Understanding Complex Systems Through Context-Dependent Models

Complexity and
Context-Dependency

Bruce Edmonds
Centre for Policy Modelling
Manchester Metropolitan University

Talk Outline

1. Accepting Complexity
2. Context-Dependency
3. Social Context
4. Looking for Context-Dependency
5. Consequences for Science

Complexity and Context-Dependency, Bruce Edmonds, IOP Seminar on “The Complexity of Complexity” , Bath, Dec 2011. slide-2

Part 1:

Complexity
– everything that is not simple


The Anti-Anthropocentric Assumption

• That the universe is not arranged for our
benefit (as academics)
• e.g. that assumptions such as 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

Versions of this assumption
• Whilst other animals have severe limitations and
biases in their cognition, we don‟t
• That our tools (writing, computers etc.) allow us to
escape our limitations and biases to achieve
general intelligence
• That simplicity (that which is easier for us to
analyse) 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
(have not worked hard enough), (3) premature
(don‟t yet have the formal tools to crack it) or (4)
mistaken
• We would simply prefer it were so, e.g. that there
are “no miracles”

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 the exception – the
exception to be sought and struggled for
• Simplicity is the exception – a science of non-simple
systems makes no more sense than a science of
non-red things

Possible modelling trade-offs

• Some desiderata for simplicity
models: validity,
formality, simplicity and Analogy
generality
• these are difficult to Abstract
generality
obtain simultaneously Simulation What
(for complex systems)
Policy
• there is some sort of formality Makers
complicated trade-off Want
between them (for each Data
modelling exercise) validity

What is Essential to an Empirical Science?

• Validity: agreement of models to what we observe (the
evidence), not science otherwise
• Formality: formal models (maths, simulation) are
precise and replicable – essential to being able to build
knowledge within a community of researchers
• Simplicity: ability to analyse/understand our models,
good to have but unattainable in general (AAA)
• Generality: the extent of the applicability/scope of a
single model, there needs to be some small generality
to apply models in places other than where developed,
but wide generality not necessary

This talk argues for the following strategy:
weakening the it another way, against the following strategy:
… or, to put generality of our formal models to achieve
weakening validity (e.g. the face of the preserve (the
more validity in to analogy) to AAA
illusion of) generality

Consequences of accepting less
generality…
• A lack of models that cover all systems
• Islands and layers of local consistency
• Rather than a reduction between layers, a
modelling relation
• Rather than a “ladder” (total order) of sciences
with the most fundamental at the base, a
patchy network (partial order) of models
• Rather than a neat system of “theories” and
“models”, related clusters of models of
different abstractions and generality

From this…
Geography

Social Sciences Ecology

Reduction
Inference

Psychology Zoology

Biology

Chemistry

Physics

…to this!
Weaker Modelling
Relations
Islands of Local
Consistency

Clusters of
Related
Models


This raises some questions…

• Does this make us all relativists?
• Does this mean that scientific knowledge is
just the same as other kinds of belief?
• Does this mean that we should abandon
formal models?
• Does this mean that we cannot attain useful
understanding of complex systems?
• Does this mean that interdisciplinary
science is hopeless?


… to which I answer “No”
• The picture I paint already represents the
reality of understanding non-simple systems
• It just differs from some of the rhetoric of
science, and hence the picture and beliefs
many have about science
• It does have some consequences for how we
do science (to come in following slides)
• Rather, accepting these realities will help us do
better science by being aware of:
– hidden assumptions
– over-generalisations
– reliance on single simple models


Part 2:

Context-Dependency
– and its cognitive roots


Cognitive Context (CC)
• Many aspects of human cognition are context-
dependent, including: memory, visual
perception, choice making, reasoning,
emotion, and language
• The brain somehow deals with situational
context effectively, abstracting kinds of
situations so relevant information can be easily
and preferentially accessed
• The relevant correlate of the situation will be
called the cognitive context
• It is not known how the brain does this, and
probably does this in a rich and complex way
that might prevent easy labeling of contexts

The Context “Heuristic” I
• A strategy for dealing with the world by
cognitively limited beings (humans)
• CCs are associated with sets of relevant
„background‟ assumptions, terms, norms,
knowledge, etc. against which the explicit
„foreground‟ learning, reasoning, events, etc.
are conceptualised as occurring
• To be useful kinds of situation needs to be
reliably recognisable as a CC…
• … and packages of foreground features need
to be retrievable from this CC

