Complexity and Context-Dependency (version for Bath IOP Seminar)

Complexity andContext-Dependency

Bruce EdmondsCentre 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

Complexity– everything that is not simple

Part 1:


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 models: validity, formality, simplicity and generality

• these are difficult to obtain simultaneously (for complex systems)

• there is some sort of complicated trade-off between them (for each modelling exercise)

simplicity

generality

validity

formality

Analogy

Abstract Simulation

Data

What Policy

Makers Want

This talk argues for the following strategy: weakening the generality of our formal models to achieve

more validity in the face of the AAA

… or, to put it another way, against the following strategy: weakening validity (e.g. to analogy) to preserve (the

illusion of) generality

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

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…

Physics

Chemistry

Biology

Psychology

EcologySocial Sciences

Geography

Zoology

Reduction

Infe

renc

e

…to this!


Islands of Local Consistency

Clusters of Related Models

Weaker Modelling Relations

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


Context-Dependency– and its cognitive roots

Part 2:


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


Social ContextPart 3:


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

Looking for ContextPart 4:


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

Size

Variance(scaled by size)

Globally coupled

Model with random noise

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


Consequences for SciencePart 5:


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

Consequences of Context-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

Atomic Model of an Ideal Gas

Macro Data Models

Micro data and understanding

Analytical Derivations using

simplifying assumptions

Simulation Models

Consequences of Context-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


Consequences of Context-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 Edmondshttp://bruce.edmonds.name

Centre for Policy Modelling http://cfpm.org

The SCID Projecthttp://scid-project.org

Complexity and Context-Dependency (version for Bath IOP Seminar)

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