IDEAS IN CONTEXT

MODELS AS MEDIATORS
Edited q, QUENTIN SK INNER (Genua/ Editor)
LORRAINE DASTON , DOROTHY Ross Perspectives on Natural and Social Science
andJAMEs TULLY

The books in this series will discuss the emergence of intellectual traditions and
EDITED BY
of related new disciplines. The procedures, aims and vocabularies that were
generated will be set in the context of the alternatives available within the con- MARY S. MORGAN and MARGARET MORRISON
temporary frameworks of ideas and institutions. Through detailed studies of
the evoiucion of such traditions, and their modification by different audiences, .
it is hoped that a new picture will form of the development of ideas in their
concrete contexts. By this means, artificial distinctions between the history of
philosophy, of the various sciences, of society and politics, and of literature
may be seen to dissolve.
The series is published with the support of the Exxon Foundation.
A list 'If books in the sems will befound at the end 'If the volume.

g CAMBRIDGE
V UNlVERSTTY PRESS
 Models as mediating instruments II

ther, neither just theory nor data, but typically involve some of both
CHAPTER 2 ('and often additional 'outside' elements), that they can mediate between
theory and the world. In addressing these issues we need to isolate the .
Models as mediating instruments nature of this partial independence and determine why it is more useful
than full independence or full dependence.
Margaret Morrison and Mary S. Morgan
fUNCTIO N I NG What does it mean for a model to function autono-
mously? Here we explore the various tasks for which models can be used.
We claim that what it means for a model to function autonomously is to
function like a tool or instrument. Instruments come in a variety of
forms and fulfil many different functions. By its nature, an instrument or
~vIodels are one of the critical instruments of modern science. We know tool is independent of the thing it operates on, but it connects with it in
that models function in a variety of different ways within the sciences to some way. Although a hammer is separate from both the nail and the
help us to learn not only about theories but also about the world. So far, wall, it is designed to fulfil the task of connecting the nail to the wall. So
however, there seems to be no systematic account of how they operate in toO with models. They function as tools or instruments and are indepen-
both of these domains. The semantic view as discussed in the previous dent of, but mediate between things; and like tools, can often be used for
chapter does provide some analysis of the relationship between models many different tasks.
and theories and the importance of models in scientific practice; but, we
feel there is much more to be said concerning the dynamics involved in REPRE SE>lT I NG Why can we learn about the world and about theo-
model construction, function and use. One of the points we want to ries from using models as instruments? To answer this we need to know
stress is that when one looks at examples of the different ways that what a model consists of. ylore specifically, we must distinguish between
models function, we see that they occupy an autonomous role in scien- instruments which can be used in a purely instrumental way to effect
tific work. In this chapter we want to outline, using examples from both something and instruments which can also be used as investigative )
the chapters in this volume and elsewhere, an account of models as devices for learning something. We do not learn much from the hammer.
autonomous agents, and to show how they function as instruments of investi- But other sorts of tools (perhaps just more sophisticated ones) can help
gation. We believe there is a significant connection between the auton- us learn things. The thermometer is an instrument of investigation: it is
omy of models and their ability to function as instruments. It is precisely physically independent of a saucepan of jam, but it can be placed into
because models are partially independent of both theories and the world the boiling jam to tell us its temperature. Scientific models work like
that they have this autonomous component and so can be used as instru- these kinds of investigative instruments - but how? The critical
ments of exploration in both domains. difference between a simple tool, and a tool of investigation is that the
In order to make good OUf claim, we need to raise and answer a number latter involves some form of representation: models typically represent
of questions about models. We outline the important questions here before either some aspect of the world, or some aspect of our theories about
going on to provide detailed answers. These questions cover four basic ele- the world, or both at once. Hence the model's representative power
ments in OUf account of models, namely how they are constructed, how allows it to function not just instrumentally, but to teach us something
they function, what they represent and how we learn from them. about the thing it represents.
CONSTRUCTION What gives models their autonomy? Part of the LEAR N I "G Although we have isolated representation as the mecha-
answer lies in their construction. It is common to think that models can nism that enables us to learn from models we still need to know how this
be derived entirely from theory or from data. However, if we look closely learning takes place and we need to know what else is involved in a
at the way models are constructed we can begin to see the sources of model functioning as a mediating instrument. Part of the answer comes
their independence. It is because they are neither one thing nor the from 'Seeing how models are used in scientific practice. We do not learn
' 10
12 Margaret Morrison and Mary S. Morgan Models as mediating instruments 13
much from looking at a model - we learn more from building the model of models, but remarkably few accounts of how they are constructed.
and from manipulating it. Just as one needs to use or observe the use of Two accounts which do pay attention to construction, and to which we
a hammer in order to really understand its function, similarly, models refer in this part of our discussion, are the account of models as analo-
have to be used before they will give up their secrets. In this sense, they gies by Mary Hesse (1966) and the simulacrum account of models by
have the quality of a technology - the power of the model only becomes :\'ancy Cartwright (1983).
apparent in the context of its use. Models function ~ot justas a means Given the lack of generally agreed upon rules for model building, let us
of intervention, but also as a means of representatIon. It ]5 when we begin with the accounts that emerge from this volume of essays. We have
manipulate the model that these combined features enable us to learn an explicit accpunt of model construction by Marcel Boumans who argues
how and why our interventions work. that models are built by a process of choosing and integrating a set of items
which are considered relevant for a particular task. In order to build a
Our goal then is to flesh out these categories by showing how the
different essays in the volume can teach us something about each of the mathematical model of the business cycle, the economists that he studied
typically began by bringing together some bits of theories, some bits of
categories. Although we want to argue for some general claims about
models - their autonomy and role as mediating instruments, we do not
empirical evidence, a mathematical formalism and a metaphor which
guided the way the model was conceived and put together. These dispar-
see ourselves as providing a 'theory' of models. The latter would provide
well-defined criteria for identifying something as a model and differen- ate elements were integrated into a formal (mathematically expressed)
tiating models from theories. In some cases the distinction between system taken to provide the key relationships between a number of vari-
ables. The integration required not only the translation of the disparate
models and theories is relatively straightforward; theones conSISt of
elements into something of the same form (bits of mathematics), but also
general principles that govern the behaviour of large groups of phenom-
that they be ntted together in such a way that they could provide a solution
ena; . models are usually more circumscribed and very often several
equation which represents the path of the business cycle.
models will be required to apply these general principles to a number of
Boumans' account appears to be consistent with Cartwright's simu-
different cases. But, before one can even begin to identify criteria for
lacrum account, although in her description, models involve a rather
determining what comprises a model we need much more information
more straightforward marriage of theory and phenomena. She sug-
about their place in practice. The framework we have provided will, we
gests that models are made by fitting together prepared descriptions
hope, help to yield that information.
