synchrony and networks
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
Social Science History Association
November 12-15 2009
Parts of the story in a nutshell
Pax Mongolica: The routes of the silk
road leading west from Central Asia
(detail of map at Tashkent University).
http://www.silk-road.com/artl/paxmongolica.shtml
Temporally: Opening and closure of the
silk roads affect globalized Eurasian
synchrony from China to Europe
Economic structure: The bicomponent
multiple independent routes between
cities as the trading nodes promote
competitive pricing.
City rise and city-fall: Population
scaling distributions change with
temporal changes in economic links.
Cycles vs. cutpoints are key to the
dynamics as polities compete for
dominance of trading routes and cities.
Parts of the story in a nutshell
Pax Mongolica: The routes are subject
to policies of polities and empires,
falling into epochs of domination
(Modelski et al. p.78,217)___Regional
N. Sung 930S. Sung 1060Genoa 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
Euro-Hegemon
examples
(Arrighi 1994)
Commercial
Financial
Constantinople
Venice
Genoa
Amsterdam
London
New York
Transaction costs, hegemony and inflation as q-correlated temporal variables
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.
from 1760
Political
Landed Armies safe
Revolutions to
1814
land routes 15001650 Maritime
Conflicts (Jan
Glete)
Baltic conflicts: connection to Novgorod and Russia (lost)
Swedish hegemony
European access
Trade net
(low cost)
versus
(high cost)
•
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.
•
•
•
•
•
•
•
•
•
•
SO WHY DOES THE MEDIEVAL EUROPEAN RENAISSANCE ECONOMY
COLLAPSE CIRCA 1300?
Trade dominance shifts from betweenness centrality (Genoa) to global Flow
Centrality (Bruges)
China invaded, change in Silk routes
Credit crisis between North and Southern Europe
Major problem in Population Growth/Resource base
Internecine struggles
Major collapse, long recovery "Long 13th century” reaches to today
Whole period 900 - 1950
Are there inter-region synchronies? 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.
Cities in the region of
“MiddleEast&Afghan&India” are
initially inversely related to but
then affect Chinese Cities with
100-150 year lags
city systems in the last millennium
Moving to closer inter-Asian regions excluding India but on the Silk Road
Time-lagged cross-correlation effects of Mid-Asian q on China
(1=50 year lagged effect)
mle_MidAsia with mle_China
Coefficient
Upper Confidence
Limit
0.9
Lower Confidence
Limit
0.6
CCF
0.3
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
city systems in the last millennium
Moving between endpoints further away on the Silk Roads
Time-lagged cross-correlation effects of China q on Europe
(100 year lagged effect)
mle_China with mle_Europe
Coefficient
Upper Confidence
Limit
0.9
Lower Confidence
Limit
0.6
China with Europe4
0.3
Coefficient
Upper Confidence
Limit
Lower Confidence
Limit
0.6
0.0
0.3
-0.3
CCF
CCF
0.9
0.0
-0.3
-0.6
Robust Chinese Cities affect
Robust European Cities with
100 and 300 year lag
-0.9
-0.6
-0.9
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
Lag Number
-7
-6
-5
-4
-3
-2
-1
0
1
Lag Number
2
3
4
5
6
7
(non-MLE result for q)
city systems in the last millennium
Time-lagged cross-correlation effects of the Silk Road trade on Europe
(50 year lagged effect)
logSilkRoad with EurBeta10
Coefficient
Upper Confidence
Limit
0.9
Lower Confidence
Limit
0.6
mle_MidAsia with mle_Europe
0.3
Coefficient
Upper Confidence
Limit
Lower Confidence
Limit
0.0
0.6
0.3
-0.3
CCF
CCF
0.9
0.0
-0.3
-0.6
Chinese Silk road trade affects
Elite tails of European Cities
with 50 year lag
-0.9
-0.6
-0.9
Robust Mideast Cities small
effect on Robust European
Cities with 150 year lag
-7
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
Lag Number
Lag Number
city systems in the last millennium
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
Elite tails of European Cities
maintain Paris as Euro Elite
Capital with 100 year decay
-7
-6
-5
-4
-3
-2
-1
0
1
Lag Number
2
3
4
5
6
7
Probability distribution q shapes for
a person being in a city with at least
population x (fitted by MLE estimation)
Pareto Type II
q measures the shape
of the body of the
curve, while beta10
measure fits the loglog slope of the tails,
which vary
independently of q.
Shalizi (2007) right graphs=variant fits
Goodness of fit for q
and beta10 are found
by bootstrap
probability simulation,
where with added
iterations around each
of four periods
city systems in the last millennium
Variations in q and the power-law slope
β for 900-1970 in 50 year intervals
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
Cohesive extension of trade routes leads to a host of other developments…
(figures courtesy of Andrew Sherratt, ArchAtlas)
Multiconnected regions => structural cohesion variables
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)
0900 AD
From first stirrings of globalization to the 21st Century
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)
1650 AD
Renewed network links characterize low q
(power law tail) – China 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
(here: tenuous interregional connectors)
Broken network links typify high q – trifurcated
world – but China developing power-law tail
1875 AD
(here: tenuous interregional connectors)
Broken network links typify high q – bifurcated China power-law tail thinning toward low-q
1900 AD
Broken network links typify high q – trifurcated
Eurodominant - China leads shift to low-q 50 yrs
1925 AD
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 (city rise/fall) :
fragments
Is there Eurasia synchrony?
Yes: but it is not simultaneous.
Rather, it is time-lagged synchrony
and not always in the direction.
It goes from leading to trailing
economies following the dynamics of
trade.
And the dynamics of trade is
influenced by whether the trading
network is monopolized by
chokepoints or is competitive.
Competition is defined by
biconnectivity.
(A special case of structural cohesion)