Definition 1

• Interaction is the joint action of at least two interaction partners.

Definition 2

• Spatial Interaction connects different locations by the means of moving people, goods or knowledge between the locations.

Definition 3

• Communication is the exchange of information.

Conflict

• contradicting goals of the two interaction partners
• limitation of the other’s capability
• hamper the other’s efforts Cooperation
• similar goals of the two interaction partners
• extension of the other’s capability
• supporting the other’s efforts

Power and Leverage

Traditional history is about events, when people interact. It is about gaining and applying power and influencing and controlling the behaviour of other people using different means.

Social structures

Social structures are a kind of infrastructure of effective interaction. Social structures are defining the acceptable and unacceptable kinds of interaction. The negotiation of social status is a process of interaction.

Interaction

Interaction supports the fulfilment of needs and to overcome shortages by changing the distribution of commodities and conducting services:

• trade
• division of labour
• services
• …

Innovations

Interaction supports innovations by

• enabling the required knowledge base by the collaboration of developers
• distributing the innovation

Transportation

If people are at different places, they need means of transportation or telecommunication for conducting interaction. It is required to move people, commodities or ideas/knowledge. The means of transportation and the transportation infrastructure is at the same time enabling and restricting interaction. The system of transportation:

Daily live and culture

Interaction is an essential part of the daily live. Every contact to another individual represents a process of interaction, even if the purpose is not clear.

Daily live and culture

If a certain behaviour becomes a custom and is shared with others, we call it culture. Since interaction causes common standardisations, culture is a kind of effect of interaction.

Definition 4

• Culture covers standardisations which are valid in collectives.

Culture

• Formal and abstract definition which covers most other
• Spatial archaeological cultures as special case

• interaction is the driving force of soical, economic, cultural and historical processes and present in many aspects of daily live
• interaction is very abstract and is able to cover different aspects of human behaviour hence
• we need not to start our investigation with distinguishing different kinds of interaction
• interaction is a key term for different geographical and archaeological topics
• we can easily connect to other disciplines

Physics

• Newton
• gravity law \[I = \frac{m_1*m_2}{d^k} \]

Ethnology

• Malinowski
• Kula ring
• gift exchange

Economy

• Polanyi
• market, redistribution, reciprocity

Sociology

• Blumer
• symbolic interaction

Psychology

• Garrod/Pickering
• alignment in dialogues

Geography

• Christaller
• central place theory

Definition 5

Centrality is the relative surplus of meaning due to fulfilling central functions for the surrounding area.

• I Intensity of Interaction
• R Reach of Interaction
• H Level of Hierarchy
• K Control of Interaction

Definition 7

A possible realisation in which all valid sentences of a theory T are satisfied is called a model of T.

A model is characterised by:

• mapping
• reduction
• pragmatism

Definition 8

\(O_1\) and \(O_2\) are objects and \(O_2\) is a model of \(O_1\) for \(k\) in the time interval \(t\) regarding a certain purpose \(Z\) if in \(t k\):

• is L-rational
• performs a description \(P_1\) of \(O_1\)
• performs a description \(P_2\) of \(O_2\)

Definition 12

A model is an artefact, used for a certain purpose by a specific community. The model is analogue to the original. A model has certain methods for development and usage and is based on certain theories and assumptions.

Peter Haggett

• New Geography
• Locational Analysis in Human Geography, 1965
• Models in Geography, 1967, together with R. Chorley

David L. Clarke

• New Archaeology
• Analytical Archaeology 1968
• Models in Archaeology, 1972

Definition 14

A model is a simplified and intelligible picture of the world.

• physical - conceptual
• natural - technical
• stochastic - deterministic
• continuous - discrete
• dimension
• field of application

• phenomenological - mechanistic
• stationary -instationary
• lumped - distributed
• direct - inverse

Voronoi graph

• tesselation
• influence of centre depends on distance
• distance to centre is equal for all points of the border
• \(a = b\)
• territory is optimized for transportation

Voronoi graph

geographical space

• economical space (least cost distance)
• cultural space

Voronoi graph

• geographical space

economical space (least cost distance)

• cultural space

Voronoi graph

• geographical space
• economical space (least cost distance)

cultural space

Fetter modell

• weighted Voronoi-graph
• market areas on the basis of costs of transport
• Fetter 1924; Haggett 2004

X-tent

• weighted Voronoi-graph
• Renfrew & Level 1979

Weighted Voroni

• \(\alpha_s\) static additive weight
• \(\alpha_d\) dynamic additive weight
• \(\gamma_s\) static multiplicative weight
• \(\gamma_d\) dynamic multiplicative weight
• \(t_\alpha\) 1=dynamic additive
• \(t_\gamma\) 1=dynamic multiplicativeweight
• \(\psi\) distance manipulating function
• \(x_z\) x reference point
• \(y_z\) y reference point

Weighted Voronoi

• Princely seats
• weighted Voronoi graphs
• weighted with number of rich graves
• Software: Grass
• today a Grass-addon is available: r.xtent

Weighted Voronoi

• Princely seats
• weighted Voronoi graphs
• weighted with number of rich graves and wagon graves
• least cost distance
• Software: R

Quantitative analysis

1. Problem: Put your question.
2. Theory: Which theoretical frame is adequate for solving the problem?
3. Data: Which data can be used for solving the problem? Are they available as database etc.? How can you access the data?
4. Method: Which methods can solve the problem? Learn the methods!
5. Tool: Learn the tools to apply the methods.