from the empirical domain with a mathematical representation
coming from the theory (Cartwright 1983). In Boumans' description of
2.1 CONSTRUCTIO~ the messy, but probably normal, scientific work of model building, we
find not only the presence of elements other than theory and phenom-
2.1.1 Independence in construction ena, but also the more significant claim that theory does not even
When we look for accounts of how to construct models in scientific texts determine the model form. Hence, in his cases, the method of model
we find very little on offer. There appear to be no general rules for model construction is carried out in a way which is to a large extent indepen-
construction in the way that we can find detailed guidance on principles dent of theory. A similar situation arises in Mauricio Suarez's discus-
of experimental design or on methods of measurement. Some might sion of the London brothers' model of superconductivity. They were
argue that it is because modelling is a tacit skill, and has to be learnt not able to construct an equation for the superconducting current that
taught. Model building surely does involve a large amount of craft skill, accounted for an effect that could not be accommodated in the exist-
but then so does designing experiments and any other part of sClentlfic ing theory. Most importantly, the London equation was not derived
practice. This omission in scientific texts may also point to the creative from electromagnetic theory, nor was it arrived at by simply adjusting
element involved in model building, it is, some argue, not only a craft but parameters in the theory governing superconductors. Instead, the new
also an art, and thus not susceptible to rules. We find a similar lack of equation emerged as a result of a completely new conceptualisation of
advice available in philosophy of science texts. We are given definitions superctmductivity that was supplied by the model. So, not only was the
14 Margaret Morrison and Mary S. Morgan Models as mediating instruments 15
model constructed without the aid of theory, but it became the impetus this role; it provides a more or less idealised context where theory
for a new theoretical understanding of the phenomena. plied. I From an initially idealised model we can then build in the
The lesson we want to draw from these accounts is that models, by ap corrections so that the model becomes an increasingly
virtue of their construction, embody an element of independence from re8iJjstlC representation of the real pendulum.
both theory and data (or phenomena): it is because they are made up It is equally the case that models which look at first sight to be con-
from a mixture of elements, including those from outside the original Ill'Ucted purely from data often involve several other elements. Adrienne
domain of investigation, that they maintain this partially independent van den Bogaard makes a compelling case for regarding the business
status. barometer as a model, and it)s easy to see that such a 'barometer' could
But such partial independence arises even in models which largely Dot be constructed without imposing a particular structure onto the raw
depend on and are derived from bits of theories - those with almost data. Cycles are not just there to be seen, even if the data are mapped
no empirical elements built in. In Stephan Harunann's example of the into a simple graph with no other adjustments to them. Just as the bag
MIT-Bag Model of quark confinement, the choice of bits which went .tory told MIT physicists what bits were needed and how to fit them
into the model is motivated in part by a story of how quarks can exist together, so a pa;ticular conception .of economic life (that it ~o~sists of
in nature. The story begins from the empirical end: that free quarks certain overlappmg, but different lime-length, cycles of actIvIty) was
were not observed experimentally. This led physicists to hypothesise required to isolate, capture and then combine the cyclical elements nec-
that quarks were confined - but how, for confinement does not follow etSary for the barometer model. The business barometer had to be con-
from (cannot be derived from) anything in the theOIY of quanJ:um structed out of concepts and data, just as a real barometer requires some
chromodynamics that supposedly governs the behaviour of quarks. theories to interpret its operations, some hardware, and calibration from
Instead, various models, such as the MIT-Bag :vlodel, were proposed past measuring devices.
to account for confinement. When we look at the way these models We claim that these examples are not the exception but the rule. In
are constructed, it appears that the stories not only help to legitimise other words, as Marcel Boumans suggests, models are typically con-
the model after its construction, but also playa role in both selecting structed by fitting together a set of bits which come from disparate
and putting together the bits of physical theories involved. Modelling lOurces. The examples of modelling we mentioned involve eielllclils of
confinement in terms of the bag required modelling what happened theories and empirical evidence, as well as stories and objects which
inside the bag, outside the bag and, eventually, on the surface of the could form the basis for modelling decisions. Even in cases where it ini-
bag itself. tially seemed that the models were derived purely from theory or were
At first sight, the pendulum model used for measuring the gravita- simply data models, it became clear that there were other elements
tional force, described in Margaret Morrison's account, also seems to involved in the models' construction. It is the presence of these other ele-
have been entirely derived from theory without other elements ments in their construction that establish scientific models as separate
involved. It differs importantly from Harunann's case because there is from, and partially independent of, both theory and data.
a very close relationship between one specific theory and the model. But But even without the process of integrating disparate elements,
there is also a strong empirical element. We want to use the pendulum models typically still display a degree of independence. For example, in
to measure gravitational force and in that sense the process starts not cases where models supposedly remain true to their theories (and/ or to
with a theory, but with a real pendulum. But, we also need a highly the world) we often see a violation of basic theoretical assumptions.
detailed theoretical account of how it works in all its physical respects.
Newtonian mechanics provides all the necessary pieces for describing
1 Although the model pendulum is an example of a notional object, there are many cases where real
the pendulum's motion but the laws of the theory cannot be applied objects have functioned as models. Everyone is familiar with the object models of atoms, balls con-
directly to the object. The laws describe various kinds of motion in nected h;th rods, which are widely used in chemistry, appearing both in the school room and in
idealised circumstances, but we still need something separate that allows the hands of Nobel prize winners. Most people are also familiar with the early object models of
the planetary system. Such object models have played an important role in scientific research from
us to apply these laws to concrete objects. The model of the pendulum an earlyitime, and were particularly imponant to nineleemh-cemury physicists as we shall see later.
 Margaret Morrison and Mary S. Morgan Models as mediating instruments '7
Geert Reuten's account of :\1arx's Schema of Reproduction, found in onomie laws interact with the institutional arrangements for money
volume II of Capital, shows how various modelling decisi~ns created a ~ the economy, involves a set of 'vessels' supposed to contain the world
structure which was partly independent of the general reqUJremenl~'lald ~ores of gold and silver bullion. These vessels constitute negative ana-
down in Marx's verbal theories. On the one hand, Marx had to dehber- ~ogical features, being neither part of the monetary theories of the time
ately set aside key elements of his theory (the crisis, or cycle, element) in nor the available knowledge in the economic world. Both models
order to fix the model to demonstrate the transition process from one depend on the addition of these negative analogical features and
stable growth path to another. On the other hand, it seems ~hat Mar." enabled Fisher to develop theoretical results and explain empirical
became a prisoner to certain mathematical condItIons Imphed by hIS findings for the monetary system. '
early cases which he then carried through in constructmg later verSlOns
of the model. Even Margaret Morrison's example of the pendulum
model, one which is supposed to be derived entirely from theory and to 2.1.2 Independence and the power to mediate
accurately represent the real pendulum, turns out to rely o.n a senes of There is no logical reason why models should be constructed to have
modelling decisions which simplify both the mathematIcs and the these qualities of partial independence. But, in practice they are. And,
physics of the pendulum. if models are to play an autonomous role allowing them to mediate
In other words theory does not provide us with an algorithm from between our theories and the world, and allowing us to learn about one
which the model i; constructed and by which all modelling decisions are or the other, they require such partial independence. It has been conven-
determined. As a matter of practice, modelling always involves ce~tain tional for philosophers of science to characterise scientific methodol-
simplifications and approximations which have to be decided indepen- ogy in terms of theories and data. Full dependence of a theory on data
dently of the theoretical requirements 2 or of data con d'ItlOns.
