A talk give at the York Center for Complex Systems, 20th May 2016.

1. The Modelling of Context-Dependent
Causal Processes
A Recasting of Robert Rosen’s Thought
Bruce Edmonds
Centre for Policy Modelling
Manchester Metropolitan University

2. Some Meta-Information
• I read Rosen’s books 20 years ago, whilst doing a
PhD on the nature and definition of complexity, then
spent years arguing with some of his ‘disciples’
• I found his works intriguing but difficult, he was one
of the thinkers who stimulated and challenged me
• In this talk I use issues raised by Robert Rosen as a
springboard to talking about context-dependency
and how to simulate complex systems
• I mostly talk about my thoughts on these issues
(albeit influenced by Rosen’s)
• These issues are complicated and interrelated and I
will only present one narrative route through them
• I briefly return to Rosen at the end and re-cast
some of his conclusions in the light of my thinking
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 2

3. Robert Rosen
• Dissident/prophet/philosophical biologist
• Thought about the nature of modelling
when faced with complex phenomena
• Argued against reductionist approaches
• Distinguished between mechanistic
systems and complex systems
• Sought for alternative modelling
approaches (e.g. using category theory)
• Highlighted how anticipatory systems might
differ from mechanistic systems
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 3

4. A Sharp Distinction between Machines
and the Complex
• Systems that correspond well to a formal
model are simple (artifacts that are made to do
so, planets etc.) others are complex
• Sought to prove that reductionist formal
modelling techniques can not represent many
systems (e.g. biological)
• Complexity is not a comparative here – the
earth before life emerged/arrived was just as
complex as the earth after this event
• He pointed out some of the characteristics of
complex systems: senescence, anticipation,
embeddedness, etc.
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 4

5. Formal Systems
• Formal systems are implemented using
finite sets of symbols/states that are
manipulated according to given rules
• E.g. mathematics, logic, computing
• These formal systems can talk about sets
of things that can’t be directly expressed
(infinity, real numbers, etc.)
• To be useful they need to be related to the
world in terms of ‘mapping relations’
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 5

6. Limitations of Formal Systems
• There are limits to provability/computability
• Many, including Rosen, don’t like their
apparent predictability & simplicity feeling that
(most) reality is different (which it obviously is)
• To combat reductionist approaches which
over-simplify they attempt to prove that formal
systems are (sometimes) inadequate
• However this confuses:
– formal systems with reductionist approaches
– the micro-foundations of formal systems with what
can be implemented out of them
• And their proofs fail (Edmonds 1999)
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 6

7. Alternative formal systems
• Rosen sought a non-reductionist alternative
formal system in category theory
• Others have claimed continuous systems
different from discrete ones
• They are wrong – all these apparently different
systems can be embedded within each other –
formally they can express the same set of
things/relationships
• But with each it is easier to express some
kinds of things than others, using a different
system might make the modelling simpler
• In particular, what is analytically solvable is
significantly restricted
The Modellig of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 7

8. The Anti-Anthropocentric Assumption
• That the universe is not arranged for our
benefit (as academics)
• e.g. that assumptions like the following are
likely to be wrong:
– Our planet is the centre of the universe
– Planetary orbits are circles
– Risky events follow a normal distribution
– Humans act as if they followed a simple utility
optimisation algorithm
• The one that I am particularly arguing against
here is that our brains happen to have evolved
so as to be able to understand models
adequate to the phenomena we observe
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 8

9. Versions of this assumption
• Whilst other animals have severe limitations and
biases in their cognition, we don’t
• Our tools (writing, computers etc.) allow us to
escape our limitations to effectively achieve a
universal and general intelligence
• That simplicity (that we can analyse easier) is any
guide to truth (other things being equal etc.)
• If your model is not simple enough to analyse and
understand, you are: (1) not clever enough, (2)
lazy (not worked hard enough), (3) premature (the
tools to crack it not yet available) or (4) mistaken
• That we may not be able to model some
phenomena exactly but we can still use simple
models to gain enough insight into them
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 9

