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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

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R HARRE Subfaculty of Philosophy, University of Oxford

substituted-for or modelled by Hypothetical generative mechanism

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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

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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