. . (and vice versa) is regarded as unhelpful, for how can we legitimately
Another way of characterising the constructlOn of models IS use our data to test our theory if it is not independent? This is the basis
through the use of analogies. For example, in the work of Mary Hesse of the requirement for independence of observation from theory. In
(1966), we find a creative role for neutral analogICal features m the con- practice however, theory ladenness of observation is allowed provided
struction of models. \ IVe can easily r~interpret her account by vIewmg that the observations are al ieasl neutral with respect to the theory
the neutral features as the means by which something independent and under test.
separate is introduced into the model, something which was n~t We can easily extend this argument about theories and data to apply
derived from our existing knowledge or theoretIcal structure. ThIS to models: we can only expect to use models to learn about our theo-
account too needs extending, for in practice it is not only the neutral ries or our world if there is at least partial independence of the model
features but also the negative features which come in from outside. from both. But models must also connect in some way with the theory
Mary Morgan (1997a, and this volume) provides two examples from or the data from the world otherwise we can say nothing about those
the work of Irving Fisher in which these negatIve analogIcal features domains. The situation seems not unlike the case of correlations. You
play a role in the construction of models. In one of ~he cases, she learn little from a perfect correlation between two things, for the two
describes the use of the mechanical balance as an analogJcal model for sets of data must share the same variations. Similarly, you learn little
the equation of exchange between money and goods in the economy. from a correlation of zero, for the two data sets share nothing in
The balance provides not only neutral features, but also negatlv~ fe~­ common. But any correlation between these two end-values tell you
tures, which are incorporated into the economIC model, ~rovldm~ It both the degree of association and provides the starting point for learn-
with independent elements which certainly do not appear m the ong- mgmore.
inal equation of exchange. Her second example, a model of how The crucial feature of partial independence is that models are not sit-
uated in the midtlle of an hierarchical structure between theory and the
:2 For a discussion of when modelling decisions are independent of theory, see M. Suarez's paper World. Because models typically include other elements, and model
in this volume. bUilding prdceeds in part independently of theory and data, we construe
18 Margaret Morrison and Mary S. Morgan Models as medwting instruments 19
models as being outside the theory-world axis. It is this feature which odds, these chemical formulas were not only the referents of the new
enables them to mediate effectively between the two. PI nception but also the tools for producing it. Through these models
Before we can understand how it is that models help us to learn new
things via this mediating role, we need to understand how it is that
:'e conception of a substitution linked, for the first time, the theory of
roportion to the notIons of compound and reactIon. We see then how
models function autonomously and more about how they are connected ~e formulas (models) served as the basis for developing the concept of
with theories and the world. a substitution which in turn enabled nineteenth-century chemists to
provide a theoretical representation for empirical knowledge of organic
2.2 FUNCTION transformatIons.
'''hat we want to draw attention to/however is a much wider charac-
Because model construction proceeds in part independendy of theory terisation of the function of models in relation to theory. Models are
and data models can have a life of their own and occupy a unique often used as instruments for exploring or experimenting on a theory
place in the production of scientific knowledge. Part of what it means that is already in place. There are several ways in which this can occur;
to situate models in this way involves giving an account of what they for instance, we can use a model to correct a theory. Sir George Francis
do - how it is that they can function autonomously and what advan- fitzGerald, a nineteenth-century British physicist, built mechanical
tages that autonomy provides in investigating both theo ries and the models of the aether out of pulleys and rubber bands and used these
world. One of our principle claims is that the autonomy of models models to correct Maxwell's electromagnetic theory. The models were
allows us to characterise them as instruments. And, just as there are thought to represent particular mechanical processes that must occur in
many different kinds of instruments, models can function as instru- the aether in order for a field theoretic account of electrodynamics to be
ments in a variety of ways. possible. When processes in the model were not found in the theory, the
latter was used as the basis of correction for the former.
2.2.1 Models in theory construction and exploration A slighdy different use is found in Geert Reuten's analysis of how
Marx used his model to explore certain characteristics of his theory of
One of the most obvious uses of models is to airl in t.heory construc- the capilalis< economy. In particular, ~1arx's modelling enabled him to
tion. 3 Just as we use tools as instruments to build things, we use models see which requirements for balanced growth in the economy had to hold
as instruments to build theory. This point is nicely illustrated in Ursula and which (such as price changes) could be safely neglected. Marx then
Klein's discussion of how chemical formulas, functioning as models or developed a sequence of such models to investigate the characteristics
paper tools, altered theory construction in organic chemistry. She shows required for successful transition from simple reproduction (no growth)
how in 1835 Dumas used his formula equation to introduce the notion to expanded reproduction (growth). In doing so he revealed the now
of substitution, something he would later develop into a new theory well-known 'knife-edge' feature of the growth path inherent in such
about the unitary structure of organic compounds. This notion of sub- models.
stitution is an example of the construction of a chemical conception But we also need models as instruments for exploring processes for
that was constrained by formulas and formula equations. Acting as which our theories do not give good accounts. Stephan Hartmann's
, This of course raises the sometimes problematic issue of distinguishing ben·.een a model and a discussion of the MIT-Bag Model shows how the model provided an
theory; at what point does the model become subsumed by, or attain the status of, a theory. The explanation of how quark confinement might be physically realised.
rough and ready distinction followed by scientists is usually to reserve the word model for an Confinement seemed to be a necessary hypothesis given experimental
aCCQum of a process that is less certain or incomplete in important respects. Then as the model
is able to account for more phenomena and has survived extensive testing it evolves imo a theory. results yet theory was unable to explain how it was possible.
