Transcript ISA Conference, Historical Long Run Session

Discovery of oscillatory dynamics
of city-size distributions in world
historical systems
Douglas R. White, Nataša Kejžar, Laurent Tambayong
UC Irvine
University of Ljubljana
UC Irvine
Calouste Gulbenkian Foundation Seminar at IIASA on “Globalization as Evolutionary
Process: Modeling, Simulating, and Forecasting Global Change”
April 2006
Powerpoint at
http://eclectic.ss.uci.edu/~drwhite/Conferences.html
Paper at
http://
Figure 1: Spatiotemporal PMN classification of
Political/Military Networks & mergers (Wilkinson)
All the measures of city size oscillations correlate
to form a 3:1 single factor structure.
Table 1: Single Factor Variance (PCA) for
City-size Distributional Scaling
2.29:1 factor ratio
Component 1
C1987_2
.840
ChinaPlus50
.561
C1974
.797
SPI_centralPMN
.794
Variance
2nd Eigenvalue
3.07:1 factor ratio
Component 1
C1987_2
.922
C1987_1
.866
C1974
.713
SPI_centralPMN
.734
ChinaPlus50
.653
57.2% Variance
nd
.825 2 Eigenvalue
3.76:1 factor ratio
Component 1
c1987_2
.945
c1987_1
.943
C1974
.897
SPI_centralPMN
.773
SPIplus50
.762
61.4% Variance
nd
.802 2 Eigenvalue
75.1%
.623
The 1974
Candler and
Fox data
were greatly
improved by
Chandler
1984, but the
q-results are
very similar,
as reported
for the 1factor test.
EAST-WEST SYNCHRONIES
IN TRADE AND
CITY
SIZE DISTRIBUTIONS:
Zipfian
Flattened
Q-2 (trade synchrony)
Q-1 (trade synchrony)
Q0 ‘’ & city synchrony
Q1 ‘’ & city synchrony
Q2 ‘’ & city synchrony
Q3 ‘’ ‘’ ‘’ ‘’ ‘’
Q4 ‘’ ‘’ ‘’ ‘’ ‘’
Q5 (loss of synchrony)
Q6
c1987_1
Coefficient
1.0
Upper Confidence
Limit
Lower Confidence
Limit
ACF
0.5
Autocorrelation
tests are
positive
0.0
-0.5
-1.0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16
Lag Number
SPI_central with c1987_1
Coefficient
1.0
Upper Confidence
Limit
Lower Confidence
Limit
CCF
0.5
Cross-index
Autocorrelation
tests are
positive
0.0
-0.5
-1.0
-7
-6
-5
-4
-3
-2
-1
0
1
2
Lag Number
3
4
5
6
7
Silk road multiconnectivities in the more global trading periods synchronize regions,
and when these are interrupted the respective trading networks break apart
We do Q-scaling from Chandler’s 1987 data by creating city-size bins as powers of
1.26 times the lowest bin size (e.g., 40,000 people), then constructing a
cumulative population distribution in cities at least as large as the bin size.
Table 4: Six largest Chinese cities in medieval and recent periods (as per Fig. 5)
SPI=Standardized Primacy Index for cities
The SPI index
is computed as
0 or more
negative
deviation from
a Zipfian for
the top five
cities, e.g., as
here for China.
Q-scaling uses
all the city
sizes and
weights the
lower bins
more highly.
Alpha (α) is the
slope of the
large-city tail
entailed by Q.
