New approaches to the Theran Eruption - Amazon S3 · 2015. 12. 4. · Thera (Santorini) in 1988 (almost Icarus II!) Thera is North of Crete: • Summer winds are Northerly [ • Winter

New approaches to the Theran Eruption

Ray Rivers (Physics, IC)

Collaboration with Carl Knappett (Art, Toronto) Tim Evans (Physics, IC)

Maritime Networks Toronto 2013

Roughly self-contained in space and time -c.2000 BC Distinct Minoan culture starts

Middle Bronze Age (MBA) Aegean

Roughly self-contained in space and time -c.2000 BC Distinct Minoan culture starts -c.1700 BC Knossos plays a dominant role

Knossos


Roughly self-contained in space and time -c.2000 BC Distinct Minoan culture starts Thera: ‘Gateway’ for Minoanisation of S. Aegean

Knossos

Thera


Thera as gateway:

Knossos

Thera


Thera as gateway: Destroyed by volcanic eruption in 1575 ± 50 BC ! (LMIA/LMIB border)

Knossos

Thera



Knossos

Thera

• Huge ash (tephra) deposits


Thera now uninhabitable, but Minoan maritime network continues to thrive!


Knossos

Thera

• Huge ash (tephra) deposits


Thera now uninhabitable, but Minoan maritime network continues to thrive!

End of Minoan culture much later - ‘Burning of the Palaces’

© Imperial College London Page 9

• Have a rich network which can survive local disaster!

- A little like an extreme case of crop failure!

• Advantage: Have some knowledge of before and after, which we don’t for drought.

Answer:

Network resilience: Straightforward test for network modelling!

Question: How do we understand this?


Networking Thera:

• Vertices = Major Population or Resource Sites

• Edges = Exchange between sites

- physical trade of goods or transmission of culture

- soft power and hard power

• Interactions controlled by physical limitations of ancient sea travel -- Simple Links


Modelling Cycle

ARCHAEOLOGICAL DATA

‘Predictions’

MODEL

Input settings:

‘Geophysical’

Input parameters:

‘Sociophysical’

Consistency check

12

MBA Nodes/Site settings:

39 key sites:

Knossos (1)

Thera (10)


Model:

Settings


Model:

Settings

Parameters


Model:

Settings

Parameters

Output


Outputs:

• ‘Exchange’: Tij

Conflation/flattening of ‘exchange’ into a single measure

• Centrality: Page Rank

Sites with strong exchange activity

• ‘Betweenness’:

Measures how sites and links are on paths between other sites.

Several definitions in each case!

• Population: Pi


Agency: Networks come into existence and survive for many reasons.

Optimisation: Assume networks are ‘optimal’ in some sense

Simple division:

• Most ‘likely’ networks

• Most ‘beneficial’ networks

Page 18

‘Most likely’ Networks: Epistemic approach

– Maximum Entropy modelling

1. Generalised gravity models: Alonso models

• Gravity models

• Transport models

• Retail models – Iron Age Greek city states

Tribute? - Rihll and Wilson

2. Intermediate opportunity models

• Migration/commuting models

• Include generalisations of PPA

Page 19

‘Most likely’ Networks: Epistemic approach

– Maximum Entropy modelling

1. Generalised gravity models: Alonso models

• Gravity models

• Transport models

• Retail models – Iron Age Greek city states

Tribute? - Rihll and Wilson


• Migration/commuting models

• Include generalisations of PPA

Page 20

• Don’t expect too much

- very broadbrush!

• E.g. Unadorned simple gravity model or PPA

• But still very useful

Very few knobs

Page 21

Example: Urban transport (e.g. Toronto)

1. Decide on basic network settings e.g.

• Tram stops (nodes/sites)

• Fare structure

• Total daily expenditure

• Total daily mileage

2. Construct all networks commensurate with this ,

Labelled by # of passengers on each route (exchange)

and take a picture of each:

3. Give each equal weight and Look for the (statistically)

most likely network:

- the answer - no knobs!