10. Living with the AAA
• Accepting that that much of the world around us is
fundamentally beyond modeling that is both
adequate and sufficiently simple and general for us
to cope with
• Acknowledging our (brain+tools) biases and
limitations and so considering how we might extend
our scientific understanding as much as possible
• Phenomena that are simple enough for us to
scientifically understand are rare – to be sought and
struggled for (or built)
• Simplicity is the exception – a science of non-simple
systems makes no more sense than a science of
non-red things
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 10

11. Some modelling trade-offs
• Some desiderata for
models: validity,
formality, simplicity and
generality
• these are difficult to
obtain simultaneously
(for complex systems)
• there is some sort of
trade-off between them
(for each modelling
exercise)
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 11

12. What is Essential to (empirical)
Science?
• Validity: agreement (in some way) of models to what we
observe, not science otherwise
• Formality: formal models (maths, simulation, etc.) are
precise and replicable – essential to being able to build
knowledge within a community of researchers
• Simplicity: ability to analyse/understand our models,
nice to have but unattainable in general (due to AAA)
• Generality: the extent of the applicability of a single
model (i.e. its scope), there needs to be some small
generality to apply models in places other than where
developed, but wide generality not necessary
This talk suggests the following trade-off:
reducing the generality of formal models to
achieve more validity in the face of the AAA
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 12

13. Kinds of Context
• ‘ Context’ is a tricky word to use, has
various related but distinct uses (its not
even clear that ‘the’ context is always
defined or indeed definable)
• It can refer to the exterior situation but this
is indefinitely detailed, more usefully it
refers to a kind of situation
• In particular, when a whole lot of different
kinds of knowledge and models are
applicable in the same kind of situation
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 13

14. A useful context is one that:
– includes related models with similar scope
– is reliably recognisable
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 14
Clusters of Model Scopes suggest a
Cognitive Context
M1 M2
M1
suggests a context

15. Cognitive Context
• Many of our cognitive abilities are known to be
context-dependent, including: memory,
language, preferences, perception, reasoning
and creativity
• We seem to have evolved to recognise
different kinds of situation and think/behave
differently according to this
• Whilst this has particularly strong connections
to our fundamental social abilities
• It also seems relevant to our relationship with
our surrounding ecologies
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 15

16. A (simplistic) illustration of context from the
point of view of an actor

17. The Context Heuristic
• Divide the world into different sorts of situation
(hereafter called a context)
• Learn/recognise these contexts in a rich and
“fuzzy” manner
• “Crisp” knowledge is “packaged” “within” such
contexts for reasoning, update etc.
• Makes within-context reasoning, models,
update etc. more feasible
• Whilst each model has limited scope, together
they might cover more ground, albeit in a more
“patchy” manner
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 17

18. Shifting between Modelling Contexts
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 18

19. Why might the world we study be split
into meaningful contexts
• In some domains, e.g. ecology or social
science contexts might be co-developed
over time between the entities (e.g. a niche,
or social context like a lecture)
• In some others it may be the only practical
way to proceed, as argued above
• In yet others our cognitive, unconscious
tendency to deal with the world in terms of
contexts might lead us to try and divide the
world along less useful lines
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 19

20. (Social) Embeddedness
• Granovetter (1985) AJS 91 (3): 481-510
• That the particular patterns of interactions
between individuals matter
• In other words, only looking at individual
behaviour or aggregate behaviour misses
crucial aspects
• In such systems the causes of behaviour
might be spread throughout a society –
“causal spread”
• Shown clearly in some simulation models
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 20

21. Illustration of Causal Complexity
Lines indicate causal link in behaviour over time, each box
an agent’s talk or action decision (Edmonds 1999)
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 21

22. Implications of Embedding
• Interacting and adaptive entities, particularly if they
are subject to selective pressures can mutually
embed in complex ‘ecologies;
• Which ecologies develop can be historically
contingent but then are ‘locked in’
• What emerges is distinct but not predictable
• This does not mean they are unchanging or have
reached an equilibrium but are recognisably
(especially by its members)
• I think that this kind of situation is what Rosen was
working towards, but he was wrong in his thesis that
anticipation changes the nature of a system (i.e. it
does not make it any less amenable to formal
modelling)
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 22

