European Conference on Complex Systems Paris, 14-18 November 2005
Civilizations as dynamic
networks
Cities, hinterlands,
populations, industries,
trade and conflict
Douglas R. White
© 2005 All rights reserved
50 slides - also viewable on drw conference
paper website version 1.3 of 11/12/2005
acknowledgements
Thanks to the International Program of the Santa Fe Institute for support of the
work on urban scaling with Nataša Kejžar and Constantino Tsallis, and thanks
to the ISCOM project (Information Society as a Complex System) principal
investigators David Lane, Geoff West, Sander van der Leeuw and Denise
Pumain for ISCOM support of collaboration with Peter Spufford at Cambridge,
and for research assistance support from Joseph Wehbe. Also thanks to David
Krakauer and Luis Bettencourt at SFI in suggesting how our multilayered
models of rise and fall of city networks could be guided by sufficient statistics
modeling principles and to Lane and van der Leeuw for suggestions on the
slides. This study is complemented by others within the ISCOM project concerned
with urban scaling and innovation and draws several slides from those projects.
Thanks to Peter Spufford for his generous support in providing systematic
empirical data on intercity networks and industries in the medieval period to
complement the data in his book, Dean Anuska Ferligoj, School of Social
Sciences, University of Ljubljana, for five weeks of support for work carried out
with Kejžar in Ljubljana in summer, 2005, Céline Rozenblat (ISCOM project) for
providing the historical urban size data, and Camille Roth (Polytechnic, Paris) for
collaborations on representing evolutions of multiple industries across city netwks.
A jointly authored on this project is in draft with Spufford and possibly others. 2
Outline re: civilizations as dynamic networks
some main approaches and areas of findings
1 Urban scaling: distributional scaling and historical transitions
City functions (Geoff West , Luis Bettencourt, José Lobo 2005)
City growth and inequality parameters: From Zipf's rank size laws to power laws to a
stronger scaling theory of q-exponentials
Periodizing: Historical q-periods and their correlates
• Commercial vs. Financial capital and organization
• Market equilibrium vs. Structural Inflation
2 Rise and fall of intercity networks (e.g., trade and conflict)
Key concept: structural cohesion and its effects, such as market zones and price
equilibrium vs. inflation in cohesive cores versus peripheries (White and Harary
2002 SocMeth, Moody and White 2003 ASR)
Similarly, effects of network betweenness versus flow centrality on commercial vs.
financial capital and institutional organization
3 Interactive dynamics: world population, cities and hinterlands, polities
economic growth versus sociopolitical conflict
organizational change at macro level and micro level.
General approach: interactive multi-nets, networks among and between
different types of entities in time series with changing links and attributes
3
Co-evolution time-series of Cities and City Networks
City attributes and
distributions
begin Dynamics from
Urban Hierarchy-Industries,
_______Commerce, Finance
City Sizes Hierarchy
Hinterland Productivity
Structural Cohesion
Routes, Capacities
Unit Formation (e.g. polities)
Velocities and Magnitudes
of trade
Demography/Resources
Conflicts
periodize
STATES
from factions & coalitions
to sovereignty - emergent
Spatiopolitical units
City Networks
Interference and
attempts at regulation
Sources of boundary
conflicts
Organizational transformation
of nodes
MARKETS
from structurally cohesive
k-components - emergent
Network units (overlap) 4
Urban Scaling: Functions
Geoff West, Luis Bettencourt, José Lobo. 2005 (Pace of City Life):
Innovation-Dependent (Superlinear), Linear, and Scale-Efficient (Sublinear) Power Laws
City Functions
70000
R&Dchina-superlinear
60000
R&Dfrance-superlinear
50000
Elec.Cons.-linear
Gas Sales-sublinear
40000
30000
20000
10000
0
0
2000000
4000000
6000000
8000000
10000000
City Sizes
5
Superlinear ~ 1.67
Linear ~ 1
Sublinear ~ .85
ISCOM working paper
6
Urban Scaling: City Sizes
the next few slides compare the scale K and α coefficients of the power-law
y(x) ≈ K x-α (and Pareto β= α+1) with the q-exponential parameters for q
slope and scale κ in y(x) ~ [1 + (1–q) x/κ)]1/(1–q), fitted to entire size curves
(White, Kejžar, Tsallis, and Rozenblat © 2005 working paper)
1000000000
10000
α=1
β=2
100000000
1000
10000000
100000
1000000
10000000
Not a good fit to
inset: y = cumulative
overall city size
number of people
100
distributions
in these cities
Vertical axis y =
Power laws and Zipf’s law
cumulative number
might fit upper bin frequencies
10
for city sizes but not the whole
of cities at this log
curve
bin or higher
Dashed line = portion of distribution that is "power-law“
(but is exaggerated in the upper bins)
1
100000
1000000
10000000
Horizontal axis x = binned (logs of city size)
Example: 1950 United Nations data for world cities
7
+ fit
At time
t, populationscaling
y(x) ≈ ~
y(0)
+ to
(1–q)
x/κ)]1/(1–q), as
of q, κ,distributions
binned size x
Q-exponential
.99[1
18 post-1800
andfunction
22 pre-1800
power law coef. β = 1/(q-1) equals 2 for q = 1.5,
thus more equality at the asymptote …
for 2005:
α=1
β=2
q = 1.5
In this segment of the data
series the upper bin slope
is going from q ~ 2 in 1800
(inegalitarian, α = 1) to q ~
1.5 (egalitarian) in 2000.