A good example is the 'sta ndard model' in elementary particle physics. It accounts for particle In other cases, models are used to explore the implications of theories
interactions and provides extremely accurate predictions for phenomena governed by the weak,
strong and electromagnetic forces. Many physicists thin k of the standard model as a theory; even
in concrete situations. This is one way to understand the role of the
though it has several free parameters its remarkable success has alleviated doubts about its fun- twentieth-century conception of 'rational economic man'. This ideal-
damental assumptions. ised and h(ghly simplified characterisation of real economic behaviour
20 Margaret Morrison and Mary S. Morgan Models as mediating instruments 21
has been widely used in economists' microecono~ic the~ries as a tool to was simultaneously produced. Due to these calculational powers, the
explore the theoretical implications of the most smgle-mmded econom- formulas became surrogates for the concrete measurement of sub-
ising behaviour (see Morgan 1997b). More recently this 'model ~an' has stances involved in chemical transformations. They functioned as
been used as a device for benchmarkmg the results from expenm~ntal models capable of singling out pathways of reactions in new situations.
economics. This led to an explosion of theories accountl~g for th~ dIver- Because the formulas could link symbols with numbers it was possible
gence between the observed behaviour of real people m expenmental to balance the mgredlents and products of a chemical transformation
situations and that predicted from the theory of such a model man m - a crucial feature of their role as instruments for experiments.
the same situation.
Yet another way of using models as instruments focuses not o~ explor-
ing how theories work in specific contexts but rather o,n applymgtheo- 2.2.2 Models and'measurement
ries that are otherwise inapplicable. Nancy Cartwnght s contnbutIon to An import~nt, b~t overlooked function of models is the various but spe-
the volume provides an extended discussion of how. mterpretatIve cific ways In whIch they relate to measurement. 4 Not only are models
models are used in the application of abstract concepts like force func- instruments that can both structure and display measuring practices but
tions and the quantum Hamiltonian. She shows how the successful use the models themselves can function directly as measuring instruments.
of theory depends on being able to apply these abstract notIons not to What is involved in structuring or displaying a measurement and how
just any situation but only to those that .can be made to fit the model. does the model function as an instrument to perform such a task? Mary
This fit is carried out via the bndge pnnclples of the theory, they tell us Morgan's analysis of Irving Fisher's work on models illustrates just how
what concrete form abstract concepts can take; but t?e,se c~ncepts can this works. The mechanical balance, as used by merchants for weighing
only be applied when their interpretative models fit. It IS. m thIS sense. that and measunng exchange values of goods, provided Fisher with an illus-
the models are crucial for applying theory - they hmlt the domam of tration of the equation of exchange for the whole economy. What is
abstract concepts. Her discussion of superconductIvIty illustrates the interesting about Fisher's model is that he did not actually use the
cooperative effort among models, fundamental theory, empIrIcal knowl- balance model directly as a measuring instrument, but he did use it as
edge and an element of guesswork. ... . an instrument to display measurements that he had made and cali-
In other cases we can find a model functIOnIng dIrectly as an mstru- brated. He then used this calibrated display to draw inferences about the
ment for experi~ent. Such usage was prominent in nineteenth-centu~'Y relative changes that had taken place in the trade and money supply in
physics and chemistry. The mechanical aether models of Lord Kelvm the Amencan economy over the previous eighteen years. In a more
d FitzGerald that we mentioned above were seen as replacements for s~btle way, he also used the model of the mechanical balance to help
:~tual experiments on the aether. The models provided a ~echanical him conceptuahse certam thorny measurement problems in index
structure that embodied certain kinds of mechanIcal propertIes, conn.ec- number theory.
tions and processes that were supposedly necessary for the propagatIon An example where it is considerably more difficult to disentangle the
of electromagnetic waves. The successful manIpulatIon of the models measurement functions from model development is the case of
was seen as equivalent to experimental evidence for the eXIstence of nati?nal income accounts and macroeconometric models discussed by
these properties in the aether. That is, ma~ipulating the model was tan- Adnenne van den Bogaard. She shows how intimately the two were
tamount to manipulating the aether and, m that s~nse, th~ model func- connected. The model was constructed from theories which involved
tioned as both the instrument and object of expenmentatIon. a certain aggregate conception of the economy. This required the
Similarly, Ursula Klein shows us how chemical. formulas were reconception of economic measurements away from business-cycle
applied to represent and structure experi~ents - expenments that ~ere data and toward national income measures, thereby providing the
paradigmatic in the emerging sub-dISCIplIne of organIc chemIStry.
Using the formulas, Dumas could calculate how much chlonne was
4 We ?o not include here examples of using models as calculation devices _ these are discussed in
needed for the production of chloral and how much hydrochlonc aCId section 2.3.2,~vhen we consider simulations.
 Margaret Morrison and Mary S. Morgan Models as medw.ting instruments
model with its empirical base. At the same time, the particular kinds of ,dvance. When these models are run on a computer, they generate
measurements which were taken imposed certain constraints on the reJatively precise measurements of whatever trend and cyclical compo-
way the model was built and used: for example, the accounting ~ature pents are present in the data and provide an analysis of the interrelation-
of national income data requires certain identities to hold In the ships between them.
model. Models could fulfil their primary measurement task - measur-
ing the main relationships in the economy from the measurements on the
2_2.3 Modelsfor design and intervention
individual variables - only because the model and the measurements had
already been structured into a mutually compatible form.. . The final classification of models as instruments includes those that are
As we mentioned above, models themselves can also functlon dlrectly used for design and the production of various technologies. The inter-
as measuring instruments. A good example of this is the Leontief esting feature of these kinds of mOdels is that they are by no means
input- output model. Based on the Marxian reproduction model (pis- limited to the sorts of scale models that we usually associate with design.
cussed by Reuten), the Leontief model can be used to measure the tech- That is, the power of the model as a design instrument comes not from
nical coefficients of conversion from inputs to outputs in the economy. the fact that it is a replica (in certain respects) of the object to be built;
This Leontief matrix provides a measurement device to get at the empir- instead the capacity of mathematicalltheoretical models to function as
ical structure of the economy, and can be applied either at a very fine- design instruments stems from the fact that they provide the kind of
grained or a very coarse-grained level, depending on the number of information that allows us to intervene in the world.
sectors represented within the model. Another good example 15 provlded A paradigm case of this is the use of various kinds of optics models
in Ylargaret Morrison's discussion of the pendulum referred.to above. It in areas that range from lens design to building lasers. Ylodels from geo-
is possible using a plane pendulum to measure lo~al grav>tatlonalaccel- metrical optics that involve no assumptions about the physical nature of
eration to four significant figures of accuracy. Thl5 15 done by begmnmg light are used to calculate the path of a ray so that a lens can be pro-
with an idealised pendulum model and adding corrections for the duced that is free from aberration. A number of different kinds of geo-
different forces acting on various parts of the real pendulum. Once all metrical models are available depending on the types of rays, image
the corrections have been added, the pendulum model has become a distance and focal lengths that need m he considered. H owever, technol-
reasonably good approximation to the real system. And, although the ogy that relies on light wave propagation requires models from physical
sophistication of the apparatus (the. pendulum itselfj is what determines optics and when we move to shorter wave lengths, where photon ener-
the precision of the measurement, lt 15 the analysl5 and addmon of all the gies are large compared with the sensitivity of the equipment, we need
correction factors necessary for the model that determmes the accur"9' of to use models from quantum optics. For example, the design of lasers
the measurement of the gravitational acceleration . What this means is sometimes depends on quantum models and sometimes on a combina-
that the model functions as the source for the numerical calculation of tion of quantum and classical. The interesting point is that theory plays
G; hence, although we use the real pendulum to perform the measure- a somewhat passive role; it is the model that serves as an independent
ment that process is only possible given the correctlons performed on guideline for dealing with different kinds of technological problems (see
the n:odel. In that sense the model functions as the instrument that in Morrison 1998).