The Context “Heuristic” II
• Integrates the rich, “fuzzy”, and unconscious pattern
recognition of CC with relatively “thin”, crisp and
conscious learning and reasoning within a CC
• Makes within CC reasoning, belief update feasible
• Is dependent on the world being usefully separable
into CCs – which is not necessarily the case
• Also that learnt CC can be reliably recognised later
• CC are learned flexibly – what counts as a
meaningful CC but it is essential that relevant CC
are reliably recognisable later
• Considering the same situation w.r.t. different CC is
often a useful cognitive tool

Talking about Context
• What corresponds to CC in the brain may well not
be: accessible to consiousness, introspection,
clearly identifiable, or simple enough to defineThus
it may not be meaningful to talk about “the” context
of any particular event
• Indeed people may consider the same situation
using very different CCs
• However sometimes, in retrospect, the CC can be
roughly identified (especially if socially entrenched)
• Even then it is frequently not explicitly described
• For the sake of the discussion I talk about CC as if it
were definite, given you understand that this is a
simplification

About Context-Dependency
• Context-dependency is not relativity since contexts
can be reliably recognised (and/or corrected if
wrongly recognised)
• It is also not merely the “current audience” since
contexts are developed, taught and reinforced over
time (e.g. within academic fields)
• But since it might be recognised in a “fuzzy” and
unconscious manner the bounds of the context may
not be reifiable in crisp terms
• This is a heuristic – a strategy that may help push
forward the boundaries of formal empirical science
• There is some evidence that our cognition is
context-dependent in many ways which means that
to a considerable extent it may be unavoidable

Why might the world we study be
usefully split into such “contexts”
• In some cases (e.g. in 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
• 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

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”
(Granovetter)
• 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
it excludes most possibilities

Transcending 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 what is
essential for the case)
• What one can leave out is a hypothesis only
determinable by evidence and experiment

Context and Analogical Thinking
• Humans are good at using analogies, relating an
idea or example from one context to another
• They build the mapping from the analogy to the a
context “on the fly” largely unconsciously
• The mappings are different each time an analogy is
applied, thus not a reliable source of knowledge and
each person might build a different mapping but can
yield new insights and can guide research direction
• Many published models do not have an explicit
mapping to a domain, but are used as analogy
• This is sometimes hidden, so when a simulation (or
analytic model) models an idea which applies as an
analogy to a domain and not directly, given a
spurious impression of generality

Part 3:

Social Context


Social Intelligence Hypothesis (SIH)
• Kummer, H., Daston, L., Gigerenzer, G. and Silk, J. (1997)
• The crucial evolutionary advantages that
human intelligence gives are due to the social
abilities and structures it facilitates
• This explains the prevalence of specific
abilities such as: imitation, language, social
norms, lying, alliances, gossip, politics etc.
• Social intelligence is not a result of general
intelligence applied to social organisation, but
the essential core of human intelligence
• in fact our “general” intelligence could be
merely a side-effect of social intelligence

An Evolutionary Story
Social intelligence implies that:
• Groups of humans can develop their own,
very different, (sub)cultures of technologies,
norms etc. (Boyd and Richerson 1985)
• These allow the group with their culture to
inhabit a variety of ecological niches (e.g.
the Kalahari, Polynesia) (Reader 1980)
• Thus humans, as a species, are able to
survive catastrophes that effect different
niches in different ways (specialisation)

Social Intelligence and Multi-Agent Systems, Bruce Edmonds, MALLOW 2010, Lyon, 31st August, slide 26

Social Context
• Since humans are fundamentally social beings…
• …social context is often most important
• e.g. an interview, a party or a lecture
• But social context may be co-determined, since:
– Special rules, norms, habits, terms, dress will be
developed for particular social contexts
– The presence of special features, rules etc. make the
social context recognisable distinct
• Over time social contexts plus their features
become entrenched and passed down
• Social Context arises and is so recognisable as a
result of cognitive and external features (e.g.
building a lecture hall)

Implications of Context-
Dependency in Social Science
• Behaviour of observed actors might need to change
sharply across different social contexts
• The relevant behaviour, norms, kinds of interaction
etc. might also need to change
• Social contexts might need to be co-developed,
changing and sometimes instituted (e.g. a lecture)
• These may need to be different for different groups
• Some kinds of social behaviour are necessarily
context-dependent (compliance)
• It is unlikely that a lot of key social knowledge,
behaviour etc. will be generic and hence amenable
to explicit programming