If these distributions were
actual
power
laws, they
fitted
q-exponential
should
straight line
fits in
distributions,
q, κ.
this log-log graph.
1950
% Urban in Europe
more inequality
at the asymptote:
(for 1800)
α = 0.24
β = 1.24
q = 1.8
α=1
β=2
q = 1.5
City-size bins
The entire city-size distributions for these 18 time periods are
fitted here by q and κ ( not just the Zipfian upper size bins)
Dotted lines here are city numbers for each size bin.
The x axis has the city sizebins, e.g., 20.0 = 200,000
people or more.
The dotted lines show
number of cities in multiples
of two: 2,4,8,16,32,etc.
Units of 10K
8
Log cumulative populations in cities at least this bin size
Stylized q-exponentials
β~2
α ~ 1 (high)
q ~ 1.5 (low) more
egalitarian thin tail :
like the standard
Zipfian
β<2
α < 1 (low)
q ~ 2 (high)
Inegalitarian fat tail:
possibly heterarchical
with the Adamic effect
of average local
Realistic critical
nghbhood
feature different
heterogeneity wrt hubs
than power laws:
city size truncation
(L Adamic et al 2003)
Log city bin size
(note the connection here to networks: city links to other nearby cities)
Stylized contrasts and
historical examples in
unlogged graphs:
α ~ 1, high
e.g., year 2005
egalitarian thin tail;
few hubs (bigger towns) in
average neighborhoods
α < 1, low
e.g., year 1800
inegalitarian fat tail; e.g.,
industrial revolution pushes out
to fatten smaller towns; hubs in
average neighborhoods
9
β=2 (α=1) long thin tail; greater size equality
β → 1 (α → 0)
thicker tail; greater
size inequality
430 BCE to 1750
The q-slopes for all
periods are well
bounded from β → 1
(inequality, i.e., fat
tails) to β =2 (i.e., thin
tails, equality)
Tails truncate because
the city numbers are
discrete (dotted line =
1 city), with limits
above which there are
no larger cities.
Truncation at a finite
limit allows a powerlaw distribution to
flatten as α (=β-1)→0.
This is more realistic
than a scale-free
model.
