Old world city systems and
economic networks 950-1950
how the growth and decline of cities and the rise and fall
of city-size hierarchies is related to
the network structure of intercity connections
Doug White UC Irvine
November 20 2009 talk
Social Dynamics and Complexity
ASU
economic networks and city systems: using physics models &
measures with large samples, time series, & inferential statistics
Physical measures
1 Entropy – minimum energy configuration
given constraints/processes
2 LDC: Long-distance correlations
3 q-scale entropy is (1) with (2) and power
law tails when q > 1
4 q-scale network – degree distribution
parameter for a network where size is a
LDC q-scale attractor to & between hubs
5 Time-lag cross-correlations for city size
distribution q-scale parameters.
P(X ≥ x) ~ (1-(1-q)x/κ)1/(q-1) (1 < q ≤ 2)
As x max and P  0 the tail of this
distribution converges to a log-log powerlaw slope -ß  1/(1-q), so P ~ (1- ßx/κ)-ß
examples
1.Species, species populations, & energy in
habitat areas (J Harte)
2.Cities depend on trading partners
3.City size distributions, power law tails 1 <
q<2
4.q-scale social circles simulation model of
complex networks (White,Tsallis,
Kejzar,Farmer,White 2006)
5.q-scales of cities in city-system regions
show temporal time lags from 0
(synchrony) to hundreds of years
As q → 1, q-scale entropy converges
to Boltzmann-Gibbs entropy
Probability distribution q-fits for a person being in a
city in the region with at least population x (fitted by MLE)
Smooth lines are fitted curves in successive time periods, jagged lines bootstrap point distributions used to estimate error bounds
Each distribution is for all the cities of a region, e.g., China, in one of the 8 time periods, at 50 year intervals from Chandler 1987
1.0
Cum prob P(X ≥ x) on a log scale
Cum prob P(X ≥ x) on a log scale
1.0
.1
.01
.001
The mle Pareto Type
II q-scale. Measures
the shape of the body
of the curve, while
beta10 measure fits
the log-log slope of
the tails, which vary
independently of q.
x = City size log of
10 thousand
.1
.01
.001
Goodness of fit for q and
beta10 are found by
bootstrap probability
simulation, with iterations
added around each of
four of the 8 periods
0001
1 million
Shalizi (2007) right graphs=variant q-fits
City size log of
10 thousand
city systems in the last millennium
1 million
Whole period 900 – 1950
Credits: White, Tambayong, Kejzar 2008
Are there inter-region synchronies? Time-lag cross-correlations give
lag 0 = perfect synchrony
lag 1 = state of region A predicts that of B 50 years later
lag 2 = state of region A predicts that of B 100 years later
lag 3 = state of region A predicts that of B 150 years later, etc.
The relation of q-scales in region
“MiddleEast&Afghan&India” to
Chinese cities is (1) synchronously
inverse but with (2) 100-150 year
lags affects them positively
(2)
(1)
Moving to inter-Asian regions on the Silk Road, excluding India:
Time-lagged cross-correlation effects of Mid-Asian q-scale on China q-scale
mle_MidAsia with mle_China
Coefficient
Upper Confidence
Limit
0.9
Lower Confidence
Limit
0.6
CCF
0.3
These and the
other crosscorrelations hold
on average for
the 1000 year
time period.
0.0
-0.3
-0.6
MiddleEast&Afghan Robust
Cities affect Robust Chinese
Cities with 50 year lag
-0.9
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
Lag Number (1=50 year lagged effect, 2=1 year lag, etc.)