23. Context and Causality
• In almost all situations (and all social situations)
there are an unlimited number of things that could
be attributed as a cause
• Related to “Causal Spread” (Wheeler) “Wild
Disjunction” (Fodor) and “Embeddedness”
(Grannovetter)
• Without a limitation as to the scope causation
makes no sense
• However given a context there are many factors
that can be assumed to be insignificantly relevant
and/or constant
• Thus causality makes sense given a context, since
the context excludes most possibilities
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 23

24. “The” Simulation Context
• Several relevant things, implying context:
1. The CC of the simulator
2. The intended scope of the simulation
3. The assumptions behind the simulation
4. The actual scope of the simulation
• Whilst presumably these are related they are often
somewhat different
• That a simulation is published implies that there is
some application outside the specific scope
reported in the paper
• However there are no completely general social
simulations (and rarely general in other fields)
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 24

25. Consequences of Context-
Dependency I: clusters of models
• Instead of having one model for one
phenomena we may end up with a cluster
related models that each represent different
aspects of it
• Separate but related models may avoid
over-generalised models that do not directly
relate to anything observed (or another
model) but rely on imprecise interpretation
• Does require us to be more careful about
when models are and are not applicable –
in other words caring about their scope
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 25

26. Consequences of Context-
Dependency II: layers of models
• Given we need both rigour (understanding our
models) and relevance (clear mapping to what
is observed) in our models...
• We might have complicated, descriptive
simulations that relate in a more direct way to
evidence and data models of what we observe
• But then need to model the complex models
with simpler simulations to understand it and
check its programmed correctly
• Later (maybe, hopefully) to be able to
generalise from sets of descriptive simulations
to generalisations with a wider scope
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 26

27. Data Evidence
Simple Model
Data Evidence
Simple Model
Complex Model
Staging Abstraction in the SCID
Project
Work described in http://arxiv.org/abs/1604.00903 (soon in PLoSOne)
and http://arxiv.org/abs/1508.04024 (further simplification step, soon in EPJ-B)
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 27
Data Evidence
Simple Model
Data Evidence
Simple Model
Complex Model
Analytically
Solvable Model
Analytically
Solvable Model
Representation
Simplification

28. Consequences of Context-
Dependency III: dealing with noise
• Some noise comes from an identified
source within a system (e.g. heat noise)
• Other noise due to measurement errors in
obtaining data
• But other noise comes from outside the
current context (e.g. the babble of a crowd
around a conversation)
• Extra-contextual ‘noise’ is not modelled well
using randomness, but can disrupt or
undermine the reliability of a model
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 28

29. About Shifting between Simulation
Contexts
• Simulations can be used as an analogy where
the mapping into a case is done with
unconscious fluidity but this effectively
changes the model, since its reference can be
very different in different cases
• If a more precise and fixed mapping to what is
being modelled is intended, then shifting
between different scopes (e.g. applying a
simulation for a different purpose and case)
can be subtly broken, due to background
assumptions and goals changing
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 29

30. Transcending Simulation Contexts
• It is often desired that a model be
generalised to a broader scope
– From: M holds in context A & M’ holds in
context B → if A then M if B then M’
– However A and B rarely precisely reifiable
• Simplifying does not necessarily lead to
greater generality (by leaving out the
essential for the case & goal)
• What one can leave out is a hypothesis
only determinable by evidence and
experimentThe Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 30

31. Bridging Simulation Contexts
• Related to Multi-Perspective Modelling talk
• Two approaches:
– Upwards via Context: Find a more general CC
that encompasses the contexts of both
simulation contexts
– Downwards via Contents: Via common
referents in subject matter, data/results, or
software description
• Both are difficult, but not always impossible
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 31