‘Most beneficial’ Networks: Ontic approach

3. ‘Cost – benefit’ analysis:

• Considerable freedom in choosing costs and benefits

• More like a construction kit than a black box!

Some generalities but ultimately bespoke


‘Most beneficial’ Networks: Ontic approach

3. ‘Cost – benefit’ analysis:

• Considerable freedom in choosing costs and benefits

• More like a construction kit than a black box!

Need to worry that you are not getting out what you put in!

Some generalities but ultimately bespoke


Question:

What is special about the MBA Aegean?

How universal are network exchange models?

How would we know that our output is not equally acceptable as an iron age network or even a contemporary exchange network?


Model:

Settings

Parameters


Regional groupings connect at sea distances of D ≈ 110km

Sea distance from Knossos to Thera!

Key point: MBA Marine technology matches distances:

Distance scale D ≈ 110km crucial:


Key point: MBA Marine technology:

• Sail replaces\supplements oar for large distances

• Single journeys of 100km possible and

relatively easy

• For the first time in the BA, technology is good enough to enable a fully connected exchange network to form

• This is what singles out MBA from any other network analysis on the same set of sites

• Should only choose models whose dynamics are sensitive to geography!


Key point: MBA Marine technology:

• Sail replaces\supplements oar for large distances

• Single journeys of 100km possible

• For the first time in the BA, technology is good enough to enable a fully connected exchange network to form

• This is what singles out MBA from any other network analysis on the same set of sites

• Should only choose models whose dynamics are sensitive to geography!

Effective distances: Sea journey (round headlands) + (frictional) land journey For the moment ignore wind – assume it averages over travel season Will repair this later!

Minoan Civilisation: 3 phases

• Pre-eruption

Vigorous maritime exchange network

• Eruption!

• Post-eruption resilience

(Even more?) vigorous maritime exchange network

• (In)stability and Fire Destruction

Internal collapse/external invasion/earthquake

29

Page 30

1. Generalised gravity models:

• Simple Gravity Model (NULL)

• Singly constrained Gravity model

• Doubly constrained gravity model

• Retail models - Rihll and Wilson


• PPA (NULL)

• Directed PPA

Pre-eruption: ‘Most likely’ model selection (D given)

Cost/benefit analysis: ariadne • Benefits in establishing links • Benefits from local resources • Costs in supporting links, supporting population

Imperfect rational choice : ‘Optimisation’

• Trade off ‘costs’ against ‘benefits’ to best advantage

- minimising ‘social potential’

31

Pre-eruption: ‘Most beneficial’ model selection (D given)


Model:

Model aims for ‘best’ Settles for the ‘good’

Stochastic Optimisation!

is not

Strong restrictions!

• familiar ‘catastrophe’ fold in site exploitation (population) if exchange drops while lacking self-sufficiency

Agrees with Broodbank et al. (2005) “For the southern Aegean islands

in the late Second and Third Palace periods, ... there may often have been precariously little middle ground to hold between the two poles of (i) high profile connectivity, wealth and population, or (ii) an obscurity and relative poverty in terms of population and access to wealth that did not carry with it even the compensation of safety from external groups”.

is more



‘Goldilocks’ scenario:

• not too ‘cold’

• not too ‘hot’

• ‘just right’

is more



Alternatively: harrys – greece.com?

‘Complete’ networks

– change models! (e.g. LBA?)

• distance less important

• short-distance ‘Brownian’ motion replaced by ‘non – geographic’ motion

- Toronto Transport Commision?


Tactics:

1. See which models describe the pre-eruption pattern of exchange?

Weed out models that don’t work!

2. Do surviving models help us understand the survival of the network?

Weed out further models!

Pre-eruption: Model selection

Model Sensitivity to D*

Directed Weak links

Minoan

Standard Gravity model: D (NULL)

Hi-B, Hi-

W

Singly constrained gravity model: D

Hi-B, Lo-

W

Doubly constrained (transport) gravity model: D

Hi-B, Lo-

W

Retail (Rihll & Wilson) gravity model: D + ‘attraction’

**

Lo-B, Lo-

W

PPA (k=4) (NULL) ***

Directed PPA (k=4) ***

Ariadne : D + local resources + pop./network costs

Ranking tables for vertices not a good guide – links are more important here!