For endpoints further away on the Silk Roads:
Time-lagged cross-correlation effects of China q-scale on Europe q-scale
mle_China with mle_Europe
(100 year lagged effect)
Coefficient
Upper Confidence
Limit
0.9
Lower Confidence
Limit
0.6
CCF
0.3
0.0
-0.3
-0.6
Chinese cities q-scale affect
European cities q-scale with 100
and 300 year lags
-0.9
-7
-6
-5
-4
-3
-2
-1
0
1
Lag Number
2
3
4
5
6
7
Time-lagged cross-correlation effects of the Silk Road trade on Europe’s beta
(beta is the slope of the power-law tail of the urban distribution)
(50 year lagged effect)
logSilkRoad with EurBeta10
Coefficient
Upper Confidence
Limit
0.9
Lower Confidence
Limit
0.6
mle_MidAsia with mle_Europe
Coe
0.3
Upp
Lim
Low
Lim
0.6
0.0
0.3
-0.3
CCF
CCF
0.9
-0.6
0.0
-0.3
Chinese Silk road trade affects
Elite tails of European Cities
with a 50 year lag
-0.9
-7
-6
-5
-4
-3
-2
-1
0
1
Lag Number
2
3
4
5
6
-0.6
-0.9
7
Mideast cities q have a small
effect on European cities q with
150 year lag
-7
-6
-5
-4
-3
-2
-1
0
1
Lag Number
2
3
4
5
6
7
mle_Europe with ParisPercent
Coefficient
Upper Confidence
Limit
0.9
Lower Confidence
Limit
0.6
CCF
0.3
0.0
-0.3
-0.6
-0.9
European cities q-scale synchrony
with % of France population living
in Paris, with 100 year decay
-7
-6
-5
-4
-3
-2
-1
0
1
Lag Number
2
3
4
5
6
7
Variations in q and the power-law slope
β for 900-1970 in 50 year intervals
Credits: White, Tambayong, Kejzar, Tsallis, 2006, 2008
3.0
China
Mid-Asia
Europe
MLEqExtrap
2.5
Beta10
MinQ_Beta
2.0
1.5
1.0
0.5
0.0
911111111111111111111111191111111111111111111111119111111111111111111111111
001122334455566778888999900112233445556677888899990011223344555667788889999
0 0 0 5 0 5 0 590 1
50
05
02
01
0 5101510 1
50
05
25
70
50
5 7101510 1
50
25
1 5171015 1
10121517 1
151710 1
1 5101517 9
101510 1
1 7101215 1
1 0101510 1
15101510 1
1 2951710 1
171
000000000005000005050500 000000000005000005050500 000000000005000005050500
1111111111111111111
001122334455566778888999900112233445556677888899990011223344555667788889999
000505050505705050257025700050505050570505025702570005050505057050502570257
0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 0 5 0 5date
00 000000000005000005050500 000000000005000005050500
date
city systems in the last millennium
Are these random walks or historical
Periods? Runs Test Results
Runs Tests at medians across all three regions
Test Value(a)
Cases < Test Value
Cases >= Test Value
Total Cases
Number of Runs
Z
Asymp. Sig. (2-tailed)
MLE-q
1.51
35
36
71
20
-3.944
.0001
Beta10
1.79
36
37
73
22
-3.653
.0003
Min(q/1.5,
Beta/2)
.88
35
38
73
22
-3.645
.0003
Runs Test for temporal variations of q in the three regions
mle_Europe
mle_MidAsia
mle_China
Test Value(a)
1.43
1.45
1.59
Cases < Test Value
9
11
10
Cases >= Test Value
9
11
12
Total Cases
18
22
22
Number of Runs
4
7
7
Z
-2.673
-1.966
-1.943
Asymp. Sig. (2-tailed)
.008
.049
.052
a Median
city systems in the last millennium
Is there Eurasian synchrony or are there
time-lagged effects?
Some synchrony when dependent variable
closely related in same region but
conservative (Euro beta, Paris %)
Mostly time-lagged effects of leading
regions, i.e., directional not symmetric, with
lagging regions, consistent with Modelski &
Thompson 1996 w Devezas 2008, i.e.,
globalizing econ./pol. leaders
Next: we test whether, if economic
competition is increased by multiconnectivity
(structural cohesion):
The dynamics of trade is influenced by the
trading network: whether monopolized by
chokepoints or competitive.
Leaders-to-lagger economic effects follow
the dynamics of trade.
0900 AD
From first stirrings of globalization to the 21st Century Credits: White, Tambayong, SFI
Europe
Central Asia
Medit.
