105

*Manuscript received December 2001; revised July 2002.

† To contact the author, please write to Eric Winsberg, Department of Philosophy, The
University of South Florida, FAO 226, 4202 Fowler Ave., Tampa FL 33620; e-mail:
winsberg@chuma1.cas.usf.edu.

‡ I thank Arthur Fine, Mathias Frisch, Karen Darling, and Joanne Waugh for their
comments and criticisms, as well as many people who offered helpful comments when
I presented earlier versions of this paper at the University of South Florida and at
Wichita State University. I am greatly indebted to three anonymous reviewers—espe-
cially one, whose efforts went well beyond the norm.

Philosophy of Science, 70 (January 2003) pp. 105–125. 0031-8248/2003/7001-0009$10.00
Copyright 2003 by the Philosophy of Science Association. All rights reserved.

1. See quotation from Galison below.

Simulated Experiments:
Methodology for a Virtual World*

Eric Winsberg†‡

This paper examines the relationship between simulation and experiment. Many dis-
cussions of simulation, and indeed the term “numerical experiments,” invoke a strong
metaphor of experimentation. On the other hand, many simulations begin as attempts
to apply scientific theories. This has lead many to characterize simulation as lying be-
tween theory and experiment. The aim of the paper is to try to reconcile these two
points of view—to understand what methodological and epistemological features simu-
lation has in common with experimentation, while at the same time keeping a keen eye
on simulation’s ancestry as a form of scientific theorizing. In so doing, it seeks to apply
some of the insights of recent work on the philosophy of experiment to an aspect of
theorizing that is of growing philosophical interest: the construction of local models.

1. Introduction. Many complex systems in the physical sciences are studied
by developing models of their underlying physics on a computer, and by
using computationally intensive methods to learn about the behavior of
those systems. These methods are called “simulations,” or “numerical ex-
periments”; names that strongly evoke the metaphor of experimentation.
At the same time, the mathematical models that drive these particular
kinds of simulations are motivated by theory. Prima facie, they are nothing
but applications of scientific theories to systems under the theories’ do-
main. So where “on the methodological map”1do techniques of computer



 106

2. For example, see Morgan and Morrison 1999, Cartwright 1999, and Giere 1999.

simulation lie? What features do simulations actually share with labora-
tory experiments?

While there is nothing like a received view of the relation between simu-
lation and experiment, I will piece together and critically examine three
perspectives from the scientific, philosophical, and other “STS” literature.
I will argue that while each of these views can contribute to an understand-
ing of simulation, none of them is quite suitable for understanding how
simulation can have methodological and epistemological features in com-
mon with experimentation, while still playing the role of a form of scien-
tific theorizing. This examination will apply some of the insights of recent
work on the philosophy of experiment to understand how, and to what
extent, theoretical principles guide the construction of locally representa-
tive models.2

My examination will both amplify and illuminate Mary Morgan and
Margaret Morrison’s recent characterization of “autonomous models”:

One of the points we want to stress is that when one looks at examples
of different ways that models function, we see that they occupy an
autonomous role in scientific work. We want to outline . . . an account
of models as autonomous agents, and to show how they function as
instruments of investigation. . . . It is precisely because the models are
partially independent of both theories and the world that they have
this autonomous component and so can be used as instruments of
exploration in both domains (Morrison and Morgan, 1999, p.10,
original emphasis).

For our purposes, the term “autonomous models” is somewhat mislead-
ing. A better term would be “semiautonomous.” The claim frequently
made by Morrison and Morgan that models are autonomous or indepen-
dent of theory is meant to emphasize the fact that there is no algorithm
for reading models off from theory. While models generally incorporate
a great deal of the theory or theories with which they are connected, they
are usually fashioned by appeal to, by inspiration from, and with the use
of material from, an astonishingly large range of sources: empirical data,
mechanical models, calculational techniques (from the exact to the out-
rageously inexact), metaphor, and intuition. But to call these models com-
pletely “autonomous,” at least in this context, is to deny the obvious and
strong connections these models have to theory.

Examining the methodological role and epistemic status of simulation
techniques will help to clarify the relevant notion of a “semiautonomous
model.” Clarifying Morgan and Morrison’s notion of “autonomy” is a
special case of a wider objective: in simulation studies, model building is



     107

3. A note on language: In this paper I move back and forth between talk of models
and talk of simulation. I use the term “simulation” to refer to comprehensive process
of building, running, and inferring from computational models. Simulations are based
on models, they incorporate model assumptions, and they in turn produce models of
phenomena. For a more thorough discussion of the role different kinds of models play
in the simulation process, see my 1999.

carried out in the open. That is, unlike in other scientific domains where
modeling assumptions are often swept under the rug with a phrase like “it
can easily be shown” in simulation studies, modeling assumptions are of-
ten much more explicitly motivated and scrutinized by the practitioners
themselves. Simulation provides a clear window through which to view
the model making process.3

2. Motivating Models.

Equation (1.2–9) is a second order, nonlinear, vector, differential
equation which has defied solution in its present form. It is here there-
fore we depart from the realities of nature to make some simplifying
assumptions . . . (Bate, Mueller, and White 1971)

Computer simulations are techniques for studying mathematically com-
plex systems. They have applications in almost every field of scientific
study—from quantum chemistry to meteorology and from paleontology
to the study of traffic flow patterns. Simulations are typically classified
according to the type of algorithm that they employ. “Discretization”
techniques transform continuous differential equations into step-by-step
algebraic expressions. “Monte Carlo” methods use random sampling al-
gorithms even when there is no underlying indeterminism in the system.
“Cellular automata” assign a discrete state to each node of a network of
elements, and assign rules of evolution for each node based on its local
environment in the network.

