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

About the Book
  · title page
  · home*
  · cover artwork
  · jacket text
  · table of contents
  · the author*
  · ordering information
Book Contents
  · three themes
  · part synopses
  · selected excerpts
  · all figures from book
  · quotes from book
  · glossary from book
  · bibliography
  · slide show
Source Code
  · overview &
  · FAQ list*
  · download source code
  · java applets
  · news*
  · reviews & awards
  · errata
  · for educators
  · bibliography (BibTeX format)
  · other links
Three Themes: #3

3. Science is doomed to uncertainty---but this is a good thing

The interesting things mentioned above are often found to have computationally profound qualities. For instance, even if you had a perfect model or theory of how something worked, chances are that it would still be impossible to perfectly predict the future of that which you have modeled. A related result guarantees just the opposite: regardless of how much ``data'' one collects, it's not always possible to build a perfect theory. Taken together, these two results insure that there will never be an end to science, or suprises.

The bottom line here is that whenever something is so rich as to be related to something akin to a universal computer, it is impossible (in the general case) to completely understand the underlying phenomenon. This has deep implications for how we do science. Consider the figure below (from Chapter 24).


In the past, there were two different methods for how science was performed. In one method, an experimentalist fiddles with some natural phenomenon so that data can be collected in the form of observations. These data are then compared with the current state of knowledge.

Coming from the opposite direction, a theorist derives a model for how a natural process works. The new model is then used to make predictions for how the natural process will behave at a future time.

With the advent of computers, a new and hybrid method of science has emerged. This new type of scientist, known as a simulationist, simultaneously performs experimentation in a universe of theories by simulating natural phenomena within the confines of a computer.

Neither of these methods of performing science is intrinsically superior to the others. Each of them are, in a sense, incomplete. But simulation allows for a type of exploration that neither experimentation nor theorization can provide. Pure theory fails when a phenomenon does not obey models that can be analytically solved. Pure experimentation fails when complex effects cannot be correlated to simple causes. But simulation hovers about these two extremes, allowing for a new type of science that mirrors (if only approximately) the complexity and beauty that we see in the real world.

The good news here is that there will never be an end to science. For science to end, one of two things must happen: (1) we would need a Theory of Everything that could be used to predict and explain all things, or (2) we would reach a clear and identifiable point at which no further progress could be made. But because nature's most beautiful phenomenon contain computational richness, there will always be surprises and new discoveries just beyond our reach.

Copyright © Gary William Flake, 1998-2002. All Rights Reserved. Last modified: 30 Nov 2002