Phys Eauc V@
13l078
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Models in
science
formal mode of study. is too coarse grained to bring
out the features of most importance to understanding
science.
Expressed in the material mode the basic scheme of
scientific theorising runs as follows:
Observed pattern in nature
t
produced b>*
Unobservable generative mechanism
t
R HARRE
Subfaculty of Philosophy, University of Oxford
substituted-for or modelled by
Hypothetical generative mechanism
t
modelled on
Observed source process
Science is representation
a
of the
patterns
and
processes of the world, both natural and social. The
means by which we represent the world to ourselves
are
quite
various,
including
linguistic, abstract
symbolic and iconic (pictorial) ways
of representing.
Ourrelationship with theworld
is very imperfect.
defective
both
in scale
and
depth.
Scientists
feel
themselves
forced
propose
to hypotheses
about
structures and processes both on a much larger scale
thananyonecouldexperience
evenwiththe
most
powerfulinstruments.and
on amuchsmallerscale
than
one
could
ever
reach
by
observation.
Cosmologists
ascribe
structure
and
process
the
to
universe.
and
large-scale
to
features
within
it.
Sociologists go beyond individual people and their face
tofaceinteractionstopostulateglobalsocialprocessesandpatterns
in theseindividualinteractions
taken together as a single system. Similarly, cognitive
and dynamic (Freudian) psychologists, just as much
chemists,
as
physicists
and
geologists.
form
hypotheses about inner and minute mechanisms whose
workings and even whose components are not capable
of being perceived by anobserver,however cleverly
equipped.
How are scientists to know how to formulate their
descriptions of these vast and hidden things?
It is in
solving this problem that models play a central role in
scientific thinking. To see how this process works we
couldexamineeitherthe
scientific
discourse-the
statementsthatscientistsmakeaboutthe
world-or
we could examine the organisation of and connections
betweenthesubjectmatter
of their discourse-what
theyaretalkingabout.
To discussthediscourse
we
adopt the ‘formal mode’ of philosophising: to discuss
whatthediscourseisabout
we adoptthe‘material
mode’.One’s choiceofphilosophicalmode
is determined very much by convenience and by considering
which way of approaching a problem is likely to be
most perspicuous. For various reasonsit is desirable to
adopt the material mode in discussing science. This is
mainly because logical analysis, the main tool
of the
The crossrelations in this scheme are as follows:
( I ) Thehypotheticalgenerativemechanism
must
heha\>e analogouslytotheunkown
real generative
mechanism. That is. it must be able to be imagined to
produce the observed pattern in nature, or something
very similar to it.
( 2 ) The hypothetical generative mechanism must be
sufficiently like theobservablesourceprocesses
on
which it is modelled. but is also certain to be different
in various ways.
I n thisschemethehypotheticalgenerativemechanism is a model ofthe unknown real mechanism and is
modelled on theobservableprocesses
which are its
source.Thetermmodel
is used confusingly.sometimes for the hypothetical generative mechanism as in
the
phrase
’the
molecular
model of a gas’. and
sometimes for the source asin ‘the rule model of social
action’.
Some examples
Let me f i l l outthisabstractdiscussion
with some
examples.
Darwin
observed
the
patterns
of distribution
of
differing
species
of
animals
and
plants-but
he could not observe the processes which
caused these patterns. He had to invent the
selection
model.
He
imagined
process
a
by which
small
variationsoccurred in successivegenerations, which
against the background of the physical and biological
environment led to differentrates
of reproduction
among the bearers of the variations. The source of his
idea. as he candidly remarks in The Origin of Species,
was his ownandother
people’s deliberate selection
procedures to improve a stock. We could
call this the
domesticselectionsourcemodel.Darwinimagined
natural selection processes as
like domestic selection,
in that he thought ofit as leading todifferential rates of
reproduction,but
unlike domestic selection in that
therewas no intelligent agent involved acting as the
breeder.deliberatelyselectingvariantsaccordingto
some plan for improving the species.
Another simple example is Faraday’s lines of force.
215
They are the imagined mechanisms to explainall kinds
ofelectromagneticphenomena.Theyare
like elastic
threads in that they tend to shorten. they store energy
and so on, but unlike suchthreadsthe
field is continuous andnonmaterial.Morecomplexandsubtle
examplescan
be found in thesocialsciencesand
psychology. where a complex of source models may
be serving as the original of the concepts employed in
forming ideas of hypothetical generative mechanisms.