turn enables us to use the pendulum to measure G. A similar situation occurs in nuclear physics. Here there are several
Models can also serve as measuring instruments in cases where the different models of nuclear structure, each of which describes the
model has less structure than either the pendulum or the input- output nUcleus in a way diffe rent from and incompatible with the others. The
cases. One example is the use of multivariate structural time-series liquid drop model is useful in the production of nuclear fission while the
models in statistical economics. These are the direct descendants of the optical model serves as the basis for high energy scattering experiments.
business barometer models discussed above and share their general A!though we know that each individual model fails to incorporate sig-
assumption that certain economic time series consist of trends a~d nificant features of the nucleus, for example, the liquid drop ignores
cycles, but they do not specifY the time length of these components 111 quantum iltatistics and treats the nucleus classically while others ignore
 Margaret Morrison and Mary S. Morgan Models as mediating instruments
24
different quantum mechanical properties, they nevertheless are able to of instruments, they fulfil a representative function , the nature of
map onto technologies in a way that makes them successful, mdepen- is sometimes not obvious from the structure of the model itself.
dent sources of knowledge.
In economics we can point to the way that central banks use eco-
2.3 REPRESENTATION
nomic models t; provide a technology of intervention to control money
and price movements in the economy. There IS no one ,,:odel that The first question we need to ask is how an instrument can represent.
governs all situations - each bank de~elops a model appropnat~ for ItS We can think of a thermometer representing in a way that includes not
own economy. This modellmg activIty usually mvolves. trackmg . the simply the measurement of temperature but the representation of the
growth in various economic entities and momtonng v.a~lOu~ re~auon~ rise and fall in temperature through the rise and fall of the mercury in
ships between them. More recently monetary cond,tlOn mdlcators the column. Although the thermometer is not a model, the model as an
(YICIs) have been developed; these indicators are denved from mo~els instrument can also incorporate a representational capacity. Again, this
and function as measurement tools. W,th the help of th~lf model(~) and arises because of the model's relation to theory or through its relation to
MCls, the central bank decides when and how much to mtervene m the the world or to both.
money market in order to prevent inflation. The model provlde~ the
technology of intervention by prompting the tlfnmg, and perhaps md,-
2.3.1 Representing the world, representing theory
cating the amount of intervention need~d. Sometimes the model-based
intervention is triggered almost automatIcally, sometImes a large amount Above we saw the importance of maintaining a partial independence of
of judgement is involved. (Of course some central banks are more suc- the model from both theory and the world; but, just as partial indepen-
cessful than others at using this technology!) The more complex case of dence is required to achieve a level of autonomy so too a relation to at
macroeconometric modelling and its use as a technology of mterventlon least one domain is necessary for the mQdel to have any representative
is discussed below (in section 2.4 on learning). , . . function whatsoever. In some cases the model may, in the first instance,
As we stressed above, part of the reason models can function as mstru- bear its closest o~ strongest relation to .theory. For example, in Morrison's
ments is their partial independence from both theory and data. Yet, ~s caoe the model of' a pendulum functions specifically as a model of a
we have seen in this section, models fulfil a WIde range of funCtlons m theory - Newtonian mechanics - that describes a certain kind of
building, exploring and applying theories; in various measurement ac?v- motion. In other words, the pendulum model is an instance of harmonic
ities; and in the design and production of technolOgies for mterventlon motion. Recall that we need the model because Newton's force laws
in the world. These examples demonstrate the variety. of ways m whIch alone do not give us an adequate description of how a physical pendu-
models mediate between theories and the world by utlhsmg thelr pomts lum (an object in the world) behaves. The pendulum model represents
of intersection with both domains. Indeed, these intersections are esp~­ certain kinds of motion that are both described by the theory and pro-
cially evident in cases like the optical models and nucl~ar models m duced by the real pendulum. To that extent, it is also a model of the
physics and the monetary and macroeconomic models m economIcs. physical object. Fisher's mechanical balance model (discussed by
Although they draw on particular aspects of .hlgh level theory, th~y are Morgan) provided a representation of the theory of the monetary
by no means wholly dependent on theory for either thelr formulation or system. This model enabled him to explore theoretical aspects of the
decisions to use a particular model m a speCIfic context. . dynamic adjustment processes in the monetary economy and the phe-
'''''e want to caution, however, that our view of n:od~ls as mstr~ments nomena of the business cycle in a way that the existing theoretical rep-
is not one that entails a classical instrumentalIst mterpreta.uon of "'"entation (the equation of exchange) did not allow.
models. To advocate instrumentalism would be to unde:mme the . Alternatively, the model-world representation may be the more prom-
various ways in which models do teach us about both theones. and the ment one. The early statistical business barometers, constructed to repre-
world by providing concrete information about :eal phySIcal and ~nt (in graphic form) the path of real-world economic activity through
economic systems. They can do this because, in add,tlOn to playmg the I1me, were {,sed to help determine the empirical relationships between
 Margaret Morrison and Mary S. Morgan Models as mediating instruments
various elements in the economy and to forecast the turning points in that to the Navier-Stokes equations that could apply in the boundary layer.
particular economy's cycle. In contrasting cases, such model-world repre- The fluid flow was dIVIded conceptually mto two regIons, one of whIch
sentations may be used to explore theory by extending ItS basIc structure treated the fluid as ideal whilc the other required taking account of the
or developing a new theoretical framework. Such was the case with the boundary layer close to a solid body. The mathematical model of a fluid
nineteenth-century mechanical aether models of Kelvin and FitzGerald with a boundary layer functioned as a representation of both classical
discussed above. Recall that their function was to represent dynamical theory and the Navier-Stokes equations because each played a role in
relations that occurred in the aether, and based on the workings of the describing the fluid, yet neither was capable of such description taken
model FitzGerald was able to make corrections to Maxwell's field equa- on its own. In that sense the model was a representation of certain
tions. In the previous section we saw how manipulating these models had aspects of theoretical structure in addition to representing the actual
the status of experiment. This was possible only because the model itself phenomena involved in fluid flow past a solid body. In the first instance,
was taken as a representation of the aether. however, the model-world representation was established by the water
The more interesting examples are where the practice of model build- tunnel and it was this that formed the foundation for the model-theory
ing provides representations of both theory and the world, ena~ling us to representation as exemplified by the mathematical account of fluid flow.
