civilizations as dynamic networks

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

European Conference on Complex Systems Paris, 14-18 November 2005

http://complexsystems.lri.fr/

2

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.

http://www.santafe.edu/sfi/research/inResidence/june99.html

3

some main approaches and areas of findings

1 Urban scaling: distributional scaling and historical transitionsCity 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-exponentialsPeriodizing: 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 conflictorganizational change at macro level and micro level.

Outline re: civilizations as dynamic networks

General approach: interactive multi-nets, networks among and between different types of entities in time series with changing links and attributes

4

City Networks

Routes, Capacities

Velocities and Magnitudes of trade

Organizational transformationof nodes

STATES MARKETSfrom factions & coalitions from structurally cohesiveto sovereignty - emergent k-components - emergent Spatiopolitical units Network units (overlap)

City attributes and distributions

Urban Hierarchy-Industries, _______Commerce, Finance

City Sizes Hierarchy

Hinterland Productivity

Dynamics from

Structural Cohesion

Unit Formation (e.g. polities)

Demography/Resources

Conflicts

Co-evolution time-series of Cities and City Networks

Interference and attempts at regulation

Sources of boundary conflicts

begin

periodize

5

Geoff West, Luis Bettencourt, José Lobo. 2005 (Pace of City Life):

Innovation-Dependent (Superlinear), Linear, and Scale-Efficient (Sublinear) Power Laws

0

10000

20000

30000

40000

50000

60000

70000

0 2000000 4000000 6000000 8000000 10000000

City Sizes

Cit

y F

un

ctio

ns

R&Dchina-superlinear

R&Dfrance-superlinear

Elec.Cons.-linear

Gas Sales-sublinear

Urban Scaling: Functions

6

Superlinear ~ 1.67

Linear ~ 1

Sublinear ~ .85

ISCOM working paper

7

1

10

100

1000

10000

100000 1000000 10000000

(White, Kejžar, Tsallis, and Rozenblat © 2005 working paper)

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

Not a good fit to overall city size distributions

Power laws and Zipf’s law might fit upper bin frequencies for city sizes but not the whole curve

inset: y = cumulative

number of people

in these cities

Dashed line = portion of distribution that is "power-law“ (but is exaggerated in the upper bins)

Horizontal axis x = binned (logs of city size)

Vertical axis y =

cumulative number

of cities at this log bin or higher

10000000

100000000

1000000000

100000 1000000 10000000

Urban Scaling: City Sizes

α=1β=2

Example: 1950 United Nations data for world cities

8

% Urban in Europe

fitted q-exponential distributions, q, κ.

power law coef. β = 1/(q-1) equals 2 for q = 1.5, thus more equality at the asymptote …

more inequality α = 1at the asymptote: α = 0.24 β = 2

β = 1.24 q = 1.5 q = 1.8

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 should straight line fits in this log-log graph.

The x axis has the city size-bins, 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.

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.

(for 1800)

for 2005:

City-size bins

1950

Units of 10K

Q-exponential scaling ~ .99+ fit to 18 post-1800 and 22 pre-1800 distributionsAt time t, population y(x) ≈ y(0) [1 + (1–q) x/κ)]1/(1–q), as function of q, κ, binned size x

α = 1 β = 2 q = 1.5

9

Stylized contrasts and historical examples in unlogged graphs:

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

Log city bin size

Realistic critical feature different than power laws: city size truncation

inegalitarian fat tail; e.g., industrial revolution pushes out to fatten smaller towns; hubs in average neighborhoods

of average local nghbhood heterogeneity wrt hubs (L Adamic et al 2003)

Log cumulative populations in cities at least this bin size

egalitarian thin tail; few hubs (bigger towns) in average neighborhoods

α ~ 1, high e.g., year 2005

α < 1, low e.g., year 1800

Stylized q-exponentials

(note the connection here to networks: city links to other nearby cities)

10

β=2 (α=1) long thin tail; greater size equality

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 power- law distribution to flatten as α (=β-1)→0. This is more realistic than a scale-free model.

β → 1 (α → 0) thicker tail; greater size inequality

430 BCE to 1750

11

Kappa detrended

y = 12298x-1.5684

R2 = 0.8263

y = 0.000052x + 1.700698

R2 = 0.016064

0.01

0.10

1.00

10.00

100.00

0 5 10 15 20 25Hundreds

World city sizes scaled in 28 reliable-estimate periods, fitted slope q & scale κ (kappa)

2000 1750 1500 1250 1000 750 500 250 0 -250

-4

-2

0

2

4

6

8

-250 0 250 500 750 1000 1250 1500 1750 2000

q (NLS)

