The Globalization of the World Systems
with Sequences of their Power Structures
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-
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
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
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
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
(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
PHASE I: TWO CONFIGURATIONS
PHASE II: SEVEN CONFIGURATIONS