see the tremendous power, that models can have as representauve mstru- Another case where the model bears a relation to both theory and the
ments. Margaret Morrison's discussion of Prandtl's hydrodynamic model world is Fisher's hydraulic model of the monetary system discussed by
of the boundary layer is a case in point. At the end of the nmeteenth Mary Morgan . The representative power of the model stems from both
century the theory of fluid ffow was in marked conflict with experiment; domains, with the structure of the model (its elements, their shapes and
no account could be given of why the very small frictional forces present their relationships) coming from theory while the model could be manip-
in the flow of water and air around a body created a no-slip condition at ulated to demonstrate certain empirical phenomena in the world.
the solid boundary. What Prandtl did was build a small water tunnel that Because the model represented both certain well-accepted theories (e.g.
could replicate fluid flows past different kinds of bodies. In a manner the quantity theory of. money) and could be shown to represent certain
similar to a wind tunnel, this mechanical model supplied a representation of well-known empirical phenomena (e.g. Gresham's law that 'bad money
different kinds of flows in rlifferent regions of the fluid, thereby allowing drives out good'), the model could be used to explore both the contested
one to understand the nature of the conflict with experiment. That is, the theory and problematic phenomena of bimetallism.
water tunnel furnished a visualisation of different areas in the fluid, those As we can see from the examples above, the idea of representation
close to the body and those more remote. The understanding of the used here is nOt the traditional one common in the philosophy of
various flow patterns produced by the tunnel then provided the elements science; in other words, we have not used the notion of 'representing' to
necessary to construct a mathematical model that could represent certain apply only to cases where there exists a kind of mirroring of a phenom-
kinds of theoretical structures applicable to the fluid. a
enon, system or theory by modeL s Instead, a representation is seen as
But, the idea that a model can represent a theoretical structure is one a kind of rendering - a partial representation that either abstracts from,
that needs clarification. In the hydrodynamics case the two theories used or translates into another form, the real nature of the system or theory,
to describe fluids, the classical theory and the Navier-Stokes equations or one that is capable of embodying only a portion of a system.
were inapplicable to real fluid flow. The former could not account for !'.Iorrison's example of the pendulum is about as close to the notion of
frictional forces and the latter was mathematically intractable. The 'mirroring' that we get. The more corrections that are added to the pen-
mathematical model, developed on the basis of the phenomena dulum model the closer it approximates the real object and gives us accu-
observed in the water tunnel, allowed Prandtl to apply theory in a spe- rate measurements. Many, perhaps most cases, are not like this. Even cases
cific way. The tunnel enabled him to see that, in certain areas of fluid where we begin with data (rather than theory) do not produce reflecting
flow, frictional forces were not important, thereby allowing the use of models. For example, the business barometers of van den Bogaard's
classical hydrodynamics. And, in areas where frictional forces were
present the mathematical model provided a number of approximations 3 s~ R. I. G. Hughes (1997) for a discussion of the notion of representation.
 Margaret Morrison and Mary S. Morgan Models as mediating instruments
chapter are thought to " iflect rather closely the time path of the economy. limitations to a model itself. A simulation, by definition, involves a
But they are by no means simple mirrors. Such a model mvolves both the similarity relation yet, as in the case of a model's predictions mapping
abstraction of certain elements from a large body of data provIded by the onto the world, we may be able to simulate the behaviour of phenom-
economy and their transformation and recombination to make a sunple ena without necessarily knowing that the simulated behaviour was pro-
time-series graphic representarion which forms. the barometer. duced in the same way as it occurred in nature. Although simulation and
Often, models are partial rendenngs and m such cases, we cannot modelling are closely associated it is important to isolate what it is about
always add corrections to a stable structure to mcrease the accuracy of a model that enables it to ' represent' by producing simulations. This
the representation. For example, models of the nucleus are able to rep- function is, at least in the first instance, due to certain structural features
resent only a small part of its behaviour and somenmes repres~nt nucle~r of the model, features that explain and constrain behaviour produced in
structure in ways that we know are not accurate (e.g. by Ignonng certam simulations. In the same way that general theoretical principles can con-
quantum mechanical properties). In this case, the addinon of parameters strain the ways in which models are constructed, so too the structure of
results in a new model that presents a radically different account of the the model constrains the kinds of behaviour that can be simulated.
nucleJs and its behaviour. Hence in describing nuclear processes, we are R. 1. G. Hughes' discussion of the Ising model provides a wealth of
left with a number of models that are inconsistent with each other. . information about just how important simulation is, as well as some ir:tter-
There are many ways that models can 'represent' eco~omlc o~ phySI- ,sting details about how it wqrks. H e deals with both computer simula-
cal systems with different levels of abstraction appropnate m different tions of the behaviour of the Ising model and with simulations of another
contexts. In some cases abstract representations simply cannot be type of theoretical model, the cellular automaton . The Ising model is
improved upon; but this in no way detracts from their value. When we especially intriguing because despite its very simple structure (an array of
want to understand nuclear fission we use the hqUld drop ~odel whIch points in a geometrical space) it can be used to gain insight into a diverse
gives us an account that is satisfactory for mappmg tbe model s pr~dlCtlons group of physical systems especially those that exhibit critical point beha-
onto a technological/experimental context. Vet we know th'~ model viour, as in the case of a transition from a liquid to a vapour. If one can
cannot be an accurate representation of nuclear structure. SImilarly we generate pictures from the computer simulation of the model's behaviour
often use many different kinds of models to represent a s.mgle system. For (as in the case of the twu-dimensional Ising model) it allows many features
example, we find a range of models being used for different purposes of critical behaviour to be instantly apprehended. As Hughes notes
within the analytical/research departments at central banks. They are all however, pictorial display is not a prerequisite for simulation but it helps.
designed to help understand and control the monetary and finanCIal His other example of simulation involves cellular automata models.
systems, but they range from theoreti~al small-scale rr:~cro-models repre- These consist of a regular lattice of spatial cells, each of which is in one
senting individual behaviour, to empIrical models whIch track finanCIal of a finite number of states. A specification of the state of each cell at a
markets, to large-scale macroeconometrlC ,:,odels represent~ng the whole particular time gives the configuration of the cellular automata (CA) at
economy. Sometimes they are used in conJunCtIon, other t~es they are that time. It is this discreteness that makes them especially suited to com-
used separately. W~ do not assess each .model based on Its abilIty to accu- puter simulations because they can provide exactly computable models.
rately mirror the system, rather the legttunacy of each different represen- Because there are structural similarities between the Ising model and the
tation is a function of the model's performance m speCIfic contexts. CA it should be possible to use the CA to simulate the behaviour of the
L~g model. His discussion of why this strategy fails suggests some inter-
esting points about how the structural constraints on these simple models
2.3.2 Simulation and representation
are intimately connected to the ways in which simulations can provide
There is another and increasingly popular sense in which a ,:,odel can knowledge of models and physical systems. Hughes' distinction between
provide representations, that is through the process of sunulanon. computer simulation of the model's behaviour a~d the use of computers
Sometimes simulations are used to mvesngate systems that are otherwISe for calculational purposes further illustrates the importance of regarding
inaccessible (e.g. astrophysical phenomena) or to explore extensIOns and th. model 'as an active agent in the production of scientific knowledge.