10
World city sizes scaled in 28 reliable-estimate periods, fitted slope q & scale κ (kappa)
8
q (NLS)
κ detrended
6
4
2
Kappa detrended
heterarchy
MoreHi inequality
q of city sizes
Hi
Hi
Lo
Lo
Scale κ of city sizes, detrended
0
-250
Lo
0
250
500
750
1000
1250
1500
1750
2000
-2
-4
At time t, population y(x) ≈ y(0) [1 + (1–q) x/κ)]1/(1–q), as function of q, κ, binned size x
100.00
y = 0.000052x + 1.700698
R2 = 0.016064
10.00
Detrending method: κ
increasing and headed
to singularity post-2000
1.00
0
5
10
15
0.10
20
25
Hundreds
-1.5684
y = 12298x
2
R = 0.8263
0.01
2000 1750 1500 1250 1000 750 500 250
11
0 -250
World city sizes scaled in 28 periods, fitted slope q, scale κ (kappa)
8
q (NLS)
κ detrended
6
4
2
Hi
Lo
Hi
Lo
Hi
Lo
0
-250
0
250
500
750
1000
1250
1500
1750
2000
-2
-4
At time t, population y(x) ≈ y(0) [1 + (1–q) x/κ)]1/(1–q), as function of q, κ, binned size x
100.00
y = 0.000052x + 1.700698
R2 = 0.016064
10.00
Time is reversed in the two graphs
1.00
0
5
10
15
0.10
20
25
Hundreds
-1.5684
y = 12298x
2
R = 0.8263
0.01
2000 1750 1500 1250 1000 750 500 250
12
0 -250
Contiguous time periods (verified by runs test), discrete (1-7) periods
1985
15.00
1980
World cities
phase
diagram
kDetrended
10.00
1965
1975 1960
1950 1955
5.00
1970
>1950 Mass
urbanization
1700
1650
1600
1250
1100
0.00
1200 1150
1.20
1.40
egalitarian hierarchy
361
-200
622
800 100
1850
1750
1000 1400
1450
1925
1800 1825
1.60
1.80
qNLS
q
2.00
1900
2.20
inegalitarian hierarchy
13
Co-evolution of Cities and City Networks
City attributes and
distributions
Dynamics from
City Networks
Pop. Size Hierarchy
Structural Cohesion
Routes, Capacities, Markets
Urban Industries plus
Unit Formation (e.g. polities)
Velocities and Magnitudes
of trade
Commerce, Finance
Hinterland Productivity
Demography/Resources
Conflicts
Organizational transformation
of nodes, periods;
commercial, financial, religious
periodize
for the Circum-Mediterranean all major industries and their
distributions across cities in the trading city networks are also coded in
generational (25 year) intervals, and the capacities of transport routes
are similarly coded in 25 year intervals. All-Eurasia coding incomplete.
14
q-dependent variables
historical q-correlates? (Circum-Mediterranean)
– Alternation in inflationary market trends?
Evaluated with 13 datasets (near-equilibrium vs. inflation
periods from Spufford 1982, Fischer 1996)
– Alternation of trade hegemony with new q-periods?
Evaluated with dates of q-alternations and other periods
(commercial vs. financial centers)
– Alternation of periods of organization forms?
Evaluated with Arrighi data, 1994, 5 periods, 1100-1990
(commercial vs. financial capital)
15
Summary of historical correlates of hierarchy variable q
Inegalitarian q (high)
q
Egalitarian q (low)
κ below trend line
κ
κ above trend line
Periods of Low Inflation
Inflation?
Periods of High Inflation
(#s are q - κ periods)
High
2-3
-1320
1350-1520
Low
3
High
3-4
1500-1650
1650-1780
Low
4
High
4-5
1750-1810
1830-1910
Low
5
High
5-6
1925-2005
Periods: Commercial Capital
Hegemony
(1340-85)
Financial Capital :Periods
of European
hubs
c.1000
Constantinople
Venice
c.1100-1297
1298-1380
Genoa
Holland
1610-1730
1797-1917
Britain
U.S.A.
1950-?
16
Euro-Hegemon
examples
(Arrighi 1994)
Commercial
Financial
(hegemonic cities
in historic order)
Amsterdam
Constantinople
Venice
Genoa
Amsterdam
London
New York
17
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
18
Given its 13th C betweenness centrality, Genoa generated the most wealth
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.
19
Bipartite network cohesion in Hanse saintly brotherhood trade organization
Medieval Hanse trading towns had religious brotherhoods under a Patron
Saint for a distant church of the same Saint (kaufmannskirch), which hosted
the traders and protected their goods. The more distant the trading locations,
into foreign lands, the more frequent the construction of matching
kaufmannskirchen.