In this paper, I will be focusing on simulations that employ methods
of discretization. This method begins with a mathematical model that de-
picts the time-evolution of the system being studied in terms of rules of
evolution for the variables of the model. For discretization techniques to
apply, these rules of evolution come in the form of differential equations.
In some cases (typically in the physical sciences) the mathematical model
is motivated by well-established theoretical principles. In other cases, the
model may be based on speculation, the consequences of which need to
be studied. In this paper, I will focus on theoretically motivated models.

When a theoretically motivated model is to be discretized, the original
differential equations transformed into a computable algorithm that can
be run on a digital computer, and the evolution of the dependant variables



 108

on the computer is said to “simulate” the evolution of the system in ques-
tion. Sophisticated graphical techniques are often used to transform the
output into graphics and videos that sometimes resemble images such as
might be produced by laboratory instruments trained upon the system in
question.

We can see here the importance of emphasizing the semiautonomy of
models. In these simulations, the principle model is hatched directly out
of theory. But as the quotation at the beginning of this section suggests,
it is one thing for theory to directly yield a model, and quite another for
theory to be able to yield a model for which we can find solutions.

In fact, for many of the systems that are of interest in the computa-
tionally intensive sciences, the models that are suggested directly by theory
consist of second-order, non-linear differential equations; and finding use-
ful and reliable solutions for these models, even using numerical methods,
is an unrealistic goal. Successful numerical methods, therefore, invariably
require of the simulationists that they transform the model suggested by
theory in significant ways. Idealizations, approximations, and even self-
conscious falsifications are introduced into the model. In the end, the
model that is used to run the simulation is an offspring of the theory, but
it is a mongrel offspring. It is also substantially shaped by the exigencies
of practical computational limitations and by information from a wide
range of other sources.

A concrete example might help to clarify these remarks. Suppose we
are interested in understanding how vortices are generated when a shock
wave passes through an inhomogeneous medium at supersonic speeds.
One way to study the problem is in the laboratory. Skilled experimenters
have conceived of idealized experiments involving the interaction of shock
waves in air with spherical and cylindrical bubbles of various gases of
various densities. The purpose of these experiments is to help shed light
on the general dynamical features of these kinds of shock waves. Shad-
owgraph images of these experiments can reveal a great deal of valuable
information. (See Winkler et al. 1987)

But by “simulating” these same experimental setups on a computer, a
much wider variety of initial conditions can be studied and much more
detailed data can be gathered. In order to run such a simulation, the sim-
ulationist begins by choosing a principle model—a model that characterizes
the system in terms of both the arrangement of its constituent parts, and
the rules of evolution that govern the changes of state that the system un-
dergoes over time. In our case, the choice of how to do this is motivated by
our understanding of the experimental setup, and by our best theories of
the flow of compressible fluids—in this case the Euler equations for an
inviscid compressible gas. These equations describe a fluid that is compress-
ible but they describe neither the effects of viscosity nor of heat conduction.



     109

Since these equations are analytically unmanageable under all but the
most symmetric and time-independent conditions, simulation requires
computational methods, that, given reasonable computer resources, can
accurately trace out the patterns of flow. This is not a matter of simple-
mindedly taking continuous differential equations and transforming them
into discrete algebraic equations. Given limitations on computer speed and
memory, these techniques also invariably resort to other approximations,
idealizations, and even “falsifications”—that is, model assumptions that
directly contradict theory. Making the simulation work, and making it
produce results that the simulationist is willing to sanction as reliable, is
a skill that has been developed in a lengthy period of trial, error, and
comparison with both theory and known results from physical experi-
ments. In sum, by the semiautonomy of a simulation model, one refers to
the fact it starts from theory but one modifies it with extensive approxi-
mations, idealizations, falsifications, auxiliary information, and the blood,
sweat, and tears of much trial and error.

In our example, the primary difficulty in modeling these supersonic
fluid flows is capturing the discontinuities—abrupt changes in value in the
flow variables. It is in overcoming such difficulties that extra-theoretic
modeling “tricks” are invoked. In particular, in simulations of supersonic
flows, there are important effects in and around shock fronts that take
place at length and time scales that are much too small to be captured in
even the most finely grained discretizations. Thus, some kind of falsifica-
tion must be employed in the model in order to resolve these key effects
(Woodward and Collela, 1984). But this raises an important epistemolog-
ical question; one that needs to be reflected on if we are to take the notion
of an autonomous model seriously. What, if not theory, can serve to sanc-
tion these models? This question will be lurking in the background as we
investigate the relation between theory and experiment. It will return to
center stage later on.

3. It’s All Metaphorical. As mentioned, there are three different views in
the literature about how to methodologically classify simulation vis à vis
its experimental cousins. One answer is that all talk of “simulation” and
“numerical experiments” is purely hyperbolic or metaphorical—simula-
tion is nothing more and nothing less than using brute-force computa-
tional means to solve analytically intractable equations. A second view,
in which the terms “simulation” and “numerical experiment” are taken
quite literally, a simulation is a stand-in, or mimic, of a real-world system,
and can therefore be experimented on just like any other experimental
target. Finally, there is the view that simulation is a brand new “third
mode” of science, neither experimental nor theoretical. In what follows, I
will weigh the merits of these three views, emphasizing how much each of



 110

these views can contribute to understanding how models are to be evalu-
ated.

I should point out that I know of no published references that them-
selves argue for exactly the view that simulation is just a fancy word for
using brute-force computational means to solve analytically intractable
equations. It is, however, a not-uncommon opinion expressed in conver-
sation.

One perspective from which to see clearly that this view is very wide of
the mark has been offered by the philosopher R. I. G. Hughes, who has
urged a distinction between “the use of computer techniques to perform
calculations, on the one hand, and [genuine] computer simulation, on the
other” (Hughes 1999, 128). For Hughes, the distinction hinges on the
“thoroughly realist mode of description” that is used to describe the results
of genuine simulations, and to the images that are produced by simulation,
which often resemble photographs of material physical models. Thus,
what distinguishes genuine simulations from mere number crunching is
that simulations have genuinely “mimetic” (Hughes’ word) characteristics.

