The Computational Beauty of Nature
Computer Explorations of Fractals, Chaos,
Complex Systems, and Adaptation

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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 real-world 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 real-world 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 real-world 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 simulations---especially if they are simplifications---can 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 ]
Copyright © Gary William Flake, 1998-2002. All Rights Reserved. Last modified: 30 Nov 2002