Core towns
Northeast
Linking
kaufmannskirchen
(by Saint name)
Southwest
Distant towns
Additional linking
kaufmannskirchen
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
Financial capital
FFFFFFF
FFFFF
FFF
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
time-series data coded by 25 year periods, hegemonic economic organization:
C = Commercial capital (e.g., colonizing or diaspora traders)
F = Financial capital (e.g., corporate traders)
supported propositions:
initial C, F => L (low inflation), little or no time lag
initial C => I (inegalitarian city hierarchy)
initial F => E (egalitarian city hierarchy)
L gives way to h (high inflation) within E(galitarian) and I(negalitarian)
21
Type of 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
Financial capital
FFFFFFF
FFFFF
FFF
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
time-series data coded by 25 year periods, hegemonic economic organization:
C = Commercial capital (e.g., colonizing or diaspora traders)
F = Financial capital (e.g., corporate traders)
supported propositions:
initial C, F => L (low inflation), little or no time lag
initial C => I (inegalitarian city hierarchy)
initial F => E (egalitarian city hierarchy)
L gives way to h (high inflation) within E, I
22
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)
Trade net
(low cost)
versus
(high cost)
Swedish hegemony
European access
23
From
Dominant Routes to a Land Routes variable
Recode previous slide
predict
landed inter-national conflict
Hegemony-type 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 Heterarchy
? ? ? ? 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?
E E E q L o Hierarchy
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
Peace of
Land Routes
Conflict on Land  Sea
trade routes safer than
land, 1318-1453/4+
Land
routes
UNSAFE
versus
Land
routes
SAFE
(Spufford:407)
French Sov.
from 1760
Landed Armies  Land
Routes safer than sea
1500-1650 Maritime
Conflicts (Jan Glete)
Political
Revolutions to
1814
Landed Trade
Secure
Sea unsafe
 star bank
routes
Interactive Dynamics
Commercial capital competition
landed inter-national conflict,
with generational time lag
Westphalia Struggle
for
Sea
Empire: Global
Maritime
routes Sea
Battles Economy
safe
to 1815 Industrial Rev.
Baltic conflicts: connection to Novgorod and Russia (lost)
Hierarchy (I) city distributions
landed civil conflict, with
multiple generation time lag
Swedish hegemony
European access
Landed international
conflict is
protracted
(versus)
Landed
international
peace (incl.
WW I or II
followed by
peace)
24
Commercial and financial centers as q-correlated temporal variables
Underwarer
Sea unsafe
Sea unsafe
C
CCC
C C C C C C star bank
Commercial
star
bank routes
cohesive bank routes star bank routes
cohesive bank routes
routes
cohesive bank routes
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
F F F F F FDomestic
F
F F F F F Imported cotton, Fmanuf.
FF
Financial capital
Fustians (innov.: cotton-linen)
Industry
woven cotton
1
1
1
1
1
1
1
1
1
1
2
0
1
2
3
4
5
6
7
8
9
0
02570257025702570257025702570257025702570
05050505050505050505050505050505050505050
Constantinople
(Blue that
= Commercial
Finance
L/h
lo/hi inflation figures (L=depression) are for
year
forward
Red = Medici Bank & profits ;
controlled by Florentines)
Venice
Industrial center
Commerce center
Commercial Finance =Blue
Champaign Fairs
Red = Financial profit center
Genoa
Florence
Arras
Bruges
Shift of financial center due to civil
war of 1480
Antwerp
Amsterdam
Add: religious centered trade
London
25
Co-evolution of Cities and City Networks
City attributes and
distributions
Dynamics from
City Networks
Pop. Size Hierarchy
Structural Cohesion
Routes, Capacities
Urban Industries plus
Unit Formation (e.g. polities)
Velocities and Magnitudes
of trade
Commerce, Finance
Hinterland Productivity
Demography/Resources
Conflicts
Organizational transformation
of nodes
26
For example, among medieval merchants and merchant cities of the 13th century,
cohesive trade zones (gold nodes) and their potential for market pricing supported the
creation of wealth, with states benefiting by marketplace taxation and loans.
Lübeck
(early slide, merely
illustrative, not to scale,
network incomplete)
banking network
cohesion
The Hanse League port of Lübeck at its peak had about 1/6th the trade of Genoa, 1/5th that of Venice;
its network had a well documented colonial and religious-brotherhood trade organization.
28
the banking network, main routes only (again, geographically).
Control networks often rely
on unambiguous centralized
spines but their operation
relies on feedback in
cohesive networks.
banking network
hierarchy
the spine of the exchange
system is tree-like and thus
centralized. It is land based.
Linking the four parts was
Alessandria, a small stronghold
fortification built in 1164-1167 by
the Lombard League and named
for Pope Alexander III. At first a
free commune, the city passed in
1348 to the duchy of Milan.
Note again the closeness of
Genoa to the center, and the
exclusion of Venice.
