Selected Excerpts  Preface 

[
preface
 section 4.2
 section 10.0
 section 18.0
 section 22.0
]
Preface (portion of):
The scientist does not study nature because it
is useful; he studies it because he delights in it, and he delights in
it because it is beautiful. If nature were not beautiful, it would not
be worth knowing, and if nature were not worth knowing, life would not
be worth living. Of course I do not here speak of that beauty that
strikes the senses, the beauty of qualities and appearances; not that
I undervalue such beauty, far from it, but it has nothing to do with
science; I mean that profounder beauty which comes from the harmonious
order of the parts, and which a pure intelligence can grasp.
Henri Poincaré
A variation on an old joke goes as follows:
Engineers study interesting realworld problems but fudge their
results. Mathematicians get exact results but study only toy problems.
But computer scientists, being neither engineers nor mathematicians,
study toy problems and fudge their results.
Now, since I am a computer scientist, I have taken the liberty of
altering the joke to make myself and my colleagues the butt of it.
This joke examines a real problem found in all scientific disciplines.
By substituting experimentalist, theorist, and simulationist for
engineer, mathematician, and computer scientist, respectively, the
joke becomes generalized for almost all of the sciences and gets to
the heart of a very real division.
A theorist will often make many simplifying assumptions in order to
get to the essence of some physical process. Particles do not
necessarily look like billiard balls, but it often helps to think in
this way if you are trying to understand how classical mechanics says
things should behave. Likewise, experimentalists often have to deal
with messy processes that are prone to measurement error. So if a
physicist finds that the surface temperature of an object is between
100,000 and 200,000 degrees, it doesn't matter if the units are
Celsius degrees or Kelvin degrees, because the margin of error is
orders of magnitude larger than the difference in the two measuring
units.
A simulationist is a relatively new breed of scientist who attempts to
understand how the world works by studying computer simulations of
phenomena found in nature. A simulationist will always have to make
some assumptions when building a computer model but will also find
that the simulated results are not always a perfect match for what
exists in the real world. Hence, the simulationist, having to
incorporate principles from theory and experimental methodologies,
straddles the fence and must deal with limiting factors found in both
extreme approaches. But this is not always a bad thing.
Consider an economist who builds a simplified model of the world
economy, runs the model on a computer, and reaches the conclusion that
interest rates, unemployment, inflation, and growth will all reach a
constant level at the end of the year and stay that way forever. For
this one case, the simplified model tells us very little about how the
real world works because the simplified model has failed to capture an
important aspect of the real world. On the other hand, suppose that a
simplified model is such that it never reaches equilibrium, turns out
to be extremely sensitive to the starting conditions, and displays
surprisingly complex behavior. Even if this model fails to make
actual predictions about the real economy, it still has some
predictive power since it may reveal a deeper truth about the inherent
difficulty of predicting the economy or similar systems. In other
words, the model is predictable in its unpredictability. Hence, if a
simplified model can behave in a sophisticated manner, then it is not
too great a leap to conclude that the realworld economy can display
an even greater form of sophistication.
For the first case, if after simplifying a natural process we find
behavior that is profoundly simpler than the original phenomenon, then
it is likely that the model failed to capture some essential piece of
the realworld counterpart. On the other hand, if an analogous form
of complexity is still found even in a simplified model, then it is
highly possible that a key feature of the natural system has been
isolated. This illustrates that simulationsespecially if they are
simplificationscan yield insight into how things work in the real
world.
All of this boils down to a simple but deep idea: simple recurrent
rules can produce extremely rich and complicated behaviors. Pure
theory often fails to make accurate predictions of complicated natural
processes because the world does not always obey equations with
analytical solutions. Similarly, experiments with complicated
observations are often useless because they fail to bridge things from
a reverse direction and correlate complex effects from simple causes.
It is only through the marriage of theory and experimentation that
many claims of the complexity of nature can withstand reasonable
tests. Simulation, then, becomes a form of experimentation in a
universe of theories. The primary purpose of this book is to
celebrate this fact.
[
preface
 section 4.2
 section 10.0
 section 18.0
 section 22.0
]