Having invented an iconic model, how d o we assess
its value?Assessmentdependscritically
on whether
we are proposing the model as a convenience
or as a
representationof reality. Theformer is thesimpler
casesincea
model’s conveniencecan be judged by
reference to how well itsimaginedactivitysimulates
the real activity of theunknownrealmechanism
of
nature-and
that is judged by thestrengthofthe
relation I have called the analogy of behaviour. If our
imaginedhypotheticalmechanismproducesagood
simulacrum of the relevant pattern of nature, then
we
are entitled to regard it favourably. The strength of the
analogy of behaviour can be assessed by comparing
thelaws
of a field of phenomenaobtained
by a
generalisation of observed results, say the gas law, PV
= RT. with thecorrespondingexpressiondeduced
from a description of the iconic model and its mode of
working. p o = +nrnc2. In theextremecaseonecan
dispense with theiconicmodelaltogether
if one is
interestedonly
in convenienceandsimply
use an
abstractmathematicalstructureinstead;adiscourse
without a referent. This is called ‘mathematical modelling‘ and is used in various fields where either there is
no interest in the reality of the possiblegenerative
mechanisms, or no possibility of finding them out. as,
say. in economics.
Plausibility of models
But if we areinterested in consideringthemodel or
hypotheticalgenerativemechanismfor
its possible
reality, we havetotakeaccount
of the second, or
material, analogy, that is how far it is like what it is
modelled on. But that by itself is not an adequate test
since we mayhavemodelledourhypothetical
generativemechanism on somethingwhich we aresure
could not be a guide to the way the world
really is. For
example,Thomson’sethermodels
were modelled on
pieces of machineryincorporatinggyroscopes,
balljoints and elastic threads. All these items would themselveshave been madeof, or at leastincluded.the
electromagnetic ether in their construction. They could
notbetakenseriously
asanaloguesfortheinner
workings of ether particles. The source model must be
plausible as a picture of a general or universal kind of
thing or mode of working for the field of phenomena
we are speculating about under its guidance.
Compare the relation of these ether models to the
real world with therelation of rulemodels in social
216
psychology.
Psychologists
have
tried explain
to
the very regularandstructuredwaymanypeople
perform social actions, say introducing a stranger to a
host, by thehypothesisthat
in doing or sayingthe
appropriate things people are behaving like those who
cooperatetoperformwedding
a
ceremony.Since
weddingsareregularandstructuredeventsbecause
the people taking part are following the rules printed in
theorder ofservice. we mightreasonablyformthe
hypothesis that people have in their minds something
correspondingtosucha
set ofrulesforperforming
introductions. But. someonemightsay.
we arenot
generallyaware
of followingruleswhen
we make
introductions-we
justdo
it correctly.Thesocial
psychologistacknowledgesthat,
of course,since his
idea is offered as a model for the process, the process
of which we are unaware. But he would point out that
when we areforced to become aware of how we do
these things correctly. say because we have to instruct
a child or foreign
a
visitor,
we doexpressour
knowledge in theform of rules. Thissort of consideration leaves psychologists to judge the rule model
asaplausiblerepresentationofthe
real generative
process.
Wecandescribethisideaof
plausibility more
precisely with an example from the physical sciences.
Considerthelatticemodel
of crystalstructure. By
basing our conception of the unknown cause of difon the known
fraction patterns produced by crystals
mechanism of diffraction by gratings,
we can give a
plausiblemodel of crystalstructure. But oneshould
notice that our judgment of its plausibility comes from
abalance between thetwoanalogiesbetween
which
our
model
is suspended.
The
lattice
model
must
behave like a real crystal, that is diffract electromagnetic radiation. That is the analogy of behaviour. And
it must be areasonablesuppositionthationsare
arranged in crystals in patterns not unlike the patterns
of diffraction gratings with which we are familiar. That
is the material analogy.
The more aspects of the behaviour
of crystals can
be simulated by the behaviour of our imagined model
of crystal
behaviour
structure
while retaining
its
materialanalogytoitssource
relatively intact,the
more we are inclined to judge it plausibleas a representation of reality. In thecase of themolecular
of the
analogy
of
model of gasesthedemands
behaviour. newly discovered properties of gases, put a
heavydemand on thematerialanalogy,becausethe
model had to be modified several times to preserve its
simulation of real-gasbehaviour. But eachtimethe
changeoccurred.sayfrommerepointmassesto
molecules with
finite
volume, it strengthened
the
material analogy-molecules
became more and more
like real things
and
the
models
more
and
more
plausible. Models of this kind are called paramorphs,
and it is easy to see how they play a central role in the
creative thinking of scientists.
nonscientific example to make the point clear, a child's
doll can be looked upon as a model of a baby, but it is
also modelled on a baby. So source model and subject
Theexamples
I havedescribedhaveinvolvedthe
modelled
are
the
same.