29
With expanded coding and further road identification for the medieval network, 2nd(gold) and 3rd-order cohesiveness (red nodes) reveals multiple cohesive zones such
as those of Western Europe or the Russian plains. Again, this cohesion supported the
creation of wealth among merchants and merchant cities, with states benefiting by
taxation and loans.
Red 3-components
Middle East and its
3-component also
In Northern Europe the main Hanse League port of Lubeck had about 1/6th the trade of Genoa, 1/5th that of
30
Venice.
RISE AND FALL
Silk, Jade and Porcelain
from China - Spice trade
from India and SE Asia Gold and Salt from
Africa
The lead-up to the 13th C
world-system and its economy
was a period of population
expansion and then crisis as
environmental carrying
capacities were reached.
In the 14th C, economic depression
set in, inflation abated and
population dropped, with famines
beginning well before the Black
Death. After closure of the Golden
Horde/Mongol Corridor (1360s),
the EurAsian network crashed.
To illustrate the effects of structural cohesion in the trade route network on the
development of market pricing versus structural inflation, we could start with the
AfroEurasian world-system at the end of the pre-classical period in 500 BCE -
What came before the medieval networks rise and fall?
31
These trade routes
mostly form a tree, with a
narrow structurally
cohesive trading zone
(with market potential)
from India to Gibraltar
Trade networks before
500 BCE were smaller,
even more tree-like, and
lacking cohesion
32
Cohesive extension of trade routes leads to a host of other developments…
(figures courtesy of Andrew Sherratt, ArchAtlas)
33
Multiconnected regions => structural cohesion variables
During classical
antiquity trade
routes become
much more
structurally
cohesive from
China to France
34
Multiconnected regions => structural cohesion variables
35
Multiconnected regions => structural cohesion variables
36
Multiconnected regions => structural cohesion variables
Some
changes in
the medieval
network from
1000 CE
37
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)
38
Co-evolution of Cities and City Networks
City attributes and
distributions
Dynamics from
City Networks
Pop. Size Hierarchy
Structural Cohesion
Routes, Capacities
Urban Industries plus
Unit Formation (e.g. polities)
Velocities and Magnitudes
of trade
Commerce, Finance
Hinterland Productivity
Demography/Resources
Conflicts
Organizational transformation
of nodes
Scarcity;
Periods of: Inflation;
Competition;
Sociopolitical
violence;
39
Data sources and dynamic interaction analyses
• Peter Spufford - in Power & Profit (2002)
– shows how rises in the velocity of trade in intercity networks
causes transformations in organizations.
• Peter Turchin - in Structure & Dynamics (2005)
– demonstrates dynamic interactions between governance,
conflicts, unraveling, on the one hand, and population
oscillations on the other (structural demographic theory)
40
(Turchin 2005)
Chinese phase diagram
41
English sociopolitical violence cycles don’t directly correlate but lag population
cycles. Detrended English population cycles, 1100-1900, occur every 300-200 years.
(Turchin 2005)
Source:
Turchin
42
Turchin tests statistically the interactive prediction versus the inertial prediction for
England, Han China (200 BCE -300 CE), Tang China (600 CE - 1000)
(Turchin 2005)
43
Geoff West, Luis Bettencourt, José Lobo. 2005 (Pace of City Life):
Revisiting the Innovation-Dependent Superlinear Case
Unsustainable
superlinear growth
superlinear growth
crisis
superlinear growth
crisis
City Functions
70000
superlinear growth
crisis
R&Dchina-superlinear
60000
R&Dfrance-superlinear
50000
Elec.Cons.-linear
Gas Sales-sublinear
40000
Resetting growth
through costly
innovation
Resetting growth
through costly
innovation
Resetting growth
through costly
innovation
30000
20000
10000
0
0
2000000
4000000
6000000
City Sizes
8000000
10000000
44
Cities and hinterlands context variables
World population 'response' to power-law city growth
1250
Kremer data; Fitted Coefficients of Equation 1, Nt = CN / e(t0 – t)
k
CN
Up to (following period)
Period
Length
-5000 or earlier
1.19
560000000
Classical Antiquity
n.a.
n.a.
-200 (q turns hi?)
0.26
36000
Medieval Renaissance
c.7000
3.8
1250 (q turns hi)
0.175
19000
Industrial Revolution
c.1450
3.2
1750-1860 (ditto)
0.15
1700
Consumer Economy
c.610
2.8
?
c.100?
