

there there are long failure epochs.




        Figure 8, "Multipolar Stability"


     (5)  Empire is the stablest configuration.


     No doubt approved by Sons of Heaven, Caesars and Pharaohs, and

certainly by Dante Alighieri, what we might call ultra-imperialism

is reasonably consistent with one graph (Figure 4, Northeast

Africa), but not the rest.


     (6)  Bipolarity is more stable than multipolarity.


     Particularly identified with Kenneth Waltz, this hypothesis is

inconsistent with one graph (Figure 6, Far East), not inconsistent

with two graphs (Figures 5, SW Asia, and 7, Indic), and probably

not adequately tested in the fourth (Figure 4, Northeast Africa).


     (7)  Systems begin maximally decentralized, then endure long

cycles of increasing and decreasing centralization.


     This, the weakest hypothesis of the set, identifiable with the

late work of Toynbee (Reconsiderations), seems broadly consistent

with all but one graph (Figure 4, Northeast African); still, one

would like to know more.


     Based on visual inspection of the data, I have elaborated a

few more that seem worth a try, and will require more careful

testing than the simple, straightforward optical analysis just

employed.  Two are derivable from ancient and early modern physics,

as well as from bureaucratic experience.


     (8)  Systems are Newtonian-physical, or conservative, and will

most likely be found at any time in the same configuration they

showed at the time of last measurement.


     (9)  Systems are Aristotelian-physical, or reactionary, and

will most likely be found at any time in the configuration they

have occupied for most of their duration.


     Another hypothesis might emerge from common network

analysis. Two network types seem to have parallels in the power

configurations.  "Random" networks, with nodes linked at random,

lack such a parallel.  "Regular" networks, with neighbors highly

interconnected, best approximate the Nonpolar configuration.

"Scale-free" networks, with a small number of highly connected

nodes and a large number of weakly connected nodes, are represented

by the other six configurations, with Empire having the smallest

number of highly connected nodes, Multipolarity the largest.


     (10) A relevant hypothesis might then be: the bigger they are,

the harder they fall.  A chance of large cascading failures seems

inherent in highly interconnected systems when they are stressed:

perhaps then transitions out of the Empire configuration will tend

toward greater decentralization than those out of the less-

connected Hegemony and Unipolarity configurations.


     At this point I will stop posing hypotheses and start asking

questions, to which I hope somebody in the audience will have

answers that may either propose additional hypotheses or means of



     (11) To what extent do these world systems behave according to

Zipf's Law?  If for each of them we calculate the frequency of

occurrence of each of the seven configurations, then

logarithmically plot the frequencies in descending order, to the

degree that the slope of the plot approximates -1 (vs. 0), the

curve may be a "signal" containing information and implying

complexity of the underlying system.  (A 0 slope would be noise, a

signal with no information, attributable to chance.)  Zipfian

behavior would to some extent seem consistent with

"traditionalism," in that the more often a behavior (configuration)

was displayed in the past, the more often it would be predicted to

occur.  But is there more to it than that?


     (12) Discussion of Zipfian patterns leads to introducing the--

at least to me--difficult notion of Shannon entropy.  Verbal

descriptions of Shannon entropy, with whose mathematics I am

unfamiliar, inform me that zero-order Shannon entropy measures the

diversity of a repertoire: in this case, a world system's

repertoire would be the number of configurations which are actually

displayed by that world system over time.  For instance, the

repertoire of Northeast Africa excluded nonpolarity, as did that of

Southwest asia, which also omitted tripolarity, while all seven

configurations appear in the Far eastern and Indic timelines.


     First-order Shannon entropy measures the frequency or

probability of occurrence of each element in the repertoire.

Second-order entropy is a conditional probability: knowing an item

in a sequence of configurations, what are the chances of predicting

the next item?  The third-order entropy value is the probability of

predicting the third configuration in a sequence, given the first

two.  Higher entropy values at given orders, and non-zero high-

order Shannon entropies, imply a higher degree of predictability,

regularity and form in the whole system.


     It might be of interest to calculate the Shannon entropies of

the various world systems, and to attempt to interpret them.


     (13) It would appear by inspection that the volatility

(variance) of power configurations changes over time--compare the

first and second halves of the Figure 4 timeline--and perhaps

therefore also their Zipfianness and Shannon entropy do so as well.

Do any particular configurations or sequences predict higher or

lower volatility?  But what is an appropriate measure of volatility

in a nominal variable?


     Hypotheses 8-10, and topics 11-13, I don't feel prepared to

undertake alone; I have more pressing business in the datamaking

area.  Like the task of improving the graphics of Figures 1 and 3,

they need more sophisticated tools than I currently possess, which

leads me to a search for someone better able than I to deploy same.

So my objective at this meeting is to find a collaborator or two

who is equipped to rapidly process these data, and other data in

the making now, exploring for Zipfianness, Shannon entropy,

volatility variation etc., and jointly analyze the findings, and/or

to provide superior and more suggestive graphic displays for

existins data.



                      POWER CONFIGURATIONS