Models
of
this
sort
are
formation of the model with its two analogies, beforeit
A globe is a
commonly used forteachingpurposes.
cametobemathematicallydescribed.Sometimesa
we are all
homoeomorphicmodel of theearth,and
mathematicalformulation of atheory is madefirst.
familiar with thoseratherhorrendousdismantleable
with only the analogy of behaviour in control, but later
ear and eye models of the biology class.
thinkers are able to give it an interpretation as a desCharacteristically.
homoeomorphs
idealise
their
cription of aplausiblemechanism.by
linking it to a
subject.oftenbysimplifying,andtheymake
it more
source model by amaterialanalogy.A
nice example
manageable by scaling it. The earth is scaled down to
can be found in the psychology of perception where a
the globe. and the eye and the ear are scaled up to the
mathematicalrepresentation
of thewayhearing
is
model. Idealisation and scaling can also be useful steps
adjusted between the two ears when a person hears a
in original scientific work, if the subject of the model is
significantsound.suchas
his ownname.waslater
foundto be able to be interpreted in neurophysiolverydifficult towork on in its naturalform.River
ogicalterms.bytakingaswitchingmechanismasa
engineers use homoeomorphic models of estuaries, for
model source.
instance. By properscalingtheycan
follow in days
Sometimes
the
mathematical
formulation
defies
processes that can take years
in the real world. The
interpretation altogether. at least in terms of material
mathematicalmodels,controlledonly
by ananalogy
of behaviour to the real world, that I described earlier,
analogies to commonsense source models. This seems
can be classified along with homoeomorphs, as well as
to be the case at present with the powerful but baflling
treated asincompleteparamorphs. It all depends on
mathematicalformulation of quantummechanics.It
whether we have any hope of one day linking them
simulates the behaviour of the real worldfairly well.
thatis it enablestheprobabilitydistributions
of the
back with the real world at greater depth by setting up
results of various interactions to be predicted, but
a material analogy with which they can be interpreted.
no
successfulmaterialanalogy
to areasonablemodel
But idealisation and scaling can have another effect.
source has yet been proposed. Bohr showed how rules
It may be that some overall pattern in the subject of
could be formulated to enable two incompatible source study is clouded by too much detail. or by awkwardmodels to be used.theparticlepictureandthewave
ness of scale. This is a particularly pressing difficulty
picture.andhowtopreventthemclashing,that
is
in the social sciences where vast amounts of minutely
being used contradictorily for the same phenomenon.
differing data on all sorts of matters such as income,
At best this might provide
a psychological assistance
attitudesand child rearingpracticescanbe
all too
in grasping the mathematical treatment. but it is no use
easily accumulated. Social patterns emerge only if we
at all asamaterialanalogyupon
which to basea
idealise and
scale
the
data
to
some
manageable
judgment of plausibility.
form-sometimes
physically.
evenGraphical
There are various conclusions one could draw from
methods. for example. derive some of their power from
this impasse. Either we have reached a depth of penethe fact that a graph
is a homoeomorphic model for
trationintotheworldsystemwhereourintellectual
theprocess or distribution which it represents.Our
capacities are too feeble to cope: or we have reached
capacity to graspandrepresent its shape,always in
theultimateprocesses
in naturewhichhave no gensome idealised form.
depends
upon
scaling
and
erativemechanisms,since
if theyareultimatethey
idealisation.
providethecomponentprocessesof
all higher-order
Dangers of models
mechanisms: or quantum mechanics is incomplete and
perhaps even wrong. None of these conclusions is very
Along with the power of models to represent, and even
attractive. But I must leave the reader to form his own
more importantly to stand in for. reality, goes a corjudgment.
Each
conclusion
distinguished
has
respondingseductiveness.We
slip very easily into
advocates.
takingthemfortherealthing.Justaswhen
in the
Themodels I havedescribed so farhavehada
formal mode we study the language in which models
sourcedistinctfromthesubject
of themodel. For
are described. the language of theories, we notice the
example. the way formal ceremonies are produced
is
way similes. and particularly metaphors, slip over into
used as a model for the mechanism by which informal
literal usage. e.g. 'current' into 'electric current'. so the
but orderly behaviour patterns are generated. A gas. at underlying fluid model of electricity slips over in our
leastfor all theoriginators of themoleculartheory
thoughts
from
substitute
a
for
reality to a repknew. is different from a swarm of randomly moving
resentation of reality itself. The problem with models
Newtonianparticles. But anotherimportantclass of
comesaboutbecausesometimes
we arejustified in
models.
the
homoeomorphs.
are
characterised
by
taking them for the real thing. A good example is Van
usingthesubjectofthemodel
as itssource.They
Helmont's (1626) 'invasion'modelofthecause
of
depend on only oneanalogyrelation.