There is certainly something right about this. The “mimetic” charac-
teristics of an algorithm—one that uses sophisticated graphics and that is
treated realistically by its users—are surely an important consideration
that lead practitioners to call them simulations rather than mere compu-
tations. So psychologically, at the very least, working with a simulation is
much more like doing an experiment if the simulation produces life-like
images reminiscent of laboratory photographs.

Of course, we are looking for something deeper than a superficial, psy-
chological resemblance. In fact, if this were all that simulations, or “nu-
merical experiments”, had in common with experiments, then one might
indeed be tempted to agree that talk of simulation as numerical experi-
mentation was no more than mere hyperbole.

To illustrate this point, we need look no further than the example of
mere number crunching offered by Hughes; the use of a computer to cal-
culate the orbits of planets in a three-body problem. In such a case, there
is nothing whatsoever that prevents creators of such an algorithm from
imbuing it with high quality graphical output, and from characterizing
their results in as realistic a mode of description as they like. Since no
distinction of great philosophical import could hinge on whether or not
“mere” computation is embellished with graphic presentation, we are go-
ing to have to do more than cite the fact that some algorithms use graphics
and some don’t.

There are in fact two characteristics of true simulations that I argue
meaningfully distinguish them from mere brute-force computation, in
ways that connect them to experimental practice in an interesting fashion:



     111

4. I note that a similar point about simulations has also been made by Paul Humphrey
in his 1995. He refers to the techniques that motivate the construction of these models
as heuristics. He explicitly contrasts ‘heuristics” with determinate methods for moving
from theory to model. See also Winsberg 1999 for more details on how model construc-
tion is often guided, but not determined, by theory.

• Successful simulation studies do more than compute numbers. They
make use of a variety of techniques (most of which, pace Hughes,
involve imaging in one way or another) to draw inferences from
these numbers.

• Simulations make creative use of calculational techniques that can
only be motivated extra-mathematically and extra-theoretically.4As
such, unlike simple computations that can be carried out on a com-
puter, the results of simulations are not automatically reliable. Much
effort and expertise goes into deciding which simulation results are
reliable and which are not.

Let me elaborate on these two themes. First, simulations are interest-
ingly like experiments, because they involve, in essence, data analysis. Sup-
pose that we are confronted with a fluid flow problem like the one dis-
cussed above. In such a case, we think that we know the governing
principles (in this case, a form of the Euler equations), but we still do not
know what kind of local behavior these principles predict. One approach
would be to use a tractable, approximative, analytical technique. For ex-
ample, analysts might use a series expansion, truncate all but two or three
of the terms and end up with an equation for which one can write down
a solution. Or, one might put to work the kind of more indirect simulation
methods indicated in the last section. Both of these techniques employ
approximations, both involve creative work, and both will, in turn, give
rise to issues of justification.

One important difference between the two methods, however, is this:
the analytic method will produce an algebraic expression as its result. That
expression, in turn, can represent the behavior of a general class of sys-
tems. Various functional dependencies and patterns of behavior can easily
be read off from a closed form expression.

Numerical methods, on the other hand, result in a big pile of numbers.
If simulationists want to learn about the general qualitative features of a
class of systems, then they must apply all the usual tools of experimental
science for analyzing data: visualization, statistics, data mining, etc. If they
want to discover functional dependencies, then they must also run a bar-
rage of trials, looking at the results across a wide range of parameters. It
is without a doubt this aspect of simulation that carries the most obvious
methodological characteristics of experimental work. Furthermore, it is



 112

5. Obviously, Winkler et al. are using the expression “fundamental physics” in a manner
that is quite different than that to which philosophers might be accustomed. I take it
that they are using the expression to signify not the fundamentals laws or theories of
the system, but rather the emergent structural features of the dynamics like vortices,
waves, and surfaces and their interactions—the important, dynamically significant long-
term and long-range features of the dynamics that give insight into its time-evolution.
This notion of “fundamental” physics and its connection to accounts of scientific ex-
planation is an area worthy of further research.

the need to draw inferences from these piles of data that brings about what
Hughes calls the “mimetic” aspects of simulation—their “thoroughly re-
alistic mode of description.”

In a review article on computational methods, a group of researchers
describe the situation this way:

The most common method for observing the behavior of laboratory
flows is to make photographs using a variety of techniques that bring
out specific features. . . . Computational fluid dynamicists naturally
want to use similar techniques to display their results. Displays not
only make comparisons with laboratory data much easier, but also
are useful at getting at the fundamental physics of wave interactions,
surface instabilities, vortex generation and other phenomena that may
be involved in the flow. (Winkler et al. 1987, 29)

Recall Hughes’ insistence that genuine simulations be distinguished
from mere step-by-step calculations on the basis of the former’s mimetic
qualities. It seems to me that what underlies this distinction is really the
difference between computational methods that are used to make specific
quantitative predictions (for example, where will the fourth planet in a
five-body system be after 72 days) on the one hand and computational
methods used to “get at the fundamental physics”5 on the other. It is only
in the latter case that imaging techniques become de rigueur and that the
computational model takes on a mimetic quality, so that techniques fa-
miliar to the laboratory observer can be applied. But whether or not im-
aging techniques per se are used, simulations that aim to get at global,
diachronic features of the systems they model will invariable not only
produce numbers, but also draw inferences from those numbers in a man-
ner that is richly analogous to experimental data analysis.

The second feature of simulations with respect to which they have a
great deal in common with experimental practice is the constant concern
with uncertainty and error. As I have already emphasized, although simu-
lation often is initially motivated by well-established theory, the end model
that drives the computations generally incorporates modeling assumptions
that are not theoretically motivated. The results of the simulation, there-
fore, do not automatically come with a stamp of approval that carries the



     113

full faith and credit of the governing theory’s epistemic credentials. Quot-
ing again Winkler—“Unless uncertainties are kept under control, the com-
putational approach cannot uncover new physical phenomena” (Ibid. 29;
original emphasis).