κ detrended

HiHi HiLoLo Lo

More inequality q of city sizes

Scale κ of city sizes, detrended

At time t, population y(x) ≈ y(0) [1 + (1–q) x/κ)]1/(1–q), as function of q, κ, binned size x

heterarchy

Detrending method: κ increasing and headed to singularity post-2000

12

y = 12298x-1.5684

R2 = 0.8263

y = 0.000052x + 1.700698

R2 = 0.016064

0.01

0.10

1.00

10.00

100.00

0 5 10 15 20 25Hundreds

World city sizes scaled in 28 periods, fitted slope q, scale κ (kappa)

2000 1750 1500 1250 1000 750 500 250 0 -250

-4

-2

0

2

4

6

8

-250 0 250 500 750 1000 1250 1500 1750 2000

q (NLS)

κ detrended

HiHi HiLoLo Lo

At time t, population y(x) ≈ y(0) [1 + (1–q) x/κ)]1/(1–q), as function of q, κ, binned size x

Time is reversed in the two graphs

13

Contiguous time periods (verified by runs test), discrete (1-7) periods

1.20 1.40 1.60 1.80 2.00 2.20

qNLS

0.00

5.00

10.00

15.00

kDet

ren

ded

-200

100

361622

80010001100

11501200

12501400

1450

160016501700

1750

1800 1825

1850

19001925

1950 1955

19601965

19701975

1980

1985

egalitarian hierarchy q inegalitarian hierarchy

>1950 Mass urbanization

World cities phase diagram

14


Pop. Size Hierarchy

Urban Industries plus

Commerce, Finance


City Networks

Routes, Capacities, Markets


Organizational transformationof nodes, periods;

commercial, financial, religious

Dynamics from

Structural Cohesion



Conflicts

Co-evolution of Cities and City Networks

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.

periodize

15

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)

16

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 (1340-85)

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 of European

hubs

Financial Capital :Periods

c.1000 Constantinople Venice c.1100-1297

1298-1380 Genoa Holland 1610-1730

1797-1917 Britain U.S.A. 1950-?

17

Euro-Hegemon examples

(Arrighi 1994)

Commercial

Financial

(hegemonic cities in historic order)

Constantinople

Venice

Genoa

Amsterdam

London

New York

Amsterdam

18

Given its 13th C betweenness centrality, Genoa generated the most wealth

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.

Size of nodes adjusted to indicate differences in betweenness centrality of trading cities in the banking network

Betweenness Centralities in the banking network

Episodically, in 1298, Genoa defeated the Venetians at sea.

Repeating the pattern, England later defeats the

Dutch at sea

19

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.

Core towns

Linking kaufmannskirchen (by Saint name)

Distant towns

Additional linking kaufmannskirchen

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.

Northeast

Southwest

Bipartite network cohesion in Hanse saintly brotherhood trade organization

21

C C C C C C C C C C I ? ? ? ? I I I I I I I I I I I ? ? I I I I I I q H i ? ? ? ? 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 P P ? ? p P ? ? ? E E E E E E E ? ? E E E E E E E ? E E E q L o F F F F F F F F F F F F F F F 1 1 1 1 1 1 1 1 1 1 2 0 1 2 3 4 5 6 7 8 9 0 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 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)

Inflation Lo/hi

Financial

Commercial

Financial capital

22

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

Type of hegemony and inflation as q-correlated temporal variables

Inflation Lo/hiInflation Lo/hi

Financial

Commercial

Financial capital


23

Transaction costs, hegemony and inflation as q-correlated temporal variables

Conflict on Land Sea trade routes safer than land, 1318-1453/4+ (Spufford:407)

Inflation Lo/hi

Landed Armies safe land routes 1500-1650 Maritime Conflicts (Jan Glete)

Landed Trade Secure

Dominant Routes

Sea routes safe French Sov.

Peace of Westphalia

Baltic conflicts: connection to Novgorod and Russia (lost)

Swedish hegemony

European access

Struggle for Empire: Sea Battles to 1815

Global Maritime

Economy Industrial Rev. from 1760

Political Revolutions to 1814

Trade net

(low cost)

versus

(high cost)

Maritime (low cost)

versus

Land routes trade

(pop. growth)

Financial capital

CommercialC C C C C C C C C C I ? ? ? ? I I I I I I I I I I I ? ? I I I I I I q H i ? ? ? ? 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 P P ? ? p P ? ? ? E E E E E E E ? ? E E E E E E E ? E E E q L o F F F F F F F F F F F F F F F 1 1 1 1 1 1 1 1 1 1 2 0 1 2 3 4 5 6 7 8 9 0 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 L/h lo/hi inflation figures (L=depression) are for that year forward

24Hierarchy (I) city distributions landed civil conflict, with multiple generation time lag

Recode previous slide predict landed inter-national conflict

Hegemony-type and inflation as q-correlated temporal variables

Conflict on Land Sea trade routes safer than land, 1318-1453/4+ (Spufford:407)

Inflation Lo/hi

Landed Armies Land Routes safer than sea 1500-1650 Maritime Conflicts (Jan Glete)

Landed Trade Secure

Sea routes safe French Sov.