Date
1100
1100
1100
1100
1100
1100
1100
Date
1950
1950
1950
1950
1950
1950
1950
Top Cites
Kaifeng*
Hangchow
Soochow
Tsinchow
Ninghsin
Nanking
Wuchang
* Primate
city
Size in
1000s
442
90
88
85
80
67
61
no power
law fit α
Size in
Top Cites*
1000s
Shanghai
5406
Peking
2031
Tientsin
1795
Canton
1495
Wuhan
1150
Chungking
1055
Nanking
1020
*Zipfian
α=.82
Annual
growth
1.000998
1.001178
1.001206
1.000000
date
1150
1150
1150
1150
1150
0.999562 1150
0.999365 1150
SPI=1.67
Annual
growth
1.043343
1.018907
1.032326
1.025111
date
1970
1970
1970
1970
1970
1.022045 1970
1.037947 1970
SPI~0.87
Size
in
1000s
150
145
130
100
90
80
72
Annual
growth
0.978387
1.009538
1.013257
1.013863
Top Cites*
Kaifeng
Hangchow
Nanking
Peking
Ninghsia
Canton
1.007494
Soochow
0.995987
*subZipfian
α=.40 SPI=-3.89
(flat)
Size
Annual
in
Top Cites* 1000s
growth
Shanghai
7900
1.018968
Peking
4800
1.043004
Tientsin
3800
1.037500
Wuhan
2560
1.040012
Chungking
2300
1.021539
Canton
2300
1.038968
Nanking
2000
1.033667
*Zipfian
α=.73 SPI~0.67
Fitting the q-exponential to get the best predictors of actual distributions (q > 1)
y(s) = y(0) eq−s/κ = y(0) [1 − (1 − q)s/κ] 1/(1−q)
(e1x = ex)
(4)
Body
and
y(s)
tail of the distributions
s
China
World
The anomaly of the distribution shape parameter q varying
inversely to the scaling parameter kappa (κ), when detrended.
This helps to identify breaks in the historical dating but may
explain why low-q for the body of the distribution (which
should imply Zipfian tails) in fact varies inversly with the
direct SPI measure of the Zipfian 5-city upper tail.
Early
World Cities
Late
Lo-q
World Cities
Hi-q
q =
Qcdf
1.95
1.90
1.85
1.80
1.75
1.70
1.65
1.60
1.55
1.50
1.45
1.40
1.35
1.30
1.25
1.20
1.15
1.10
1.05
Qpdf =
1/(2-Qcdf)
β=1+
1/(Qpdf-1)
20.00
10.00
6.67
5.00
4.00
3.33
2.86
2.50
2.22
2.00
1.82
1.67
1.54
1.43
1.33
1.25
1.18
1.11
1.05
1.05
1.11
1.18
1.25
1.33
1.43
1.54
1.67
1.82
2.00
2.22
2.50
2.86
3.33
4.00
5.00
6.67
10.00
20.00
α for small
tail sizes
mixed
distribution?
0.05
0.11
0.18
0.25
0.33
0.43
0.54
0.67
0.82
1 .0 0
1.22
1.50
exp
exp
exp
exp
exp
exp
exp
flat t er exp?
exp
exp
exp
exp
exp
exp
exp
exp
exp
exp
exp
exp
exp
exp
exp
exp
exp
exp
exp
Exp + power law
Full exponent ial
Table 5: Conversion from q to the power law α or exponential
The remaining slides:
• Deal with how Q periods cross-correlate with
– Secular cycles (1/2 cycle)
– Political cycles(1/2 cycle)
– Economic innovation cycles (1/2 cycle) –K-waves
• Deal with how and why these cross-correlated
cycles embed as nested half cycles
– Secular in Q
– Political in Secular
– Economic innovation in Political
Table 6: European Secular Cycles according to Turchin and Nefedov (2006) and
Cross-Correlation of Trade Network Cycles and Secular Cycles, 600 BCE-900 CE
Q-period
From
about
Secular cycle
Cohesion and Crisis
Trade Network
N2
700BCE
Expanding - More Global
market economy ca.700
Axial Age
600BCE-375BCE
Trade Network
N3
375BCE
Contracting - Regional
– <145BCE
“Implanting”
Second Roman Cycle
Trade Network
N4
<145
27 BCE
Expanding - More Global
Trade Network
N5
Trade Network
N6
“Outgoing”
600BCE First Roman Cycle
285
“Outgoing”
Principate Cycle
<<285
Contracting - Regional
285
“Reimplanting”
E. Roman Empire/
Merovingian Cycle
<<550
650
Colonization
375BCE-27BCE
Empire, ending in turmoil 180-285
27BCE-285, followed by Dioclitian
Shift to Constantinople
285-600
Expanding - More Global
“Outgoing”
Carolingian Cycle
state management & succession crisis
0650-0900
2:1 Cycles:600 BCE-900 CE
Secular cycles follow – Network Size cycles
• Network Size Cycle
350-27BCE Global
27BCE-285 Regional
Time lag
• E. Roman Empire
• Carolingian Cycle
Time lag
• 2nd Roman Cycle
• 3rd (Principate)
Time lag
• (earlier cycle)
• 1st Roman Cycle
• Network Size Cycle
Global
600-350BCE Regional
• Network Size Cycle
285-600
Global
600-900
Regional
Here we show trade expansion/contraction leading secular cycle
phasing prior to 930 CE when there are few cities in trade networks
so there are insufficient data to to measure city size pulsations, if
any, in the first millennium and such pulsations would apply mostly
to capital or primate cities
Here we show trade expansion/contraction leading secular cycle
phasing after 930 CE when there are many cities in trade networks
and city size pulsations accompany those of trade.