That simulations and laboratory experiments both have a need to man-
age uncertainties is perhaps interesting in and of itself. But if we are in-
terested in epistemological issues surrounding autonomous models, the
really interesting question is whether or not they do so in analogous ways.
If so, then perhaps some of the insights from recent work in the philosophy
of experiment might shed some light on the sanctioning of models.

I will have more to say about these questions later on. For now it will
suffice to address the challenge of this section with the following point:
while having a mimetic quality is not in itself what gives a simulation
interesting methodological and epistemological features, it is an important
sign of other features which do. The extensive use of realistic images in
simulation is a stepping stone that simulationists use in order to make
inferences from their data. It is also a tool they use in order to draw
comparisons between simulation results and real systems; a move that is
part of the process of sanctioning their results. It is the drawing of infer-
ences and sanctioning of results that give rise to interesting philosophical
connections between simulation and experimental practice.

4. The Computer as Experimental Target. Another view on how to locate
simulation methodologically has been to interpret expressions like “simu-
lation” and “numerical experiment” literally. The idea here is to interpret
the simulation algorithm as literally “mimicking” the system or systems
of interest and to understand what scientists do as performing experiments
on the computer or computer algorithm, which acts as a stand in for, or
probe of, the system in question. Computer simulations are experiments,
and the computer is the target of the experiment.

Practitioners of simulation often emphasize this point of view them-
selves, especially in popular or semi-popular presentations that are geared
towards expounding the virtues of numerical methods. For example:

A simulation that accurately mimics a complex phenomenon contains
a wealth of information about that phenomenon. Variables such as
temperature, pressure, humidity, and wind velocity are evaluated at
thousands of points by the supercomputer as it simulates the devel-
opment of a storm, for example. Such data, which far exceed anything
that could be gained from launching a fleet of weather balloons, re-
veals intimate details of what is going on in the storm cloud. (Kauf-
mann and Smarr 1993, 4)

The germ of this idea probably comes from the father of computational
methods himself, John von Neumann—although he actually expressed the



 114

idea in reverse. Working on highly intractable fluid dynamical problems
at Los Alamos, von Neumann lamented the fact that he and his colleagues
often had to perform difficult experiments just to determine facts that
should, in principle, be derivable from well-known underlying principles
and governing equations:

The purpose of the experiment is not to verify a proposed theory but
to replace a computation from an unquestioned theory by direct mea-
surement. . . . Thus wind tunnels are used . . . as computing devices
. . . to integrate the nonlinear partial differential equations of fluid
dynamics.” (quoted in Winkler et al. 1987, 28)

Once von Neumann’s dream became ostensibly realized, and the wind
tunnel was replaced by the computer, it becomes not-entirely unnatural
to view the resulting activity as performing experiments in a virtual wind
tunnel. Something like this view of computer simulation has received the
most attention by philosophers of science. Paul Humphreys (1994), for
example, argues for a view like this vis à vis Monte Carlo simulations, on
the grounds that when a program runs on a digital computer, the resulting
apparatus is a physical system. Any runs of the algorithm, therefore, are
just experimental trials on physical target. This is also roughly the view
that is espoused by Hughes. According to Hughes, there is no reason that
we should resist thinking of computer simulations as experiments since
they lie on a “slippery slope” that makes them conceptually inseparable
from experiment. The slope looks something like this:

1. We experiment on a model water wheel in order to learn about water
wheels in general.

2. We experiment on an electrical damped harmonic oscillator in order
to learn about mechanical damped harmonic oscillators that are gov-
erned by a structurally identical equation.

3. We run experiments on cellular automata machines in order to learn
about systems with identical “symmetries and topologies.”

4. Why not also say, then, that we perform experiments on computers
running algorithms designed to simulate complex physical systems?
(Hughes, 1999, 138f)

In a similar vein, Steve Norton and Frederick Suppe argue on an ex-
plicitly epistemological basis for the claim that simulation is a form of
experiment. According to Norton and Suppe, a valid simulation is one in
which certain formal relations hold between a base model, the modelled
physical system itself, and the computer running the algorithm (Norton
and Suppe 2001). Glossing, the relation is that of realization, where a
system S1 realizes a system S2 just in case there is a many-one behavior-



     115

preserving mapping from the states of S2 onto the states of S1. When the
proper conditions are met, a simulation

can be used as an instrument for probing or detecting real world phe-
nomena. Empirical data about real phenomena are produced under
conditions of experimental control. (Norton and Suppe 2001)

Simulation modeling is just another form of experimentation, and
simulation results are nothing other than models of data. (Ibid., em-
phasis in original)

In general then, the claim being made by Hughes, and by Norton and
Suppe is that the methodological structure of simulation is like that of
experimentation because simulation proceeds in the following way:

1. Create an algorithm that accurately mimics a physical system of in-
terest.

2. Implement the algorithm on a digital computer.
3. Perform experiments on the computer, which will tell us about the

system in question—like experiments on an electrical damped har-
monic oscillator tell us about mechanical damped harmonic oscilla-
tors.

The real problem with this sort of story, from the point of view of the
present project, is that it begs the question of whether or not, to what
extent, and under what conditions, a simulation reliably mimics the physi-
cal system of interest. We are interested in applying some of the insights
of the philosophy of experiment to methodological and epistemological
issues vis à vis simulations. But to identify the methods of simulation with
the methods of experiment in this way is to tuck away all of these impor-
tant questions into step 1 and then to focus exclusively on step 3 as the
step where the connection lies between simulation and experiment.