Peace of Westphalia

Baltic conflicts: connection to Novgorod and Russia (lost)

Swedish hegemony

European access

Struggle for Empire: Sea Battles to 1815

Global Maritime

Economy Industrial Rev. from 1760

Political Revolutions to 1814

Landed inter-national conflict is protracted

(versus)

Landed international peace (incl. WW I or II followed by peace)

Land routes UNSAFE

versus

Land routes SAFE

Financial capital

Commercial

Commercial capital competition landed inter-national conflict, with generational time lag

Interactive Dynamics

Hierarchy

Heterarchy

Land Routes

From Dominant Routes to a Land Routes variable

Sea unsafe star bank routes


25

Commercial and financial centers as q-correlated temporal variables

Inflation Lo/hi

Florence

Venice

Arras

Bruges

Antwerp

Amsterdam

London

Champaign Fairs

Constantinople

Genoa

Shift of financial center due to civil war of 1480

Industrial center Commerce center Commercial Finance =Blue Red = Financial profit center

(Blue = Commercial Finance Red = Medici Bank & profits ; controlled by Florentines)

Domestic Fustians (innov.: cotton-linen) Imported cotton, manuf.

woven cotton

Commercial

Financial capital

Industry

Add: religious centered trade



Underwarer star bank

routescohesive bank routescohesive bank routes cohesive bank routesC C C C C C C C C C I ? ? ? ? I I I I I I I I I I I ? ? I I I I I I q H i ? ? ? ? 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 P P ? ? p P ? ? ? E E E E E E E ? ? E E E E E E E ? E E E q L o F F F F F F F F F F F F F F F 1 1 1 1 1 1 1 1 1 1 2 0 1 2 3 4 5 6 7 8 9 0 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 L/h lo/hi inflation figures (L=depression) are for that year forward

26


Pop. Size Hierarchy


Commerce, Finance


City Networks

Routes, Capacities



Dynamics from

Structural Cohesion



Conflicts


28

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.

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.

(early slide, merely illustrative, not to scale, network incomplete)

Lübeck

banking networkcohesion

29

the banking network, main routes only (again, geographically).

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.

Control networks often rely on unambiguous centralized spines but their operation relies on feedback in cohesive networks.

banking networkhierarchy

30In Northern Europe the main Hanse League port of Lubeck had about 1/6th the trade of Genoa, 1/5th that of Venice.

Red 3-components

Middle East and its 3-component also

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.

31

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?

http://eclectic.ss.uci.edu/~drwhite/Civ/silkjadeporcelain.gif

http://eclectic.ss.uci.edu/~drwhite/Civ/silkjadeporcelain.gif

http://eclectic.ss.uci.edu/~drwhite/Civ/spicetr.gif

http://eclectic.ss.uci.edu/~drwhite/Civ/spicetr.gif

http://eclectic.ss.uci.edu/~drwhite/Civ/goldsalt.gif

http://eclectic.ss.uci.edu/~drwhite/Civ/goldsalt.gif

32

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

33

(figures courtesy of Andrew Sherratt, ArchAtlas)

Cohesive extension of trade routes leads to a host of other developments…

34

Multiconnected regions => structural cohesion variables

During classical antiquity trade routes become

much more structurally

cohesive from China to France

35


36


37

Some changes in the medieval network from 1000 CE


38

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 25-year 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)


39


Pop. Size Hierarchy


Commerce, Finance


City Networks

Routes, Capacities



Dynamics from

Structural Cohesion



Conflicts


Scarcity; Inflation; Competition; Sociopolitical violence;

Periods of:

40

• 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)

Data sources and dynamic interaction analyses

41Chinese phase diagram

(Turchin 2005)

http://eclectic.ss.uci.edu/~drwhite/Civ/Spuf/Tur/ChinaPopWarPhaseSpace.jpg

42

English sociopolitical violence cycles don’t directly correlate but lag population cycles. Detrended English population cycles, 1100-1900, occur every 300-200 years.

Source: Turchin

(Turchin 2005)

43

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)

http://eclectic.ss.uci.edu/~drwhite/Civ/Spuf/Tur/ChinaEnglandPopWarPredictions.jpg

44

0

10000

20000

30000

40000

50000

60000

70000

0 2000000 4000000 6000000 8000000 10000000

City Sizes

Cit

y F

un

ctio

ns

R&Dchina-superlinear

R&Dfrance-superlinear

Elec.Cons.-linear

Gas Sales-sublinear


Revisiting the Innovation-Dependent Superlinear Case

Unsustainable superlinear growth

superlinear growth crisis



Resetting growth through costly

innovation


innovation


innovation

45

World population 'response' to power-law city growth

Cities and hinterlands context variables

Kremer data; Fitted Coefficients of Equation 1, Nt = CN /

e(t0 – t)

Start Yeark CN Up to (following period) Period

Length Log of Length . (linearly decreasing)

-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

Post-1962 (ditto) ? c.100? 2.0

1250

46

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.