Part 4:

Looking for Context


Kaneko (1990)
• Exhibited a system of parallel chaotic but weakly
coupled processes
• Each process seems chaotic and independent
• But as system size increases, variance as a
proportion of size does not disappear
• Law of large numbers does not apply

Globally coupled
Variance
(scaled by size)
Model with random noise
Size

An Illustration of Masked Context-
Dependency

Global
models are
simply
uninformative
when the
phenomena
is context-
dependent


Cleveland Heart Disease Data Set – the
processed sub-set used
In processed sub-set:
• 281 entries
• 14 numeric or numerically coded attributes
• Attribute 14 is the outcome (0, 1, 2, 3, 4)
• Some attributes: age, sex, resting blood
pressure (trestpbs), cholesterol (chol),
fasting blood sugar (fbs), maximum heart
rate (thalach), number of major vessels (0-
3) colored by flourosopy (ca)
• From the Machine Learning Repository

General Correlations (1% Sig)


Fitting a Global Model (R=56%)

Num = -0.01*age + 0.17*sex + 0.20*cp + 0.00*trestbps + 0.10*restecg + -
0.01*thalach + 0.23*exang + 0.18*oldpeak + 0.16*slope + 0.43*ca + 0.14*thal + -
0.60 (+/- 0.83)

Looking for Clusters in HD Data Set
(Start of Process)


After Solutions Locally Evolve

Speciation of
Solutions
In some areas
no solution
dominates
Some
Solutions
Spread over
area of
applicability

Final Set of Clustered Solutions
• Final solution
set after some
time.
• Still complex but
some structure
is revealed
• Note presence
of “fbs” despite
not being
globally
correlated and
that “chol”
helped define
the context
space


Part 5:

Consequences for Science


Consequences of Context-
Dependency I: not 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

Implications for Modelling Complex
Systems
• It is very useful to describe, as far as
possible, the intended scope of a model
• Applying a model developed within one
context elsewhere (including a more
general scope) is difficult
• No easy way to transcend context
• Difficult to reify contexts to get generality
Ignoring context may have the result that our
models are either (a) subtly and critically misleading
or (b) merely analogies in computational form

Dependency II: clusters of models
• Instead of having one model for one
phenomena we may end up with a cluster
of loosely-related models that each
represent different aspects of it
• Given that we want to understand our
models and only a few models are
analytically tractable this happens anyway
• Separate but related models may avoid
over-generalised models that do not directly
relate to anything observed (or another
model) and rely on imprecise interpretation

Example: an Ideal Gas
Ideal Gas Laws Macro Data
Models

Analytical
Derivations using
simplifying
assumptions

Simulation Models

Atomic Model of Micro data and
an Ideal Gas understanding

Dependency III: 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 data models of
what we observe: a Data-Integration Model (DIM)
• But then need to model the DIM with simpler
simulations to understand it and check its
programmed correctly
• As well as (maybe, hopefully) be able to generalise
from it (and other similar DIMs) to a model which
generalises certain aspects but to a wider scope

The Approach in the SCID Project


Dependency IV: noise
• Whilst some noise comes from an identified
source within a system (e.g. heat noise)
• Other noise comes from without (e.g. the babble
of a crowd around a conversation)
• This kind of noise is recognisable as an extra-
contextual “leak”, due to the imperfection of the
context heuristic (or poorly chosen context)
• Such noise is not necessarily random…
• …indeed it may well be more productive to look
for the context-dependency rather than “dumping”
the lack of fit as random “noise”
• (Possibilistic as opposed to probabilistic models)
• e.g. Peter Allen‟s “Invaders” in Evolution

Conclusions
• In the face of complexity, context-dependency is
unavoidable
• Accepting and thinking about context-dependency
need not lead to sloppy, relativistic or bad science
• In fact it is desirable, since simple systems are the
special case and other trade-offs are worse…
• …such as gaining generality at the loss of validity
• It may lead to pushing the boundaries of science
forward a bit more and avoiding some pitfalls
• It could motivate a move to a more complex and
structural understanding of what is observed
• We may end up with a “patch work” of locally
coherent model clusters of a lot of different kinds –
science may have to be more like zoology
• Science being imperfect or incomplete does not
invalidate its project

The End

Bruce Edmonds
http://bruce.edmonds.name
Centre for Policy Modelling
http://cfpm.org
The SCID Project
http://scid-project.org

Understanding Complex Systems Through Context-Dependent Models

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