 Margaret Morrison and Mary S. Morgan Models as mediating instruments
The early theoretical business-cycle models of Frisch (discussed by there are no rules for model building and so the very activity of construc-
Boumans) were simulated to see to what extent they could reph~ate " n creates an opportunity to learn: what will fit together and how?
generic empirical cycles in the economy (rather than speClfic hlStoncal :rhaps this is why modelling is considered in many circles an art or
facts). This was in part taken as a test of the adequacy .of the model, but craft" it does not necessarily involve the most sophisticated mathematics
the simulations also threw up other generic cycles which had empmcal or "';quire extensive knowledge of every aspect of the system . It does
credibility, and provided a prediction of a new cycle which had not yet seem to require acquired skills in choosing the parts and fitting them
been observed in the data. In a different example, the first macroecono- together, but it is wise to acknowledge that some people are good model
metric model, built by Tinbergen to represent the Dutch economy (dis- builders, just as some people are good experimentalists.
cussed by van den Bogaard and more fully in Morgan 1990), was first Learning from construction is clearly involved in the hydrodynamics
estimated using empirical data, and then simulated to analyse the effects case described by Margaret Morrison. In this case, there was visual
of six different possible interventions in the economy. The aim was to experimental evidence about the behaviour of fluids. There were also
see how best to get the Dutch economy out of the Great Depression and theoretical elements, particularly a set of intractable equations supposed
the simulations enabled Tinbergen to compare the concrete effects of to govern the behaviour of fluids, which could neither account for nor
the different proposals within the world represented in the 'model. On be applied directly to, the observed behaviour. Constructing a mathe-
this basis, he advocated that the Dutch withdraw from the gold standard matical model of the observ~d behaviour involved a twofold process of
system, a policy later adopted by the Dutch government. conceptual ising both evidence and the available theories into compat-
Consequently we can say that simulations allow you to map the model ible terms. One involved interpreting the evidence into a form that could
predictions onto empirical level facts in a direa way. ='I~t only are the Sim- be modelled involved the 'conceptualisation' of the fluid into two areas.
ulations a way to apply models but they funcllon as a kind of bndge pnn- The other required developing a different set of simplifications and
ciple from an abstract model ,:"ith stylised facts to a technologIcal context approximations to provide an adequate theoretical/mathematical
with concrete facts. In that sense we can see how models are capable of model. It is this process of interpreting, conceptual ising and integrating
representing physical or economic systems at twO distinct levels, .one that that goes on in model development which involves learning about the
includes the higher level structure that the model Itsf'lf p.mhodtcs In a~ problem at hand. This case iIIusu'ates just how modelling enables you to
abstract and idealised way and the other, the level of concrete detail learn things both about the world (the behaviour of fluids) and the
through the kinds of simulations that the models enable us to produce. theory (about the way the equations could be brought to apply).
Hence, instead of being at odds with each other, the mstrumental and rep- A similar process of learning by construction is evident in the cases
resentative functions of models are in fact complementary. The model rep- that Marcel Boumans and Stephan Hartmann describe. In Boumans'
resents systems via simulations, simulations that are possible because.of the example of constructing the first generation of business-cycle models,
model's ability to function as the initial instrument of their produCllon. economists nad to learn by trial and error (and by pinching bits from
Because of the various representative and investigative roles that other modelling attempts) how the bits of the business-cycle theory and
models play, it is possible to learn a great deal from them, not only about evidence could be integrated together into a model. These were essen-
the model itself but about theory, the world and how to connect the two. tially theoretical models, models designed to construct adequate busi-
In what follows we discuss some ways that this learning takes place. ness-cycle theories. Thereafter, economists no longer had to learn how
to construct such theoretical models. They inherited the basic recipe for
the business-cycle, and could add their own particular variations. At a
2.4 LEARNIl\G
certain point, a new recipe was developed, and a new generation of
models resulted. In Hartmann's -examples, various alternative models
2.4.1 Learningfrom construction were constructed to account for a particular phenomenon. But in the
:\fodelling allows for the possibility of learning at two points in the MIT-Bag Model and the NJL model, both of which he discusses in
process. The first is in constructing the model. As we have pomted out, detail, wd see that there is a certain process by which the model is
 Margaret Morrison and Mary S. Morgan Models as mediaJing instruments 33
gradually built up, new pieces added, and the model tweaked in response way of 'learning from using' a model is that models are manipulated to
to perceived problems and omissions. teach us things about themselves. When we build a model, we create a
kind of representative structure. But, when we manipulate the model, or
2.4.2 Models as technologies for investigation calculate things within the model, we learn , in the first instance, about
the model world - the situation depicted by the model.
The second stage where learning takes place is in using the model. One well-known case where experimenting with a model enables us
Models can fulfil many functions as we have seen; but they generally to derive or understand certain results is the 'balls in an urn' model in
perform these functions not by being built, but by being used. Models statistics. This provides a model of certain types of situations thought to
are not passive instruments, they must be put to work, used, or manipu- exist in the world and for which statisticians have well-worked out theo-
lated. So, we focus here on a second, more public, aspect of learning ries. The model can be used as a sampling device that provides experi-
from models, and one which might be considered more generic. Because mental data for calculations, and can be used as a device to conceptualise
there are many more people who use models than who construct them and demonstrate certain probability set ups. It is so widely used in
we need some sense of how 'learning from using' takes place. statistics, that the model mostly exists now only as a written description
Models may be physical objects, mathematical structures, diagrams, for thought experiments. (We know so well how to learn from this model
computer programmes or whatever, but they all act as a form of instru- that we do not now even need the model itself: we imagine it!) In this
ment for investigating the world, our theories, or even other models. case, our manipulations teach us about the world in the model - the
They combine three particular characteristics which enable us to talk of behaviour of balls in an urn under cerlain probability laws.
models as a technology, the features of which have been outlined in pre- The Ising model, discussed by Hughes, is another example of the
vious sections of this essay. To briefly recap: first, model construction importance of the learning that takes place within the world of the model.