Table 7: Cross-Correlation of City Size Cycles and European Secular Cycles
Q-period
Trade Network
Urban Size Q1
Regional CNH
Trade Network
Urban Size Q2
Global RLE
From Secular cycle
about
Contracting
th
“Infixing”
early 12 C. collapse
900 German Empire Cycle
Expanding
“Outgoing”
1150 Medieval Cycle-High Middle Ages
Trade Network
Contracting
Urban Size Q3
Regional CNH
“Infixing”
1450 First Modern Cycle
Trade Network
Expanding
Urban Size Q4
Global RLE
Crisis
“Outgoing”
1660 Second Modern Cycle
Trade Network
Single Industrial Economy
Urban Size Q5
Regional CNH
“Infixing”
not yet ending
1850 Third Modern Cycle
ca. 870? - 1120
Norman & German collapse
900-1150
ca. 1120 - 1350
crisis starting in the 14th century
1150-1450
ca. 1350 – 1560
crisis of the 17th century
1450-1660
ca. 1560 – 1850
ending in revolutionary crisis i
1660-1850
in the “troubles of our times”
1850-2050?
There may be a change in pulsation structure after 1850
2:1 Cycles: 900-2000
Secular follows – Network Size leads
along with city size distributions
• German Emp. Cycle 900-1150
Regional
• Network/City Size Cycle
• Medieval Cycle
1150-1450
Global
• 1st Modern Cycle
1450-1660
Regional
• Network/City Size Cycle
• 2nd Modern Cycle
1660-1850
Global
• 3rd Modern Cycle
1850-2006+
Regional
• Network/City Size Cycle
Conflict disruptive to expanded trade networks is key to city network cycling
Conflict produced by pop growth is key to secular cycling
Conflict within secular cycles could be key to political cycling
Secular Cycle ca. 220 years: nadirpop growthmaxdeclinenadir
Full Trade Network expansion/contraction ca. 440 years
Conflict disruptive to expanded trade networks is key to city network cycling
Conflict produced by pop growth is key to secular cycling
Conflict within secular cycles -- is it key to political cycling?
Conflict between polities and competition between cites -- is it key to the
cycling of economic innovations (K-waves)?
About
900 ?
930
990
1060
1120
1190
1250
1300
1360
1430
1492
1540
1580
1640
1688
1740
1792
1850
K-waves (global leading
sectors)
credit mechanisms?
K1 Printing and paper
K2 National market
K3 Fiscal framework
K4 Maritime trade
K5 Champagne Fair
K6 Black Sea trade
K7 Galley fleets
K8 Pepper
K9 Guinea gold
K10 Indian spices
K11 Atlantic, Baltic
K12 Asian trade (VOC)
K13 Amerasian trade-tobacco
K14 Amerasian trade-coffee
K15 Cotton, iron
K16 Steam, rail
K17 Electrics, chemicals, steel
1914
1972
2026?
K18 Autos, air, electronics
K19 Information industries
K20 ?