47


Revisiting the Innovation Dependent Superlinear Case

World pop. Downturn

World urbanization inflections

(I have added the correlations of world and NYC population shifts)

48

Economic macro variables

1900

Renaissance Equilibrium (begins with

economic depression)

Stylized facts:

1. Gross World Economic Product grows not in proportion to 1/(time to singularity), as does population, but 1/ /(time to singularity)2

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.

(David Hackett Fischer 1996)

(Turchin 2005)

49


Pop. Size Hierarchy


Commerce, Finance


City Networks

Routes, Capacities



Dynamics from

Structural Cohesion



Conflicts


50

Effects of Inflation of Land on Monetization

(Relative to Carrying Capacity) Prices Inflation Demand for Peasants money rents to cities Real wages In kind payment of serfs, Elites to cities Conspicuous (low) retainers salaried laborers consumption Demand for Poverty forces more Demand for Coinage prestige goods meltdown of silver silver mining

Monetization (Velocity of Money in Exchange)

Thresholds (Variables affecting transition)

Reorganization (to handle higher velocities)

e.g., Division of labor, new techniques, road building, bridge building, new transport

Merchants/agents Governments/agents Churches/agents Elites/agents

GET TURCHIN VARIABLES

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.

(Spufford 2002)

51

– 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/cond-mat/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.

References

52

City Networks

Routes, Capacities



STATES MARKETSfrom factions & coalitions from structurally cohesiveto sovereignty - emergent k-components - emergent Spatiopolitical units Network units (overlap)


Pop. Size Hierarchy


Commerce, Finance


Dynamics from

Structural Cohesion



Conflicts


Interference and attempts at regulation

Sources of boundary conflicts

54

0

5000

10000

15000

20000

25000

30000

35000

40000

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

-100000

-50000

0

50000

100000

150000

200000

250000

300000

350000

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Semilog y ~ log(x): poor fit

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:

Actual 1965 data on distribution at one time smoothed cumulative distributions

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.

y = 3E+06x-0.4432

R2 = 0.9714

0

50000

100000

150000

200000

250000

300000

350000

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Power-law: poor fit

Time1 Time2 Time3 Time4 Time5

“innovative bulges” in city

sizes move thru time

Fitting here uses bins with largest numbers

55

y = -40077Ln(x) + 357246R2 = 0.978

y = -78173Ln(x) + 711965R2 = 0.9913

100

50100

100100

150100

200100

250100

300100

350100

100 1100 2100 3100 4100 5100 6100 7100 8100 9100 10100

unlogged

Semilog y ~ log(x) scaling r2~.99 fits

y = -208530Ln(x) + 2E+06

R2 = 0.9956

y = -347720Ln(x) + 3E+06

R2 = 0.994

0

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1800000

100 1000 10000 100000

1950 to 2005

100

1100

2100

3100

4100

5100

6100

7100

8100

9100

10100

100 1000

1800 and earlier

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.

y = -40077Ln(x) + 357246

R2 = 0.978

y = -78173Ln(x) + 711965

R2 = 0.9913

100

50100

100100

150100

200100

250100

300100

350100

100 1000 10000

1950 and earlier

To

tal n

um

be

r of p

eo

ple

in citie

s at o

r ab

ove

the

city size b

in

city size bins, logged

Which is an integral of Zifp's law, approximately a log if the exponents are exactly 1)

Changes in slope over time are not directly comparable over historical periods: they tend to flatten further back in time but irregularly.

56

% Urban in Europe

fitted q-exponential distributions, q, κ.

power law coef. β = 1/(q-1) => (= 2 for q = 1.5) thus more equality at the asymptote

q =1.81 q =1.61

q =1.70

q =1.57 q =1.50q =2.01q =2.08q =2.01q =1.84 q =2.1 q =1.9 more inequality α = 1at the asymptote: α = 0.24 β = 2

β = 1.24 q = 1.5 q = 1.8

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 be best-fitted by a straight line in this log-log graph.

The x axis has the city size-bins, 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.

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.

(for 1800)

(for 2005)

City-size bins

1950

Units of 10K

Q-exponential scaling ~ .99+ fitAt time t, population y(x) ≈ y(0) [1 + (1–q) x/κ)]1/(1–q), as function of q, κ, binned size x

α = 1 β = 2 q = 1.5

civilizations as dynamic networks

Documents

intercity networks

dynamic networks cities

iscom support of collaboration

distributional scaling

historical urban size

generous support

weeks of support

attributescity networks