2.0
Start Year
Post-1962 (ditto)
Log of Length
.
(linearly decreasing)
45
q-dependent variables
– power-law population growth is unsustainable,
generates decreasing lengths of oscillations, also
general inflection points (e.g., flattening, crisis)
– World population growth rate is slower with q-flat city
growth, but also tends to diminish at the end of each
type of q-period. Possibly a failure of innovation rate
because leading cities depend on innovation.
46
Geoff West, Luis Bettencourt, José Lobo. 2005 (Pace of City Life):
Revisiting the Innovation Dependent Superlinear Case
World pop.
Downturn
World
urbanization
inflections
47
(I have added the correlations of world and NYC population shifts)
Stylized facts:
Economic macro variables
1. Gross World Economic Product
grows not in proportion to 1/(time
to singularity), as does population,
but 1/ /(time to singularity)2
(David Hackett Fischer 1996)
2. Inflation, however, is more
sensitive to global and local
fluctuations of population
above and below its
superlinear trend-line, which
also correlate with q-periods.
Renaissance
Equilibrium
(begins with
economic
depression)
(Turchin 2005)
1900
48
Co-evolution of Cities and City Networks
City attributes and
distributions
Dynamics from
City Networks
Pop. Size Hierarchy
Structural Cohesion
Routes, Capacities
Urban Industries plus
Unit Formation (e.g. polities)
Velocities and Magnitudes
of trade
Commerce, Finance
Hinterland Productivity
Demography/Resources
Conflicts
Organizational transformation
of nodes
49
The population and sociopolitical crisis dynamic that drove inflation in the 12th-15th
centuries also drove monetization and trade in luxury goods. Inflation of land value created
migration of impoverished peasants ejected from the land, demands of money rents for
parts of rural estates, and substitution of salaries for payments in land to retainers.
(Relative to Carrying Capacity)
Prices
Real wages
(low)
Inflation
In kind payment of serfs,
retainers salaried laborers
Demand for
prestige goods
Poverty forces more
meltdown of silver
Demand for
money rents
Peasants
to cities
Elites to cities
Conspicuous
consumption
Demand for
silver mining
Coinage
Monetization
(Velocity of Money in Exchange)
Effects of Inflation of Land
Thresholds
(Variables affecting transition)
Reorganization
(to handle higher velocities)
on Monetization
(Spufford 2002)
e.g., Division of labor, new techniques, road building, bridge building, new transport
Merchants/agents
Governments/agents
Churches/agents
Elites/agents
50
References
– Adamic, Lada, et al. 2003. Local search in unstructured networks. In, Bornholdt and Schuster, eds.,
Handbook of Graphs and Networks. Wiley-VCH.
–
Arrighi, Giovanni. 1994. The Long Twentieth Century. London: Verso.
– Fischer, David Hackett. 1996. The Great Wave: Price Revolutions and the Rhythm of History.
Oxford University Press
– Sherratt, Andrew. (visited) 2005. ArchAtlas. http://www.arch.ox.ac.uk/ArchAtlas/
– Spufford, Peter. 2002. Power and Profit: The Merchant in Medieval Europe. Cambridge U Press.
– Tsallis, Constantino. 1988. Possible generalization of Boltzmann-Gibbs statistics, J.Stat.Phys. 52,
479.
– Turchin, Peter. 2005. Dynamical Feedbacks between Population Growth and Sociopolitical Instability
in Agrarian States. Structure and Dynamics 1(1):Art2. http://repositories.cdlib.org/imbs/socdyn/sdeas/
– West, Geoff, Luis Bettencourt, José Lobo. 2005. The Pace of City Life: Growth, Innovation and Scale.
Ms. Santa Fe Institute, Project ISCOM.
– Douglas R. White, Natasa Kejzar, Constantino Tsallis, Doyne Farmer, and Scott White. 2005. A
generative model for feedback networks. Physica A forthcoming. http://arxiv.org/abs/condmat/0508028
– White, Douglas R., Natasa Keyzar, Constantino Tsallis and Celine Rozenblat. 2005. Ms. Generative
Historical Model of City Size Hierarchies: 430 BCE – 2005. Ms. Santa Fe Institute.
– White, Douglas R., and Peter Spufford. (Book Ms.) 2005. Medieval to Modern: Civilizations as
Dynamic Networks. Cambridge: Cambridge University Press.
