Transcript lecture slides - University of Bath

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
Complexity and Context-Dependency, Bruce Edmonds, IOP Seminar on “The Complexity of Complexity” , Bath, Dec 2011. slide-3
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
Analogy
generality
Abstract
Simulation
What
Policy
Makers
Want
formality
Data
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:
… or, to the
put itgenerality
another way,
the following
weakening
ofagainst
our formal
modelsstrategy:
to achieve
weakening
validity
(e.g.
to analogy)
to preserve
(the
more
validity
in the
face of the
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
Complexity and Context-Dependency, Bruce Edmonds, IOP Seminar on “The Complexity of Complexity” , Bath, Dec 2011. slide-9
From this…
Social Sciences
Ecology
Psychology
Zoology
Biology
Chemistry
Physics
Reduction
Inference
Geography
…to this!
Islands of Local
Consistency
Weaker Modelling
Relations
Clusters of
Related
Models
Complexity and Context-Dependency, Bruce Edmonds, IOP Seminar on “The Complexity of Complexity” , Bath, Dec 2011. slide-11
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?
Complexity and Context-Dependency, Bruce Edmonds, IOP Seminar on “The Complexity of Complexity” , Bath, Dec 2011. slide-12
… 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
Complexity and Context-Dependency, Bruce Edmonds, IOP Seminar on “The Complexity of Complexity” , Bath, Dec 2011. slide-13
Part 2:
Context-Dependency
– and its cognitive roots
Complexity and Context-Dependency, Bruce Edmonds, IOP Seminar on “The Complexity of Complexity” , Bath, Dec 2011. slide-14
Cognitive Context (CC)
• Many aspects of human cognition are contextdependent, 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
Complexity and Context-Dependency, Bruce Edmonds, IOP Seminar on “The Complexity of Complexity” , Bath, Dec 2011. slide-23
Part 3:
Social Context
Complexity and Context-Dependency, Bruce Edmonds, IOP Seminar on “The Complexity of Complexity” , Bath, Dec 2011. slide-24
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 ContextDependency 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
Complexity and Context-Dependency, Bruce Edmonds, IOP Seminar on “The Complexity of Complexity” , Bath, Dec 2011. slide-29
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
Variance
(scaled by size)
Globally coupled
Model with random noise
Size
An Illustration of Masked ContextDependency
Global
models are
simply
uninformative
when the
phenomena
is contextdependent
Complexity and Context-Dependency, Bruce Edmonds, IOP Seminar on “The Complexity of Complexity” , Bath, Dec 2011. slide-31
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 (03) colored by flourosopy (ca)
• From the Machine Learning Repository
General Correlations (1% Sig)
Complexity and Context-Dependency, Bruce Edmonds, IOP Seminar on “The Complexity of Complexity” , Bath, Dec 2011. slide-33
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)
Complexity and Context-Dependency, Bruce Edmonds, IOP Seminar on “The Complexity of Complexity” , Bath, Dec 2011. slide-34
Looking for Clusters in HD Data Set
(Start of Process)
Complexity and Context-Dependency, Bruce Edmonds, IOP Seminar on “The Complexity of Complexity” , Bath, Dec 2011. slide-35
After Solutions Locally Evolve
Speciation of
Solutions
In some areas
no solution
dominates
Some
Solutions
Spread over
area of
applicability
Complexity and Context-Dependency, Bruce Edmonds, IOP Seminar on “The Complexity of Complexity” , Bath, Dec 2011. slide-36
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
Complexity and Context-Dependency, Bruce Edmonds, IOP Seminar on “The Complexity of Complexity” , Bath, Dec 2011. slide-37
Part 5:
Consequences for Science
Complexity and Context-Dependency, Bruce Edmonds, IOP Seminar on “The Complexity of Complexity” , Bath, Dec 2011. slide-38
Consequences of ContextDependency 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 ContextDependency 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
an Ideal Gas
Micro data and
understanding
Consequences of ContextDependency 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
Complexity and Context-Dependency, Bruce Edmonds, IOP Seminar on “The Complexity of Complexity” , Bath, Dec 2011. slide-44
Consequences of ContextDependency 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 extracontextual “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