Hughes himself at least partially recognizes this problem. His solution
is to say that computer “experiments” reveal information about actual,
possible, or impossible worlds. To know that we are finding out about
actual worlds, according to Hughes, requires an extra step. “Lacking other
data, we can never evaluate the information that these experiments pro-
vide” (Hughes 1999, 142). This is not so much a problem for Hughes since
his analysis is not intended to be epistemological. In fact, in the last quoted
passage, Hughes is essentially disavowing any epistemological force to his
analogy. But we must face this issue if we want to offer the analogy be-
tween simulation and experiment as a way of understanding what makes
simulation results reliable. One of the central epistemological questions
about simulation is “how do we evaluate the information that these sim-
ulations provide when other data are lacking?”

This state of affairs reminds me of a passage of Wittgenstein’s, in which
he is criticizing Ramsey’s theory of identity:



 116

Ramsey’s theory of identity makes the mistake that would be made
by someone who said that you could use a painting as a mirror as
well, even if only for a single posture. If we say this, we overlook that
what is essential to a mirror is precisely that you can infer from it the
posture of a body in front of it, whereas in the case of the painting
you have to know that the postures tally before you can construe the
picture as a mirror image. (Wittgenstein P.R., sec. 121, quoted in Mar-
ion 1998, 70)

For us to adopt this particular analogy between simulation and exper-
iment would be to make the same mistake as the one identified by Witt-
genstein. Simulation is a technique that begins with well-established theo-
retical principles, and through a carefully crafted process, creates new
descriptions of the systems governed by those principles. It is a technique
that, when properly used, will provide information about systems for
which previous experimental data is scarce. Paraphrasing Wittgenstein,
“What is essential to a [simulation] is precisely that you can infer from it”
what some system in the real world is like even when other data are lack-
ing. If in our analysis of simulation we take it to be a method that essen-
tially begins with an algorithm antecedently taken to accurately mimic the
system in question, then the question has been begged as to whether and
how simulations can, and often do, provide us with genuinely new, pre-
viously unknown knowledge about the systems being simulated. It would
be as mysterious as if we could use portraits in order to learn new facts
about the postures of our bodies in the way that Wittgenstein describes.
We need to understand how, as Kaufmann and Smarr suggest, we can
reliably learn about storms from simulations, even when data about such
storms are conspicuously sparse.

Furthermore, simulations often yield sanctioned and reliable new
knowledge of systems even when nothing like the stringent conditions
required by Norton and Suppe are in place. In practice, simulationists
need not suppose—nore even begin to suppose—that their simulations
perfectly mimic any particular physical system in order to convince them-
selves that certain qualitative properties of their results can reliably be
attributed to the systems being studied.

If there is a useful analogy to be made by philosophers between simu-
lation and experiment, then that analogy ought to help make methodo-
logical and epistemological connections. These connections, in turn,
should help us to apply some of the insights of recent work in the philos-
ophy of experiment towards gaining an understanding of the conditions
under which we should take simulation results to be accurate represen-
tations of real systems. Thus far, this proposal fails to do this because it
assigns experimental qualities only to those aspects of simulation reason-



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ing that occur after it is assumed that the simulation algorithm ‘realizes’
the system of interest.

5. A Third Mode. A third view on simulation’s methodological geography
is that simulation represents an entirely new mode of scientific activity—
one that lies between theory and experiment. For example, Fritz Rohrlich,
a physicist and philosopher of science, writes:

Computer simulation provides . . . a qualitatively new and different
methodology for the physical sciences . . . This methodology lies some-
where intermediate between traditional theoretical physical science,
and its empirical methods of experimentation and observation. (1990,
507)

Historians, sociologists, and even leading practitioners of the tech-
niques themselves have expressed something like this view. In an intro-
ductory essay for a special issue of Physics Today on “computational phys-
ics,” Norman Zabusky wrote:

Supercomputers with ultrafast, interactive visualization peripherals
have come of age and provide a mode of working that is coequal with
laboratory experiments and observations, and with theory and anal-
ysis. (1987, 25)

Deb Dowling, a sociologist of science, has also suggested a similar in-
terpretation of simulation. According to her, simulation is like theory in
that it involves “manipulating equations” and “developing ideas” but is
like experiment in that it involves “fiddling with machines,” “trying things
out,” and “watching to see what happens” (Dowling 1999, 264). The his-
torian Peter Galison takes a similar view:

[Simulation] ushered physics into a place paradoxically dislocated
from the traditional reality that borrowed from both the experimental
and theoretical domains, bound these borrowings together, and used
the resulting bricollage to create a marginalized nether land that was
at once nowhere and everywhere on the usual methodological map.
(Galison 1996, 120)

Locating simulation as lying between theory and experiment provides
a natural perspective for both historians and sociologists. In Galison’s
case, it is a useful way of expressing how simulation could provide a trad-
ing zone between experimentalists and theoreticians and across disciplines.
Dowling, in turn, has argued that simulation’s ambiguity with respect to
the experiment/theory dichotomy can play important social and rhetorical
functions.

From the point of view of the project of this paper, however, it is not



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clear what we gain by saying that simulation “lies between theory and
experiment”. What is of interest philosophically is to understand (a) how
it is that what is at root a theoretical enterprise, takes on characteristics
of experimentation, (b) what those characteristics are—at the abstract,
reconstructed level, (c) what consequences there are of such a hybrid for
our understanding of the nature of modeling, theorizing, and experiment-
ing, and d) how simulation produces knowledge and what kind of knowl-
edge that is. For these purposes, making simulation out to be an entirely
new methodology and urging that it lies between theory and experiment
is, at best, a good place to start.