51
Co-evolution of Cities and City Networks
City attributes and
distributions
Dynamics from
City Networks
Pop. Size Hierarchy
Structural Cohesion
Routes, Capacities
Urban Industries plus
Unit Formation (e.g. polities)
Velocities and Magnitudes
of trade
Commerce, Finance
Hinterland Productivity
STATES
from factions & coalitions
to sovereignty - emergent
Spatiopolitical units
Demography/Resources
Conflicts
Interference and
attempts at regulation
Sources of boundary
conflicts
Organizational transformation
of nodes
MARKETS
from structurally cohesive
k-components - emergent
52
Network units (overlap)
53
Cumulative population is used because by taking only the populations in
each size bin in different growth periods differential city growth generates the
dogs-eaten-by-snake phenomena:
Time1
Time2
Time3
Time4
Time5
Actual 1965 data on distribution at one time  smoothed cumulative distributions
40000
350000
35000
“innovative
bulges” in city
sizes move
thru time
30000
25000
20000
15000
10000
5000
Power-law: poor fit
300000
250000
200000
y = 3E+06x-0.4432
R2 = 0.9714
150000
100000
50000
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0
0
A cumulative distribution has with more
population in the lower bins requires
curve fitting such as y ~ log (x) with lower
bins weighted proportional to population.
The upper bins show bias toward longer
tails compared to semi-log but less than
a power-law tendency, as in these data.
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
350000
Semilog y ~ log(x): poor fit
Fitting here uses bins
with largest numbers
300000
250000
200000
150000
100000
50000
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
-50000
-100000
54
Semilog y ~ log(x) scaling r2~.99 fits
Which is an integral of Zifp's law, approximately a log if the exponents are exactly 1)
Total number of people in cities at or above the city size bin
350100
1800000
y
y = -347720Ln(x) + 3E+06
R2 = 0.994
1600000
1400000
1200000
2
R = 0.9956
= -78173Ln(x) + 711965
R2 = 0.9913
250100
1950 to 2005
y = -208530Ln(x) + 2E+06
1000000
300100
200100
1950 and
earlier
y = -40077Ln(x) + 357246
R2 = 0.978
800000
150100
600000
400000
100100
200000
50100
0
100
1000
10000
100000
100
100
city size bins, logged
1000
10000
10100
9100
Changes in slope over time are not directly
comparable over historical periods: they tend to
flatten further back in time but irregularly.
1800 and earlier
8100
7100
6100
5100
4100
Because the curves bend at the tails, but
the Zipf parameter varies considerably
around ~ 1, these data are be nicely
modeled by q-exponentials with q and
size parameters that are more
comparable over time.
350100
y = -78173Ln(x) +711965
3100
2
R = 0.9913
300100
2100
250100
1100
200100
y = -40077Ln(x) +357246
2
R = 0.978
100
100
150100
1000
100100
50100
55
100
100
1100
2100
3100
4100
5100
unlogged
6100
7100
8100
9100
10100
1/(1–q), as function
At time t, population y(x) ≈ y(0)
[1 + (1–q) x/κ)]
of q, κ, binned size x
Q-exponential
scaling
~ .99+ fit
power law coef. β = 1/(q-1) => (= 2 for q = 1.5)
thus more equality at the asymptote
(for 2005)
α=1
β=2
q = 1.5
q =1.81
q =1.61
q =1.70
q =1.57
q =1.50
q =2.01
q =2.08
q =2.01
q =1.84
q =2.1
q =1.9
more inequality
at the asymptote:
(for 1800)
1950
α = 0.24
β = 1.24
q = 1.8
α=1
β=2
q = 1.5
In this segment of the data
series the upper bin slope
is going from q ~ 2 in 1800
(inegalitarian, α = 1) to q ~
1.5 (egalitarian) in 2000.
If these distributions were
actual power laws, they
would
beq-exponential
best-fitted by a
fitted
straight
line in this
distributions,
q, log-log
κ.
graph.
Urbanhas
in Europe
The x% axis
the city sizebins, e.g., 20.0 = 200,000
people or more.
The dotted lines show
number of cities in multiples
of two: 4, 8,16,32,etc.
City-size bins
The entire city-size distributions for these 18 time periods are
fitted by q and κ, not just the upper size bins
Dotted lines here are city numbers for each size bin.
Units of 10K
56