involves a partial independence from theories and the world but also a If we leave aside simulations and focus only on the information provided
partial dependence on them both. Secondly, models can function auton- by the model itself, we can see that the model had tremendous theoretical
omously in a variety of ways to explore theories and the world. Thirdly, significance for understanding critical point phenomena, regardless of
models represent either aspects of our theories, or aspects of Ollr world, whether elements in the model denote elemenls of any actual physical
or more typically aspects of both at once. When we use or manipulate a system. At first this seems an odd situation. But, what Hughes wants to
model, its power as a technology becomes apparent: we make use of claim is that a model may in fact provide a good explanation of the beha-
these characteristics of partial independence, functional autonomy and viour of the system without it being able to faithfully represent that system.
representation to learn something from the manipulation. To see how The model functions as an epistemic resource; we must first understand
this works let us again consider again some of the examples we discussed what we can demonstrate in the model before we can ask questions about
already as well as some new ones. real systems. A physical process supplies the dynamic of the model, a
We showed earlier (in section 2.2) how models function as a technol- dynamic that can be used to generate conclusions about the model's beha-
ogy that allows us to explore, build and apply theories, to structure and viour. The model functions as a 'representative' rather than a 'represen-
make measurements, and to make things work in the world. It is in the tation' of a physical system. Consequently, learning about and from the
process of using these technologies to interrogate the world or our ~odel's Own internal structure provides the starting point for understand-
theory that learning takes place. Again, the pendulum case is a classic 109 actual, possible and physically impossible worlds.
example. The model represents, in its details, both the theory and a real Oftentimes the things we learn from manipulating the world in the
world pendulum (yet is partially independent of both), and it functions model can be transferred to the theory or to the world which the model
as an autonomous instrument which allows us to make the correct cal- ~resents. Perhaps the most cornman example in economics of learn-
culations for measurements to find out a particular piece of information a
mg about theory from manipulation within model, is the case of
about the world. Edgeworth-Bowley boxes: simple diagrammatic models of exchange
The general way of characterising and understanding this second b"tween tivo people. Generations of economics students have learnt
34 Margaret Morrison and Mary S. Morgan Models as mediating instruments 35
exchange theory by manipulations within the box. This is done by Ib model provided a qualitative 'explanation' of certain historically
tracing through the points of trade which follow from altering the start- ~r\'ed phenomena, it could not provide the kind of quantitative rep-
ing points or the particular shape of the lines drawn according to resentation which would enable theo~etically-based prediction or
certain assumptions about individual behaviour. But these models have ctespite Fisher's attempts) actIve mterventIon In the monetary system of
also been used over the last century as an important technology for
Ibe time.
deriving new theoretical results not only in their original field of simple These manipulations of the model contrast with those discussed by
exchange, but also in the more complex cases of international econom- Adrienne van den Bogaard. She reports on the considerable arguments
ics. The original user, Edgeworth, derived his theoretical results by a about the correct use of the models she discusses in her essay. Both the
series of diagrammatic experiments using the box. Since then, many barometer and the econometric model could be manipulated to predict
problems have found solutions from manipulations inside Edgeworth- future values of the data, but was it legitimate to do so? Once the model
Bowley box diagrams, and the results learnt from these models are had been built, it became routine to do so. This is part of the economet-
taken without question into the theoretical realm (see Humphrey ries tradition: as noted above, Tinbergen had manipulated the first
1996). The model shares those features of the technology that we have macroeconometric model ever built to calcu late the effects of six
already noted: the box provides a representation of a simple world, the different policy options and so see how best to intervene to get the Dutch
model is neither theory nor the world, but functions autonomously to economy out of the Great Depression of the 1930s. He had also run the
provide new (and teach old) theoretical results via experiments within model to forecast the future values for the economy assuming no change
the box. in policy. These econometric models explicitly (by design) are taken to
In a similar manner, the models of the equation of exchange represent both macroeconomic theory and the world: they are con-
described by Mary Morgan were used to demonstrate fimnally the structed that way (as we saw earlier). But their main purpose is not to
nature of the theoretical relationship implied in the quantity theory of explore theory, but to explore past and future conditions of the world
money: namely how the cause- effect relationship between money and and perhaps to change it. This is done by manipulating the model to
prices was embedded in the equation of exchange, and that two other predict and to simulate the outcomes which would result if the govern-
factors needed to remain constant for the quantity theory relation to be ment were to intervene in particular ways, or if particular outside events
observable in the world. This was done by manipulating the models to were to happen. By manipulating the model in such ways, we can learn
show the effects of changes in each of the variables involved, con- things about the economy the model represents.
strained as they were by the equation. The manipulation of the alter-
native mechanical balance version of the model prompted the
theoretical developments responsible for integrating the monetary 2 .5 CONCLUSION
theory of the economic cycle into the same structure as the quantity We have argued in this opening essay that scientific models have certain
theory of money. It was because this analogical mechanical balance features which enable us to treat them as a technology. They provide us
model represented the equation of exchange, but shared only part of with a tool for investigation, giving the user the potential to learn about
tbe same structure with the theoretical equation of exchange, that It the world or about theories or both. Because of their characteristics of
could function autonomously and be used to explore and build new autonomy and representational power, and their ability to effect a rela-
theory. tion between scientific theories and the world, they can act as a power-
The second model built by Fisher, the hydraulic model of the mone- ful agent in the learning process. That is to say, models are both a means
tary system incorporated both institutional and economic features. It to and a SOurce of knowledge. This accounts both for their broad appli-
was manipulated to show how a variety of real world results might arise cability, and the extensive use of models in modern science.
from the interaction of economic laws and government decisions and to ?ur account shows the range of functions and variety of ways in
'prove' two contested theoretical results about bimetallism within the wh,ch models can be brought to bear in problem-solving situations.
world of the model. But, these results remained contested: for although Indeed, OUr goal is to stress the significance of this point especially in
 Margaret Morrison and Mary S. Morgan
JVfodels as mediating instruments 37
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NOTE
Two earlier users of the term 'mediators' in accounts of science should
be mentioned. :\"orton Wise has used the term in various ditlerent con-
texts in the history of science, and with slighcly different connotations,
the most relevant being his 1993 paper 'Mediations: Enlightenment
Balancing Acts, or the Technologies of Rationalism'. His term 'tech-
nologies' is a broad notion which might easily include our 'models'; and
they mediate by playing a connecting role to join theory/ideology with
reality in constructing a rationalist culture in Enlightenment France.
Our focus here is on using models as instruments of investigation about
the two domains they connect. The second user is Adam Morton (1993)
who discusses mediating models. On his account the models are math-
ematical and mediate between a governing theory and the phenomena
produced by the model; that is, the mathematical descriptions generated
by the modelling assumptions. Although our account of mediation
would typically include such cases it is meant to encompass much more,
both in terms of the kinds of models at issue and the ways in which the
models themselves function as mediators.