6. Speculation vs. Calculation. One way in which we might be able to make
this approach do more work for us is to be clearer about the concept of
“theorizing” when we say, for example, that simulation is an activity that
lies between theorizing and experimenting. A good place to start is with
Ian Hacking’s repudiation of the traditional dichotomy of theory and ex-
periment. He urges that we replace it with a tripartite division: speculation,
calculation, and experimentation:

[By calculation] I do not mean mere computation, but the mathemat-
ical alteration of a given speculation, so that it brings it into closer
resonance with the world. (Hacking 1983, 213–14)

The point that Hacking is making with his neologisms is that there are
really two quite distinct activities that we often naively lump together
under the label of “theorizing.” The first activity is that of laying out basic
theoretical principles: Maxwell’s equations, Newton’s laws of motion, Ein-
stein’s field equations, etc. This is the activity Hacking calls “speculation.”
The second activity is what Thomas Kuhn long ago called “theory artic-
ulation.” This is the hard work that is involved in making the aforemen-
tioned theoretical principles apply to the local, concrete systems that make
up the real world. Hacking calls this activity “calculation”, but I prefer
the simple expression “model building” to Hacking and Kuhn’s phrases
because it emphasizes that this is an activity that often bring us beyond
the original theoretical principles themselves. The expression “model
building” also is meant to emphasize that the model being built is not
properly seen as a component of the theory proper. The models con-
structed are offspring of theories, but they emerge as semiautonomous
agents. In this respect, Hacking’s pair of terms “speculation” and “cal-
culation”, are somewhat misleading, since in conjunction they suggest that
there is nothing speculative about the process of building models under
the guidance of theory, when nothing could be further from the truth.

The word “theorizing,” as it is naively used, expresses some amalgam
of these two distinct activities, and it effectively collapses a valuable dis-



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6. What I called “models of phenomena” in Winsberg 1999.

tinction. This sloppiness of language has persisted, in no small part, be-
cause most commentators on science, especially philosophers, have woe-
fully underestimated the importance of theory articulation, or model
building.

It is this under appreciation of the importance of model building that
Nancy Cartwright has labeled the “vending machine view of theories”
(Cartwright 1999, 179–183). On this view, criticized by Cartwright, the
ability of a theory to represent the world is captured precisely by the set
of those conclusions that can be drawn deductively from the theory—
drawn, moreover, with the ease with which we can extract candy from a
vending machine.

For Cartwright, theories do not have by themselves the power necessary
to represent real, local states of affairs. Only what she calls representative
models are fully able to “represent what happens, and in what circum-
stances.” (Ibid, 180) It is these models that represent “the real arrange-
ments of affairs that take place in the world (Ibid, 180). On her view, the
process of creating representative models from theory is complex and cre-
ative.

Having widened the field to three activities instead of the traditional
two, it is a simple point that simulation is a form of theory articulation
or “model building.” The example of a simulation described above is a
complex and creative mathematical alteration of the theory of fluids de-
signed to create a representative model of what motions occur when two
fluids collide at supersonic speeds. Using Cartwright’s language, simula-
tionists work with theories (among other elements) but what they build
are “representative models.”6 The fact that simulation work is such a cre-
ative and such an epistemologically delicate process is grist for Cart-
wright’s mill. The difficulty of obtaining reliable simulation results is a
testament to the claim that theories do not dispense representative models
as easily and conveniently as a vending machine dispenses candy.

Nevertheless, I do not want to simply make the point that simulation—
rather than being either theorizing, or experimenting, or some midway
point between the two—is actually a form of what Hacking calls “calcu-
lation”. Even with a tripartite distinction in hand, there are still aspects
of simulation that, both methodologically and epistemologically, seem to
have characteristics more commonly associated with experimental practice
rather than with the pencil and paper varieties of calculation. Nevertheless,
I think it is very important to keep a keen eye on the distinction between
the laying out of theoretical principles and the construction of local models
when we throw around the word “theorizing.”

In fact, I would argue, something like what Hacking and Cartwright



 120

7. For example, Giere (1999).

say about theorizing must be true if anything at all can be a significant
hybrid of experiment and theory. In order to avoid the appearance of there
being anything strange or paradoxical about a practice that straddles the
terrain between the theoretical and the experimental, we need to recognize
that while simulation is, in the general sense, a form of what we once
naively called theorizing, it is the kind of theorizing that has only recently
begun to attract philosophical attention—construction of local, represen-
tative models. In the end, the point is simply this: philosophers like Hack-
ing, Cartwright, and Giere7 have afforded us the insight that we can have
good, reliable theoretical knowledge in a particular domain and still have
a lot of difficult, creative work to do in building local models under that
domain. This insight is crucial if we are going to understand what goes
on in simulation.

7. The Experimental Qualities of Simulation. Hacking, Cartwright, Giere,
Morrison and Morgan and others have shown how models can function
semiautonomously from theory. What has perhaps been lacking from their
analysis is an understanding of where semiautonomous models get their
credentials. There is an enormous and controversial philosophical litera-
ture on how theories get credentialed. But even when it is established that
the theory for a given domain is credible and reliable, how do we come to
the conclusion that the local, autonomous models of the phenomena in
that domain are reliable? As we have seen, it is not simply a matter of the
model’s fidelity to theory, since, in simulation, model construction often
involves steps that go beyond, or even contradict, theory. It is also not
simply a matter of fidelity to real-world data, since we often run simula-
tions in order to learn more about the world then our observations will
allow. The literature on the philosophy of experiment may help with these
questions.

A starting point for this project is to point out that simulationists and
experimenters both need to engage in error management. In simulations,
errors can arise the as a result of transforming continuous equations into
discrete ones and of transforming a mathematical structure into a com-
putational one. All discretization techniques present the possibility of
roundoff errors or instabilities creating undetected artifacts in simulation
results. At a deeper level, any modeling assumption that goes into the
creation of a simulation algorithm can have unintended consequences.
Developing an appreciation for what sorts of errors are likely to emerge
under what circumstances is as much an important part of the craft of the
simulationists as it is of the experimenter. Precision, accuracy, error anal-
ysis and calibration are concepts that we typically associate with experi-



     121

8. See Winsberg 1999a or Weissert 1997, 122–124 for more details.

mentation, and not with theorizing, but they are also very much a part of
the vocabulary of the simulationist. There is indeed a great deal of simi-
larity and analogy between the actual techniques that experimenter and
simulationist each use to manage uncertainty.