Silk routes
China
Near East
Q (scaling sizes)
Changan
India
Bagdad & Changan (Xi’an)
In these slides I will connect the city network &
city size distributions and power-law tails
connected to q-exponential scaling of city sizes
low q with thin power law tails of global hubs
CORRELATES with global network links
1000 AD
N~3
960: Song capital at
Kaifeng, invention of
national markets, credit
mechanisms diffuse
Silk routes
Global network links characterize low q
(power law tail for city sizes)
1100 AD
Silk Routes
Global network links characterize low q (more
exponential body with power law tail for city sizes)
1150 AD
1127: No. Song capital
of Kaifeng conquered,
Song move to south,
capital at Hangchow
Silk Routes diminish
Global network links characterize low q (more
exponential body with power law tail for city sizes)
1200 AD
Song capital at
Hangchow
Golden Horde
silk routes
Silk Routes diminish
Global network links characterize low q
1250 AD
cutnodes
edgecut
Broken network links lead change to high q – led
by China, 50 years
1300 AD
1279: Mongols conquer
Song
Kublai Khan Mongol
trade
Broken network links characterize high q (here:
tenuous interregional connectors)
1350 AD
Mongols refocus on
Yuan administration of
China
Silk routes unimportant
Broken network links characterize high q (here:
tenuous interregional connectors)
1400 AD
1368 Ming retake China
Silk routes unimportant
Renewed network links characterize low q
(power law tail)
1450 AD
World population
growth turns
super-exponential
1421 Ming move capital
to Peking
Silk routes unimportant
Renewed network links characterize low q
(power law) – high q led by China, 100 years
1500 AD
Renewed network links characterize low q
(power law tail) – but China high q leads change
1550 AD
Broken network links characterize high q
1600 AD
Renewed network links will lead change to low q
(here: tenuous interregional connectors)
Britain
India
British/East India:
circumferences
of the trading
circles are small,
sufficient by 1720
and 1760 to induce
fully competitive
market pricing

Network cohesion
plus close regional
distances
COMPANY ROUTES
in 1620 evolve thru
malfeasance by ship
captains to independt
market price
capitalism from 1720
Erikson, Emily and Peter S. Bearman. 2006 Malfeasance and the Foundations for
Global Trade: The Structure of English Trade in the East Indies, 1601–1833
American Journal of Sociology (2006) 112(1):195-230. Fig. 3
1650 AD
Renewed network links characterize low q
(power law tail) – China crash synchronized
1650 AD
Renewed network links characterize low q
(power law tail) – China crash synchronized
1700 AD
Broken network links return to high q – esp. for
China leading
1750 AD
Broken network links typify high q – China
leading – bifurcated world
1800 AD
Circum-European cities
start to overtake China
in number
Broken network links typify high q – bifurcated
world
1825 AD
European cities
overtake China in
number and size
Industrial revolution
British opium
trade from India
Broken network links typify high q – trifurcated
world – best example of high local navigability
1850 AD
British benefit
from peace trea
(here: tenuous interregional connectors)
Broken network links typify high q – trifurcated
world – but China developing power-law tail
1875 AD
British benefit as
opium legalized
(here: tenuous interregional connectors)
Broken network links typify high q – bifurcated China power-law tail thinning toward low-q
1900 AD
British benefit
opium legal
Broken network links typify high q – trifurcated
Eurodominant - China leads shift to low-q 50 yrs
1925 AD
British trade but
opium banned
Britain lease on
Hong Kong from
1898
Broken network links typify high q – trifurcated rise of Japan - China returns to high q
1950 AD
Start of a low q Zipfian tail for world city
distribution – trifurcated – but linked by airlines
N-cohesion (2=competitive 1=monopoly land
trade) leads q-scale, dichotomized (city rise/fall),
in moving averages for 150 year periods:
World land
C
routes integrating
↑F
↑CF
↑F
↑C
↑F
N leads q to 1500,
competitive trade 
cities
Nq
Inverse of N  leads q
to 1750, Portuguese &
British Indian markets
create choke-point
trade  city q-scale
Nq
Nq
qN
World land routes
N.Sung S.Sung Genoa Portugal
disintegrating __________________ /Mongols /Venice
Dutch Engl.British USA--- Decol.
q  leads inverse of N
(more choke-points)
1750-1900 (industrial
revolution; maritime
displaces land trade)
Transaction costs, hegemony and inflation as q-correlated temporal variables
Europe and Mediterranean
C
CCC
CCCC CC
Commercial
I ???
?I I I I I I I I I I I ?
?I I I I I I
q Hi
? ? ? ? L ? ? ? h h h h L L L L L L L L h h h h h h L L L L h h L L L L L h h h L Inflation Lo/hi
P
P
?
? pP
? ? ? EEEEEEE?
? EEEEEEE?