Quantitative analysis

1. Problem: Put your question.
2. Theory: Which theoretical frame is adequate for solving the problem?
3. Data: Which data can be used for solving the problem? Are they available as database etc.? How can you access the data?
4. Method: Which methods can solve the problem? Learn the methods!
5. Tool: Learn the tools to apply the methods.

Type a

Meta theories

• philosophy
• research strategies
• epistemology

Low level theories

• mathematics
• database development
• logic
• theory of cluster analysis

Quantitative analysis

1. Problem: Put your question.
2. Theory: Which theoretical frame is adequate for solving the problem?
3. Data: Which data can be used for solving the problem? Are they available as database etc.? How can you access the data?
4. Method: Which methods can solve the problem? Learn the methods!
5. Tool: Learn the tools to apply the methods.

Quantitative analysis

1. Problem: Put your question.
2. Theory: Which theoretical frame is adequate for solving the problem?
3. Data: Which data can be used for solving the problem? Are they available as database etc.? How can you access the data?
4. Method: Which methods can solve the problem? Learn the methods!
5. Tool: Learn the tools to apply the methods.

Quantitative analysis

1. Problem: Put your question.
2. Theory: Which theoretical frame is adequate for solving the problem?
3. Data: Which data can be used for solving the problem? Are they available as database etc.? How can you access the data?
4. Method: Which methods can solve the problem? Learn the methods!
5. Tool: Learn the tools to apply the methods.

Quantitative analysis

1. Problem: Put your question.
2. Theory: Which theoretical frame is adequate for solving the problem?
3. Data: Which data can be used for solving the problem? Are they available as database etc.? How can you access the data?
4. Method: Which methods can solve the problem? Learn the methods!
5. Tool: Learn the tools to apply the methods.

Types of interaction models

• conceptual models
• affirmative models
• quantitative relationship models
• system models
• models of complex systems

distance

• geographical distance
• social distance
• cultural distance
• economical distance

point features

• size
• population

point distribution

• minimal requirements
• measures general degree of interaction in a region

number of exchanged objects

• small data
• can deal with individual interactions

NN-Distance

• Is there interaction between the points?
• Test on complete spatial randomness
• regular - random - clustered

Imports

• connecting a site to a provenience region
• individual interactions can be traced

Cultural distance

• interactions are producing cultural similarities
• difference in material culture
• statistical level of interaction between sites or regions

Cultural distance

• topography of cultural similarities
• territories of cultural similarities
• cultural areas
• interaction models

Theoretical Models

• Interaction decreases with distance. Distance decay functions can quantify the decrease.

Gravity models

• involve properties of the interaction partners
• based on an analogy from physics
• population, settlement size, ...
• can be used to produce distance decay functions/fall off curves, which consider population

Distance diagram (dd)

• different view-points
• different focus-points
• cultural distance as an inverse interaction proxy

Definition 16 Interaction models plot intensity of interaction over distance.

• cultural distances as inverse proxys of interaction
• different metrics and weightings

Interaction model

• fixed starting point
• fixed profile
• ceramics
• interaction friction at Black Forrest?

Interaction model

• from all points
• to all points
• fibulae and adornment
• interaction threshold at 200 km?

Modelling systems of transportation

• is essential for modelling interaction
• produces knowledge of significant parameters
• the system of transportation provides
  • the structure of the interaction model and
  • economical distances by least cost modelling

Modelling systems of transportation

• empirical model based on the sites
• theoretical least cost path model
• the comparison of both models reveals the parameters of the routes

Least Cost Path

• calculated the most efficient path between \(A and B\)

What does ’least cost’ mean?

How to find the pathway?

• costs for moving from one cell to the next one

How to find the pathway?

• costs for moving from one cell to the next one
• searching for the next connection which produces minimal cumulated costs

How to find the pathway?

• costs for moving from one cell to the next one
• searching for the next connection which produces minimal cumulated costs
• going back the pathway along the connections, which me noted down

How to find the pathway?

• costs for moving from one cell to the next one
• searching for the next connection which produces minimal cumulated costs
• going back the pathway along the connections, which me noted down

Agent based model

• dynamic model of the exchange and settlement system

Consider your own life

• make a list of your interactions
• which types of interactions can you distinguish?
• which parameters are important?
• which information would be archaeological available?

Summary

• interaction is a trans-disciplinary key term in many fields of research
• interaction is an driver of historic, economic, social and cultural processes.
• interaction is an abstract concept
• different types of distances can be used
• models of systems of interaction are based on simple interaction-distance relationships

Monday, 5th of September

1. Interaction as a key term

Tuesday, 6th of September

1. Introduction to R
2. R Basics: Frist Steps
3. R Basics: Getting used to R
4. Using R as GIS
5. Workshop: Basic Spatial Statistics