32. Ignoring Context
• Much modelling happens with a single
context in mind, in which it can be case it
can be ignored but only if
– everyone is using the same idea of this context
– there is no significant “leakage” of causation
from outside the background, that is the scope
is wide enough to include all significant
influencing factors
• Unfortunately the indication of the intended
scope is often only implicit
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 32

33. Implications for Simulation Modelling
• It is very useful to describe, as far as
possible, the intended scope of a model
• Applying a model developed with one
context elsewhere (including a more
general scope) is very difficult
• No easy way to transcend context
• Difficult to reify contexts to get generality
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 33
Ignoring context will mean that our simulations are
either (a) subtly and critically misleasing or (b)
merely analogies in computational form

34. Back to Rosen
• Rosen was right to point out:
– the poverty of reductionist approaches
– the frequent conflation of model with modelled
– the importance and limitations of formal models
• …but it is not possible (nor indeed necessary) to
prove that formal models are not adequate
approximations of the observed
• The kind of formal system used is not of absolute
importance but more a pragmatic choice
• He did not take into account the fundamental
context-dependency of our modelling and ideas
Complexity and Context-Dependency, Bruce Edmonds, ECCS, Lisbon, Sept 2010. slide-34

35. My Conclusions
• Context-dependency is not relativity since contexts
can be reliably recognised (and/or corrected if
wrongly recognised)
• This is a heuristic – a strategy that may help push
forward the boundaries of formal empirical science
• In particular by being more careful about the scope
and context of models – to indicate and describe
contextual information and and how we attempt to
generalise or cross contexts (caring more about
model scope)
• It has consequences for how we use models:
staging abstraction more carefully, use of multiple
models, not trying to jump to general models
The Modelling of Context-Dependent Causal Processes – A Recasting of Robert Rosen’s Thought, YCCSA, May 2016, slide 35

36. Papers where I discuss these issues
(online versions at the link given on last slide of talk)
Edmonds, B. (1999). Pragmatic Holism, Foundations of Science, 4:57-82.
Edmonds, B. (1999) The Pragmatic Roots of Context. CONTEXT'99, Trento, Italy, September
1999. Lecture Notes in Artificial Intelligence, 1688:119-132.
Edmonds, B. (2002) Learning and Exploiting Context in Agents. Proceedings of the 1st
International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS),
Bologna, Italy, July 2002. ACM Press, 1231-1238
Edmonds, B. (2007) The Practical Modelling of Context-Dependent Causal Processes – A
Recasting of Robert Rosen’s Thought. Chemistry & Biodiversity, 4(1):2386-2395
Edmonds, B. & Norling, E. (2007) Integrating Learning and Inference in Multi-Agent Systems
Using Cognitive Context. In Antunes, L. & Takadama, K. (Eds.) Multi-Agent-Based Simulation
VII, LNAI, 4442:142-155.
Edmonds, B. (2009) The Nature of Noise. In Squazzoni, F. (Ed.) Epistemological Aspects of
Computer Simulation in the Social Sciences. LNAI 5466:169-182.
Edmonds, B. (2013) Matching and Mismatching Social Contexts. In Dignum, V. and Dignum, F.
(eds.) Perspectives on Culture and Agent-based Simulations, Springer,149-167.
Edmonds, B. (2013) Complexity and Context-dependency. Foundations of Science, 18(4):745-
755.
Edmonds, B. (2015) A Context- and Scope-Sensitive Analysis of Narrative Data to Aid the
Specification of Agent Behaviour. Journal of Artificial Societies and Social Simulation 18(1):17
Complexity and Context-Dependency, Bruce Edmonds, ECCS, Lisbon, Sept 2010. slide-36

37. The End
Thanks: to Robert Rosen for his intriguing and challenging works,
also to Ronald Giere for his intelligent, informed and sensible
philosophy and all whose ears I have bent about these issues,
including those at: the Centre for Policy Modelling (especially
Emma Norling), the Manchester Complexity Seminar, and the
International Conferences on Modelling and Using Context.
These slides are available at: http://SlideShare.net/BruceEdmonds
Online versions of papers: http://bruce.edmonds.name/pubs.html
Centre for Policy Modelling http://cfpm.org