In his work on the epistemology of experiment, Alan Franklin (1986)
has outlined a list of common sense techniques that experimenters use to
augment our reasonable belief in the results of their work. It is a straight-
forward exercise to go through this list and see that many, if not all, of
these techniques apply directly or by analogy to the sanctioning of simu-
lation results.8 Here, I will focus on a deeper aspect of experimental epis-
temology—found in the writings of Hacking and Peter Galison (1997)—
according to which various experimental techniques and instruments
develop a tradition that gives them their own internal stability, or, put
most provocatively, that “experiments have a life of their own” (Hacking,
1988).

8. A Life of Their Own.

I [once] wrote that experiments have a life of their own. I intended
partly to convey the fact that experiments are organic, develop,
change, and yet retain a certain long-term development which makes
us talk about repeating and replicating experiments . . . I think of
experiments as having a life: maturing, evolving, adapting, being not
only recycled, but quite literally, being retooled. (Hacking 1992, 307)

The quoted passage comes from a piece in which Hacking argued that
thought experiments, unlike real experiments, do not have a “life of their
own.” I want to argue here that techniques of simulation do. More spe-
cifically, some of the techniques that simulationists use to construct their
models get credentialed in much the same way that Hacking says that
instruments and experimental procedures and methods do; the credentials
develop over an extended period of time and become deeply tradition
bound. In Hacking’s language, the techniques and sets of assumptions that
simulationists use become “self-vindicating.” Perhaps a better expression
would be that they carry their own credentials.

By the “techniques” of simulation, I am here referring to the whole host
of activities, practices, and assumptions that go into carrying out a simu-
lation. This includes assumptions about what parameters to include or
neglect, rules of thumb about how to overcome computational difficul-
ties—what model assumptions to use, what differencing sceme to employ,
what symmetries to exploit—graphical techniques for visualizing data,



 122

9. For a brief discussion of the comparative autonomy of simulation modeling tech-
niques and such analytic modeling methods as perturbation expansions and other meth-
ods from celestial mechanics see Winsberg 1999, 288–289.

and techniques for comparing and calibrating simulation results to known
experimental and observational data.

Whenever these techniques and assumptions are employed successfully,
that is, whenever they produce results that fit well into the web of our
previously accepted data, our observations, the results of our paper and
pencil analyses, and our physical intuitions, whenever they make success-
ful predictions or produce engineering accomplishments, their credibility
as reliable techniques or reasonable assumptions grows.

That is, the next time simulationists build a model, the credibility of
that model comes not only from the credentials supplied to it by the gov-
erning theory, but also from the antecedently established credentials of
the model building techniques developed over an extended tradition of
employment. That is what I mean when I say that these techniques have
their own life; they carry with them their own history of prior successes
and accomplishments, and, when properly used, they can bring to the table
independent warrant for belief in the models they are used to build. In
this respect, simulation techniques, and indeed many pre-computer cal-
culational modeling techniques as well9, are much like microscopes and
bubble chambers as Hacking and Galison describe them (Hacking 1988;
Galison 1997).

Consider, as an example, a particular computational technique now
commonly known as the “Piecewise Parabolic Method” (PPM). The PPM
is an algorithm that has been shown to be well suited to simulating fluid
flows that contain significant shock discontinuities, such as the example
given at the beginning of this paper. Different versions of the algorithm
have been used to simulate a wide variety of physical phenomena, ranging
from simple laboratory setups like the one described above to such com-
plex astrophysical systems as supernova explosions, heat convection in
red-giant stars, gas accretion disks, supersonic jets, and models of the
development of the entire cosmos.

The PPM begins as a discretization of the Euler equations but we
should not think of it simply as a purely mathematical transformation of
those equations. Recall that the primary difficulty in modeling supersonic
fluids is in dealing with shock discontinuities. The difficulty arises because
real fluids do not have discontinuities. In other words, the fundamental
theories of fluid dynamics always describe continuous variables. Instead
of discontinuities, there are very thin regions of very steep gradients.

In principle, these thin regions could be accurately modeled by includ-
ing terms for viscosity and heat conduction in the principle equations. In



     123

practice, however, viscous momentum transport and molecular heat trans-
port take place on extremely small length scales. No computer algorithm
that is computationally tractable could ever hope to capture effects on
these scales.

The earliest approach to solving this problem was suggested by von
Neumann and Richtmyer. Their solution was to artificially increase the
coefficients of viscosity and heat conduction until the point at which the
effects manifest themselves at length scales sufficiently large to be resolved
on a reasonable computer grid. The flow can then be tweaked in just the
right way to spread the shocks over a few grid cells.

The von Neumann-Richtmyer method represents the earliest attempt
at overcoming these difficulties and it is relatively simple and easy to de-
scribe. Other methods that have emerged over the last fifty years have
become progressively more complex and elaborate. The PPM represents
the state-of-the-art method. It differs fundamentally from its predecessors
in the following way. Most differencing methods are derived from Taylor
series expansions of the terms in the differential equations. This move
essentially assumes that the solution is smooth. While so called “shock
discontinuities” are not truly discontinuous in the theory of fluids, it is
nevertheless not a good assumption to treat them as smooth. So the PPM
abandons this assumption, and instead of piecing together continuous,
linear solutions, it pieces together discontinuous, non-linear solutions.
Since superposition fails to apply to these non-linear terms, this technique
then requires a special solver to compute the non-linear interactions be-
tween the discontinuous states. The construction of this solver requires
outside knowledge of the propagation and interaction of non-linear waves
(Winkler et al. 1987).

Exactly how all of these methods are achieved is a subject that is more
than a little arcane, and the details are not that important here. What is
important to note are some of the features of these methods and their
development.

Perhaps most important, the presence of “shocks” in the flow of a sys-
tem prevents any straightforward attempt to hammer the Euler equations
into discrete form from being effective. Thus, there is nothing in the Euler
equations or in the fundamental theory of fluids that tells you how to
proceed if you are unable to capture the steep gradients in the flow that
the theory predicts. The theory of fluids has been a useful guide in the
development of these methods but neither has it come anywhere close to
sufficing on its own, nor has it certified the end product.