EEE q Lo
FFFFFFF
FFFFF
FFF
Financial capital
1
1
1
1
1
1
1
1
1
1
2
0
1
2
3
4
5
6
7
8
9
0
02570257025702570257025702570257025702570
05050505050505050505050505050505050505050
L/h lo/hi inflation figures (L=depression) are for that year forward
Dominant Routes
Conflict on Land  Sea
trade routes safer than
land, 1318-1453/4+
Maritime
(low cost)
versus
Land
routes
trade
(pop.
growth)
(Spufford:407)
Landed Trade
Secure
Peace of
Westphalia Struggle
for
Sea
Empire: Global
Maritime
routes Sea
Battles Economy
safe
to 1815 Industrial Rev.
French Sov.
Landed Armies: safe
land routes 1500-1650
Maritime Conflicts
(Jan Glete)
from 1760
Political
Revolutions to
1814
Baltic conflicts: connection to Novgorod and Russia (lost)
Swedish hegemony
European access
Trade net
(low cost)
versus
(high cost)
Euro-Hegemon
examples
(Arrighi 1994)
Commercial
Financial
Constantinople
Venice
Genoa
Amsterdam
London
New York
The Medieval pause and Conclusions
•
•
WHY DOES THE MEDIEVAL EUROPEAN RENAISSANCE ECONOMY
FALTER CIRCA 1300?
Major problem in Population Growth/Resource base
Partly conflicts on land, internecine struggles
Credit crisis between North and Southern Europe
China invaded, change in Silk routes
Trade dominance in the long terms begins to shift from betweenness
centrality (Genoa; commercial capital) to global Flow Centrality (Bruges;
financial capital), with later oscillations.
Major collapse, long recovery "Long 13th century” reaches to today
•
Conclusions: city systems in the last millennium
•
City systems unstable; have historical periods of rise and fall over hundreds
of years; exhibit collapse.
City system growth periods in one region, which are periods of innovation,
have time-lagged effects on less developed regions if there are active trade
routes between them.
NETWORKS AFFECT DEVELOPMENT.
•
•
•
•
•
•
•
Parts of the story in a nutshell
Pax Mongolica: The routes are subject
to policies of polities and empires, part
of periods of pol./econ. dominance
(Modelski et al. p.78,217)___Regional
N. Sung 930S. Sung 1060Genoa/Venice 1190-___to Global____
Mongols 1250-90-1360 trans Eurasian
Portugal 1430- Global system mapping
Holland 1540- Global capital
England 1640- Global industrial exports
Britain 1740- Global organization
United States 1850-Global informationGlobal market
United States 1950- Decolonization
-1990 Depolarization - Global hyperspace
Globalization
•
•
The Mongol administrative improvements of postal routes and support for
merchants on the Silk roads were key to the rise of the Mongol Empire (on
the scale of the later British Empire) and a first planned policy attempt at
creating new routes for global trade and political globalization, i.e., going
beyond earlier Roman and Greek (Alexandrian) attempts, for example.
Modelski refers to the Mongols as a failed empire because they retreated to
the east to dominate China until 1912. Their success and the benefits of
East-West trade, however, were the spur to Portuguese and subsequent
attempts at policy engineering towards globalizing trade and the periods of
attempted West-East domination.
A next study of planned globalization will start in 1290 and review
globalization policies and pitfalls.
– Globalization as a learning process
– Globalization policies at attempts as dominance
– The cycles of leading polities
• And the two shorter economic cycles within them
– The costs of losing dominance
– The effects of wars over dominance
– Paths to mutual regional support and peaceful resolution of competition
end
Cohesive extension of trade routes leads to a host of other developments…
(figures courtesy of Andrew Sherratt, ArchAtlas)
Multiconnected regions => structural cohesion variables
(but the
circumferences
of these trading
circles are large,
not sufficient to
induce fully
competitive
market pricing)
Multiconnected regions => structural cohesion variables
Multiconnected regions => structural cohesion variables
Multiconnected regions => structural cohesion variables
Some
changes in
the medieval
network from
1000 CE
Multiconnected regions => structural cohesion variables
to 1500 CE
(note changes
in biconnected
zones of
structural
cohesion)
Project mapping is
proceeding for
cities and trade
networks for all of
AfroEurasia and
urban industries
for Europe in 25year intervals,
1150-1500
(our technology for cities / zones / trade networks / distributions of multiple industries across
cities for each time period includes dynamic GIS overlays, flyover and zoomable web images)