Pre-eruption: Model selection

Model Sensitivity to D*

Directed Weak links

Minoan


Hi-B, Hi-

W

Singly constrained gravity model: D

Hi-B, Lo-

W

Doubly constrained (transport) gravity model: D

Hi-B, Lo-

W

Retail (Rihll & Wilson) gravity model: D + ‘attraction’

**

Lo-B, Lo-

W

PPA (k=4) (NULL) ***

Directed PPA (k=4) ***

Ariadne : D + local resources + pop./network costs

Ranking tables for vertices not a good guide – links are more important here!

Gravity model:

D = 60km

D = 100km

Example: sensitivity to D

Doubly constrained Gravity model:

Immediate post-eruption: 2 Models

Model Sensitivity to D Minoan


Ariadne : D + value of local resources + pop./network costs

No Contest!

Standard Gravity Model: No rearrangement – just deletion!

Pre-eruption: Post-eruption

Ariadne (V-Rank; L-Weight)


Ariadne (V-Rank; L-Weight) Strong rearrangement through Phylakopi!

Ariadne (V-Rank; L-Weight)


“the evidence points to, if anything, an increase in Minoan trading activity in LM IB, particularly in our excavations at Ayia Irini, Keos (14) where we literally had thousands of LM IB vases imported from outside” (Davis 1980)

Keos!

Ariadne (V-Rank; L-Weight) Strong rearrangement through Phylakopi!

Later post-eruption behaviour: Endogenous Instability Increasing costs of sustaining network

“ a centralised economy which may be

working under some adversity which might be increased population … people coming in from Thera … What I think you would expect to see is not a gradual decline, but an increasing intensity in the various subsystems of the culture system, including an increasing level of trade, until the system breaks down altogether.”

Renfrew (1980)




Renfrew (1980)




Renfrew (1980)

Endogenous Instability Increasing costs of sustaining network

46

• A few strong links form at the expense of weak links

• Network collapses as the few remaining strong links disappear

• Stability correlated to existence of weak links

Alternatives: Avoiding instability Waiting for the Myceneans (?)




BUT instability generic!

Winds:

Good proof of principle but still too simple in some regards:

Meet Daedalus II ! Aka Kanellos Kannelopoulos Human-powered flight from Heraklion to Thera (Santorini) in 1988 (almost Icarus II!) Thera is North of Crete: • Summer winds are ‘Northerly’ • Winter winds are ‘Southerly’ (and stormy) • Occasional periods of Southern winds (or little wind) better weather

for travelling North

Daedalus II flew on one of the very few Spring days when weather was calm and there was a Southerly wind!

51

Winds:

Good proof of principle but still too simple in some regards:

Meet Daedalus II ! Aka Kanellos Kannelopoulos Human-powered flight from Heraklion to Thera (Santorini) in 1988 (almost Icarus II!) Thera is North of Knossos: • In general, summer winds are ‘Northerly’ • In general, winter winds are ‘Southerly’ (and stormy) • Occasional short periods of Southern winds (or little wind) in sailing period

Daedalus II flew on one of the very few Spring days when weather was calm

and there was a Southerly wind!

52

Winds: Idealised two stage process

1. Construct an effective distance dN between each pair of sites in the presence of ‘Northerly’ winds

- low ‘friction’ going ‘South’

- high ‘friction’ going ‘North’

- no change for ‘East – West (fuzzy)

Construct an effective distance dS between each pair of sites in the presence of ‘Southerly’ winds

- low ‘friction’ going ‘North’

- high ‘friction’ going ‘South’

- no change for ‘East – West (fuzzy)

53

Winds: Idealised two stage process

2. The ‘ease of travel’ function f(d/D) in the term showing benefits of exchange is replaced by

f = (1- ε ) f(dN/D) + ε f(dS/D)

where ε is the frequency of S. winds in the sailing period

But

• N. Crete more active (East-West)

• More connection Crete - Rhodes (?)