Another interesting observation can be made by tracing the history of
these methods from von Neumann’s time to the present. The history of a
simulation technique is very much like the history of a scientific instru-
ment. It begins with a relatively crude and simple technique for attacking



 124

a relatively small set of problems. Over time, the instrument or technique
is called upon to attack a larger set of problems or to achieve a higher
degree of accuracy. In order to achieve this, the technique needs to be
improved upon, reconfigured, and ever radically revised. In each case, the
knowledge relied upon to devise and sanction the tool or method can come
from a wide variety of domains.

The PPM has gained recognition as a reliable method for simulating
discontinuous flows over a fairly long history of use. The results of sim-
ulations making use of this technique have been evaluated and found to
be reliable in a wide variety of applications. Just like scientific instruments
and experimental techniques, the PPM has “matured, evolved, been
adapted and not only recycled but [not quite literally] retooled.” And just
like instruments and techniques of their use, the trust that we place in the
PPM as a reliable method has grown with every maturation, evolution,
and retooling in which it has been successfully applied. Just like the mi-
croscope and the bubble chamber, the Piecewise Parabolic Method for
calculating discontinuous compressible flows has had its own independent
history. Beginning with the von Neuman-Richtmyer method, it has ma-
tured, evolved, been adapted, recycled, and retooled. It has had a life of
its own.

REFERENCES

Bate, R., J. Mueller, and D. White (1971), Fundamentals of Astrodynamics. New York: Do-
ver.

Cartwright, Nancy (1983), How the Laws of Physics Lie. Oxford: Oxford University Press.
——— (1999), The Dappled World: A Study of the Boundaries of Science. Cambridge: Cam-

bridge University Press.
Dowling, D. (1999), “Experimenting on Theories”, Science in Context 12 (2): 261–73.
Franklin, Allan (1986), The Neglect of Experiment. Cambridge: Cambridge University Press.
Galison, Peter (1996), “Computer Simulations and the Trading Zone”, in P. Galison and D.

Stump (eds.), The Disunity of Science: Boundaries, Contexts, and Power. Stanford: Stan-
ford University Press.

——— (1997), Image and Logic: A Material Culture of Microphysics. Chicago: University
of Chicago Press.

Giere, Ronald N. (1999), Science Without Laws. Chicago: University of Chicago Press.
Hacking Ian (1983), Representing and Intervening: Introductory Topics in the Philosophy of

Science. New York: Free Press.
——— (1988), “On the Stability of the Laboratory Sciences”, The Journal of Philosophy 85

(10): 507–15.
——— (1992) “Do Thought Experiments Have a Life of Their Own?”, in A. Fine, M. Forbes,

and K. Okruhlik, (eds.), PSA 1992, Vol. 2. East Lansing, MI: The Philosophy of Science
Association, 302–310.

Hughes, R. (1999), “The Ising Model, Computer Simulation, and Universal Physics”, in
Mary Morgan and Margaret Morrison (eds.), Models as Mediators. Cambridge: Cam-
bridge University Press.

Humphreys, Paul (1991). “Computer Simulation”, in A. Fine, M. Forbes, and L. Wessels
(eds.), PSA 1990, Vol. 2. East Lansing MI: The Philosophy of Science Association,
497–506.

——— (1994), “Numerical Experimentation”, in Paul Humphreys (ed.), Patrick Suppes: Sci-



     125

entific Philosopher, Vol. 2 of Philosophy of Physics, Theory Structure, Measurement
Theory, Philosophy of Language, and Logic. Dordrecht: Kluwer Academic Publishers.

——— (1995), “Computational Science and Scientific Method”, Minds and Machines 5 (1):
499–512.

Kaufmann, W.J., and L.L. Smarr (1993), Supercomputing and the Transformation of Science.
New York: Scientific American Library.

Marion, Mathieu (1998), Wittgenstein, Finitism, and the Foundations of Mathematics. Ox-
ford: Clarendon Press.

Morgan, Mary, and Margaret Morrison (eds.) (1999), Models as Mediators. Cambridge:
Cambridge University Press.

Newell, A. and H. A. Simon (1976), “Computer Science as Empirical Enquiry”, Communi-
cations of the ACM 19: 113–126.

Norton, S., and F. Suppe (2000) , “Why Atmospheric Modeling is Good Science”, in C.
Miller and P. Edwards (eds.), Changing the Atmosphere: Expert Knowledge and Envi-
ronmental Governance. Cambridge, MA: MIT Press.

Rohrlich, Fritz (1991), “Computer Simulation in the Physical Sciences”, PSA 1990, Vol. 2.
East Lansing, MI: The Philosophy of Science Association, 507–18.

Weissert, T. (1997), The Genesis of Simulation in Dynamics: Pursuing the Fermi-Pasta-Ulam
Problem. New York: Springer.

Winkler, K., J. Chalmers, S. Hodson, P. Woodward, N. Zabusky (1987), “A Numerical
Laboratory”, Physics Today 40 (10): 28–37.

Winsberg, Eric (1999), “Sanctioning Models: The Epistemology of Simulation”, Science in
Context 12(2): 275–292.

——— (1999a) Simulation and the Philosophy of Science: Computationally Intensive Studies
of Complex Physical Systems, Ph.D. Dissertation, Bloomington: Indiana University.

——— (2001) “Simulations, Models, and Theories: Complex Physical Systems and Their
Representations”, Philosophy of Science 68 (Proceedings): S442-S454.

Woodward, P., and P. Collela (1984), “The Numerical Simulation of Two-Dimensional Gas
Flows with Strong Shocks”, The Journal of Computational Physics. 54: 115–43.

Zabusky, N. (1987), “Grappling with Complexity”, Physics Today. 40 (10): 25–27