To take a
disease. We are now convinced on very good grounds
Mathematical formulation
211
that in reality
there
are
micro-organisms
whose
activities. when they enter into our body, produce the
symptoms of disease.
How do we strike a proper balance, then, between
gullibility and scepticism? There is no formula which
canprovidetheanswer
in every case-but
it is
possible to codify the intuitions of the best scientists in
some modest procedural rules:
( 1 ) In thebalancebetweentheanalogyof
behaviourand
the materialanalogy,amodelcan
be
assessed for its plausibility as a candidate for reality,
(2) If thetechnologyexists, or canbedeveloped,
somecandidatesforrealitycanbeshowntobe
fictional. some can be shown tobe.as real as the things
thatrepresentourcurrentstandard
of reality, while
manyremainundetermined
or even undeterminable.
For example,thetechnologicaladvancesthathave
allowed close satellite surveillance of the planets have
demonstratedthattheMartiancanalsareafction.
The discovery of electron diffraction and the hvelopment of a microscope utilising the phenomenon have
shown that viruses are real. The reality of quarks, of
unconscious
thought
processes
and
of the
social
contradictions of dialectical materialism remain to be
determined.
(3) Our attitudetosourcemodelsexpresses
our
globalconceptions of what is real.Forexample,at
some time physics is especially atomistic, building its
particular pictures of the mechanisms of unknown processesonthe
ideal of amultitude of independently
existing. occasionally interacting, units. At other times
it adoptsa holistic framework in which modelsare
built on the idea of a modulated continuum of which
everypartaffectseveryother.Sociologicalmodel
building too tendstofavourone
or other of these
sourcemodels.Favouringone
or other is not just a
light-minded choice of a fashion. but ought to be seen
as a commitment to one conception
of reality rather
than another.
From
time
time
to the
scientific community
becomes impatient of the tentative character of these
proceduralrulesand
of thehistoricallyconditioned
and shifting judgments they allow. This impatience is
expressed in apositivisticattitude
to theorising-an
attitude that resolves these uncertainties at the cost of
abandoningthesearchfortherealmechanismsthat
producethepatterns
of reality.Whenthismood
sweeps across the community all models are consigned
tolimboasmerelypsychologicalaids
or teaching
devicesand reality is usuallyreservedeitherfor
our
own experiences or at best for the instruments we use
and the results we get from them.
Theseperiodsneverlast
for longand
the community returns contrite to the long and tortuous path
of tradition. trying to conceive of the way things really
are. and to subject these conceptions to whatever tests
can be devised. In thisenterprisemodelmakingand
model testing play the central roles.
'Real' models
and physical
properties
M B ORMEROD
Department of Education, Brunel Universit-v
Whilstnotwishingtoargueacasefor'integrated
physical science', I have often felt that there are topics
wherephysicsandchemistrycouldmakecommon
cause with advantage to both. There has been for too
long a watertight-or
at least. concept-tight-barrier
between the physical properties of a species of matter
and its chemical
properties.
At
secondary
level,
chemistry
teachers
have
not
been able to avoid
describingphysicalproperties.sincetheyare
tied up
with methods of preparation and purification. School
physics has been able to avoid chemical properties far
more exclusively. Itsconcern with matterhas legitimately been with physical properties, but its objectives
in this field seem to have been the definition of physical
properties.theirmeasurementandtheirrelevance
to
life. Until recently
neither
chemistry
nor
physics
teachers have felt obliged or able to explain physical
properties.
In recent
years.
however.
the
simplification
of
modern
ideas
on
chemical
bonding
has
enabled
chemistry teachers to explain chemical properties by
means of models. and these same models are capable
of explaining physical properties as well. The main objective of this article is to describe the sort of model
which has evolved in chemistry teaching for use even
at the 0-level stage. and to show by means of a
few
exampleshow it canbe used to give simpleexplanations of physicalpropertiesandphenomena
in
addition to its role in chemistry teaching.
Whyexplainratherthandescribeandmeasure.
anyway? 1 wouldarguethat
the primary role of
science
teaching
is to give all pupils, in a way
commensurate withtheir mental ability. aconsistent
explanation of the phenomena in theworldaround
them relevant to their present or expected life. This is a
daunting task. We must search for anything which will
simplifyit. What we need arewhatAusubel
(1969)
terms 'organisers'. By this he means devices which will
epitomise and interrelate some area or areas of knowledge or understanding. For instance. it could be
argued that everyone ought to know something about