SelfOrganised Criticality and Complication in the U'K' Urban Distribution

1
Self-Organised Criticality and Complication in
the U.K. Urban Distribution

• Alasdair (Sasha) Anderson
• a.anderson1_at_lancaster.ac.uk

2
Criticality

• Notion of criticality comes from the Greek
  kritikos
• ???t???? able to discern or judge
• Its application in the context of chemistry
  denotes a phase transition from one state of
  matter to another.

3
Criticality in Chemistry
4
Critical Transitions in History

• Equivalent phase transitions in human history
• c.40,000 BP Great Leap Forward
• Sophisticated co-operation in hunting networks
  of barter trade
• c.4000BC Neolithic Revolution
• Agriculture and rural settlement
• c.AD1750 Industrial Revolution
• Secondary manufacturing and urbanisation

5
Critical Transitions in History
6
Self-Organisation

• Structure appears within the system independently
  of external force.
• It is determined by local interactions of
  multiple component agents or degrees of freedom.
• Goal of system is an attractor in phase space.

7
Self-Organisation in History

• The essence of history - including that of the
  urban distribution - is the interactive process
  of constant self-organisation between four
  categories of agency
• Individuals
• Collectives (societies, families, nations,
  classes)
• Environments (location, resources, climate)
• Memes (units of replicated information, notably
  ideas)

8
Self-organised Criticality

• Per Bak et al. introduced the concept in
  Self-organised Criticality an Explanation of 1/f
  noise (1987).
• Sandpile model.
• Forest fires
• Earthquakes
• Cellular Automata (J.H. Conway)
• Evolutionary Biology (S. J. Gould)
• Size and Frequency of Wars (G.G. Brunk)
• Urban Distribution (M. Batty, Y. Xie)

9
Lessons from the Sandpile Model

• 1. System begins in a equilibrium state (i.e.
  flat).
• 2. Crosses the threshold to non-equilibrium that
  resolves to a power law distribution.
• 3. Non-equilibrium has a numerical value, the
  angle of repose (32 to 34º), suggesting a point
  attractor.
• 4. Scale Invariant Behaviour - it applies both to
  sand dunes and egg timers.
• 5. Connectivity between every grain of sand and
  every other.
• 6. Maintained by avalanches (punctuations) of
  varying sizes, also conforming to a power law.

10
Equilibrium Phase

• Early phases of settlement equate most closely to
  the random distribution of the environment
  (similar to sand in its flat configuration).
• In this scenario, individual leaders could
  exercise a strong influence on the future
  evolution of the system, reflected in the naming
  of settlements.
• Edinburgh (Din Eidyn - Eidyns Hill-fort)
• Anglo-Saxon settlements with -ing suffix (people
  of )

11
Power Law Distribution

• G.K. Zipf (1949) in Human Behaviour and the
  Principle of Least Effort proposed the
• rank-size principle from the frequency of words
  in a text.
• Thence, the Zipf Law has been applied to cities,
  on the basis of their distribution to a power
  law.

12
Line of Criticality 1520
13
Line of Criticality 1600
14
Line of Criticality 1670
15
Line of Criticality 1700
16
Line of Criticality 1750
17
Line of Criticality 1801
18
Line of Criticality 1821
19
London, Southwark, and Lambeth (1747)
20
London, Southwark, and Lambeth (1802)
21
London, Southwark, and Lambeth (1830)
22
Line of Criticality 1851
23
Line of Criticality 1861
24
Line of Criticality 1871
25
Line of Criticality 1881
26
Line of Criticality 1891
27
Line of Criticality 1901
28
Line of Criticality 1901
29
Line of Criticality 1911
30
Line of Criticality 1921
31
Line of Criticality 1931
32
Line of Criticality 1938
33
Line of Criticality 1947
34
Line of Criticality 1951
35
Line of Criticality 1961
36
Line of Criticality 1971
37
Line of Criticality 1975
38
Line of Criticality 1981
39
Line of Criticality 1985
40
Line of Criticality 1989
41
Line of Criticality 1991
42
Line of Criticality 1993
43
Are the Data Wrong?

• Data between 1901 and 1961 contain anachronism of
  Greater London post-1965 London Boroughs, rather
  than Metropolitan and Municipal Boroughs.
• Data after 1961 contain spurious administrative
  units (Kirklees, Wirral, West Norfolk).
• However, this is insufficient to account for the
  persistence of the line.

44
Is the Theory Wrong?

• Cut-off point is misleading, as it truncates the
  fat tail or long tail. Data without a cut-off
  show settlements below a point that apparently
  violates the law.
• The primate city is consistently too populous for
  the prediction (possibly for reasons which may be
  explained).
• However, the very number of settlements
  conforming to the line and its persistence across
  an extended period of time support the conclusion
  that a power law is involved.

45
Is Reality Wrong?

• Should London be depopulated to conform to power
  law?
• Town Country Planning Act (1947) Green Belt
  New Towns Decentralisation policies of 1960s and
  70s attempted this (rather as the Elizabethans
  had done).
• N. Georgescu-Roegen in Entropy and the Economic
  Process (1971) was proposing radical
  de-urbanisation.
• Should population be imposed on the smaller
  settlements?

46
Power Law Line of Best Fit
47
Panocephalicity and Catouricity
48
Panocephalicity of London
49
Panocephalicity of London
50
Catouricity

• According to the theory, the cut-off point
  excludes the rural settlements, the origins of
  the urban system. (M. Batty).
• However, the smallest settlements are not all
  characteristically rural.
• This downward morphology is evident to the very
  tip - scale invariant behaviour is an essential
  feature of the distribution.

51
Catouricity in Small Settlements
52
Decentring and Punctuations

• Fernand Braudels concept of centring,
  decentring, and recentring describes radical
  shifts of the world economic centre. These
  represent high-level landslide-like events in
  economic history
• Venice (1380s-1500)
• Antwerp (1500-1550)
• Genoa (1550-1600)
• Amsterdam (1600-1780)
• London (1815-1900s)
• New York (1900s - )

53
Decentring and Punctuations

• Shifts in rank and population size also
  correspond to the avalanches in the Per Bak
  model.
• A manifestation of complication in human systems
  is that population transfers between urban
  centres (unlike sand) can either flow up or down
  the distribution
• These shifts also equate to the punctuated
  equilibria proposed by Stephen Jay Gould in
  evolutionary biology.

54
Decentring and Punctuations
55
Decentring and Punctuations
56
Decentring and Punctuations
57
Self-Organised Criticality and Complication in
the U.K. Urban Distribution

• Alasdair (Sasha) Anderson
• a.anderson1_at_lancaster.ac.uk