• Less connection Cyclades to Dodecanese (?)

54

Too soon to see systematic behaviour - in progress!

• .MBA provides a Goldilocks environment for network formation because marine technology in step with geography.

• Entropy models too rigid – nothing special about MBA.

• ariadne takes marine technology into account; geographical sensitivity, weak links, directed links, emphasis on N. Crete and significant Thera

Preliminary conclusions:

55

• Eruption of Thera leads to plausible rearrangement

– not just link erasure.

• Network continues to thrive!

• Catastrophe fold shows existence of intrinsic instability – collapse of Minoan dominance?

• Natural way to include variable winds – more work needed!

Preliminary conclusions (cont’d):

56

References:

C. Knappett, T. Evans, and R. Rivers, 2008.

'Modelling maritime interaction in the Aegean Bronze Age', Antiquity 82, 1009-1024.

T. Evans, C. Knappett, and R. Rivers, 2009.

'Using statistical physics to understand relational space: a case study from Mediterranean prehistory',

in D. Lane, S. van der Leeuw, D. Pumain and G. West (eds.), Complexity Perspectives in Innovation and Social Change, 451-79. Berlin: Springer Methodos Series 7.

C. Knappett, T. Evans, and R. Rivers, 2011.

'Modelling maritime interaction in the Aegean Bronze Age II: The eruption of Thera and the burning of the palaces’ , Antiquity 85, 1008 – 1023

R Rivers, C Knappett, T Evans 2013,

‘Network Models and Archaeological Spaces’, Computational Approaches to Archaeological Spaces, Editor(s): Bevan, Lake, Left Coast Press, ISBN:978-1-61132-346-7

R Rivers, C Knappett, T Evans 2013,

‘What makes a site important? Centrality, gateways and gravity’, Network Analysis in Archaeology: New Approaches to Regional Interaction, Editor: Knappett, OUP, Pages:125-150

57

Thank you!

Notes and Addenda

“For the southern Aegean islands in the late Second and Third Palace periods, an age of intensifying trans-Mediterranean linkage and expanding political units, there may often have been precariously little middle ground to hold between the two poles of (i) high profile connectivity, wealth and population, or (ii) an obscurity and relative poverty in terms of population and access to wealth that did not carry with it even the compensation of safety from external groups”.

Broodbank et al. (2005)


Knossos

Thera

• Equivalent to 10 subs’ worth of tomahawk cruise missiles with W80 nuclear warheads or 2 Trident submarines fully loaded


RW Gravity model

RW Gravity model

RW Gravity model

RW Gravity model

RW Gravity model

RW Gravity model

RW Gravity model

Ariadne (V,L - betweenness)

Ariadne (V,L - betweenness)

Keos! “the evidence points to, if anything, an increase in Minoan trading activity in LM IB, particularly in our excavations at Ayia Irini, Keos (14) where we literally had thousands of LM IB vases imported from outside” (Davis 1980)

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This might be the type of network that an archaeologist would like


-c.2000 BC Distinct Minoan culture starts Thera: Important link between N. Crete and the S. Aegean

Knossos

Thera


-c.2000 BC Distinct Minoan culture starts Thera: Destroyed by volcanic eruption in 1575 ± 50 BC (LMIA/LMIB border)

Knossos

Thera


-c.2000 BC Distinct Minoan culture starts Thera: Destroyed by volcanic eruption in 1575 ± 50 BC (LMIA/LMIB border) Thera now uninhabitable, but Minoan maritime network continues to thrive!

Knossos

Thera

Documents

New approaches to the Theran Eruption - Amazon S3 · 2015. 12. 4. · Thera (Santorini) in 1988 (almost Icarus II!) Thera is North of Crete: • Summer winds are Northerly [ • Winter