Long cycles (world
powers after 1500)
Chinese
LC1 Northern Sung
Secular cycles
Trade &_City Cycles
900 SC1_______Q1≡
Regional/subZipfian
LC2 Southern Sung
Q2≡1000
LC3 GenoaFrance
1150 SC2
Global
/
Zipfian
LC4 Venice
Q3≡1290
Regional/subZipfian
LC5 Portugal Spain 1450 SC3
LC6 Dutch Republic
LC8 Britain IFrance 1660 SC4 Q4≡1600
Global
/ Zipfian
LC9 Britain II
Q5≡1785
LC10 United States
1850 SC5__
___________Britain Regional /subZipfian
United States
__________Q6≡1920
Global
/ Zipfian
Table 9: K-waves: the sequence of global leading sectors
K-wave
Leading sector
Major innovation
K1
K2
K3 Q2
K4
From
about
930
990
1060
1120
Printing, paper
National market formation
Fiscal/administrative framework
Maritime trade expansion
Learning society, book printing
North-south market unification
Monetization, paper money
Compass, large junks
K5
K6
K7 Q3
K8
1190
1250
1310
1350
Champagne fairs
Black Sea trade
Venetian galley fleets
Pepper trade
European market organized
Innovations from East Asia
New markets in North Europe
Alexandria-connection institutionalized
K9
K10
K11 Q4’
K12
Q4
K13
K14
K15
K16 Q5
1430
1494
1540
1580
Guinea gold
Indian spices
Atlantic, Baltic trades
Asian trade
“Discovery” of African trade
Operating oceanic route
American silver
Dutch East Indies Co. VOC
1640
1688
1740
1792
Amerasian trade
Amerasian trade
Cotton, iron
Steam, rail
Plantations
Tobacco
Factory production
New forms of transport
K17
K18
K19 Q6
K-20
1850
1914
1972
2026
Electrics, chemicals, steel
Electronics, autos, aerospace
Information industries
Invention of invention
New products
Computers / Electronic transfers
Source: Modelski, G. 2000. http://faculty.washington.edu/modelski/Evoweconomy.html
Table 10: Organizational evolution in the global economy
From about
V. Breakthrough to
market systems
930
Phases
Centered on
Song move to national market
China
Experiments
Nautical-Commercial revolution
Italy
Clusters
Oceanic trading
Atlantic Europe
Critical mass
Industrial take-off
Britain
Pay-off
Information Economy
United States
Experiments
Q2
1190
Q3
1430
Q4
1640
VI. World Market
Q5
1850
Q6
2080
Source: Modelski, G. 2000. http://faculty.washington.edu/modelski/Evoweconomy.html
Clusters
At the foundation of a rethinking in a network perspective of long and
convoluted world historical systems change is a compelling need to
study dynamics in terms of specific interactions, the ebbs and flows of
differential network histories that nonetheless can be seen to operate in
large part under some set of generalizable processes. Network theory
can clarify basic concepts that can be used to test specific interactional
hypotheses derived from principles that are both very general, but also
specifically tailored to the phenomena at hand.
If the reasoning of this paper is correct, then a speculative hypothesis is
that a network approach to world historical systems, coupled with other
theoretical frameworks, offers a series of supplemental hypotheses and
potential explanations for historical change that are very specific
regarding the channeling of change and that take different network
contexts into account. The speculation is that with additional
understanding of network predictions and explanations of network and
historical dynamics, we should find that what have been taken as
idiosyncratic “path dependencies” will to a large extent turn out to be
network independencies, subject partly to the role of agency, but much
more predictable than previously thought possible.
Footnotes re: networks
After 900 CE, the shapes of Chandler’s city
size distributions begin to differentiate by
historical period
These differentiations by historical period
relate to trading network
expansion/contraction
Figure 2: City Size Scaling: Zipfian
in the upper city size bins
Extreme global hubs, lesser hubs
in the neighborhood of most cities
are absent.
q-scaling is stretched exponential
scaling that models the entire size
distribution, including the
power-law slope of the upper
sized bins. (cumulative binned,
CDF)
In these periods, highest profits
are acrued by cities with the
highest glpbal flow centralities
Flow centrality (how much total network flow is reduced with removal of a node) predicts
the potential for profit-making on trade flows, emergence of financial centers, and
(reflecting flow velocities, as Spufford argues) organizational transformations in different
cities. Here, Bruges is a predicted profit center, prior to succession by Amsterdam.
This type of
centrality is
conceptually very
different. It maps
out very differently
than strategic
betweenness
centers like
Genoa, which are
relatively low in
flow centrality.
Figure 3: City Size Scaling:
sub-Zipfian in the upper city size bins
Global hubs less differentiated,
but lesser hubs in the neighborhood
of most cities are present.
In these periods, highest wealth
is accrued by cities with the
highest betweenness centralities
Betweenness centrality in the trade network predicts accumulation of mercantile wealth
and emergence of commercial hegemons. e.g., in the 13th century, Genoa has greatest
betweeness, greatest wealth, as predicted. Later developments in the north shift the network
betweeness center to England.
Episodically,
in 1298,
Genoa
defeated the
Venetians at
sea.
Repeating
the pattern,
England later
defeats the
Dutch at sea
Size of nodes adjusted
to indicate differences in
betweenness centrality
of trading cities in the
banking network
Betweenness Centralities in the banking network
Given its 13th C betweenness centrality, Genoa generated the most wealth