Showing Web View For Page 109 | Show full page with images

For when one deals with systems in nature it is normally impossible to set up or measure them with perfect precision—and indeed it can be a challenge even to make a traditional experiment be at all repeatable.

But for the kinds of computer experiments I do in this book, there is no such issue. For in almost all cases they involve programs whose rules and initial conditions can be specified with perfect precision—so that they work exactly the same whenever and wherever they are run.

In many ways these kinds of computer experiments thus manage to combine the best of both theoretical and experimental approaches to science. For their results have the kind of precision and clarity that one expects of theoretical or mathematical statements. Yet these results can nevertheless be found purely by making observations.

Yet as with all types of experiments it requires considerable skill and judgement to know how to set up a computer experiment that will yield meaningful results. And indeed, over the past twenty years or so my own methodology for doing such experiments has become vastly better.

Over and over again the single most important principle that I have learned is that the best computer experiments are ones that are as simple and straightforward as possible. And this principle applies both to the structure of the actual systems one studies—and to the procedures that one uses for studying them.

At some level the principle of looking at systems with the simplest possible structure can be viewed as an abstract aesthetic one. But it turns out also to have some very concrete consequences.

For a start, the simpler a structure is, the more likely it is that it will show up in a wide diversity of different places. And this means that by studying systems with the simplest possible structure one will tend to get results that have the broadest and most fundamental significance.

In addition, looking at systems with simpler underlying structures gives one a better chance of being able to tell what is really responsible for any phenomenon one sees—for there are fewer features that have been put into the system and that could lead one astray.

At a purely practical level, there is also an advantage to studying systems with simpler structures; for these systems are usually easier to

Exportable Images for This Page:

From Stephen Wolfram: A New Kind of Science [citation]