of books by Stephen Wolfram

STEPHEN WOLFRAM is a physicist and entrepreneur who published research on complexity and cellular automaton, the central topic of his book 'A new kind of Science'. He his best known as the author of the software 'Mathematica' and the interactive learning site Wolfram Demonstrations Project.

A New Kind of Science
by Stephen Wolfram
Wolfram Media, 2002

In this book Stephen Wolfram discusses in detail an old idea already found in ornamental art and self-evident to computer scientists that simple rules can produce complex patterns (turing machines). Yet unlike ornamental art, the pattern Wolfram presents require so many generations of applying rules that only computing can show the consequences, namely that some rules create complex patterns reminiscent of patterns found in living organisms. Complex patterns cannot be easily characterized or represented by equations that take an input and calculate a single output. There are no mathematical shortcuts to explain the pattern such that the next generation (or any thereafter) can be accurately predicted. This lack of predictability is central to complex systems and the core idea of Wolframs new kind of science (NKS) is that the future has to be calculated in real time, i.e. cannot be calculated ahead of time, as can be done with simple systems such as planetary movement (next years calendar).

Complex patterns are characterized by local symmetry, but overall the symmetry is broken and the pattern cannot be divided into a set of repetitive smaller pieces of equal form. They are neither fractals nor repetitive patterns. For instance, fractals look complex but are really nested patterns with repetitive symmetry going from larger to smaller scale or reverse. Fractals are not a useful model for living systems, because the rules at a particular scale completely predict the rules at any higher or lower scale as well. Hierarchical organization in living systems exhibit emerging properties from smaller to higher scales and the properties at lower scales, while fundamental to the system, are only useful to predict the behavior at its own level, but not any other level.

An interesting feature of complex patters is the time component, the fact that rules have to play out to generate the patterns and that there are not mathematical substitutes (laws or equations) that could calculate the same pattern without going through each generation. In this sense complex systems are restricted to move from the present to the future, but not into the past. The important question is what constitutes rules in real systems, since Wolfram operates with abstract objects of color/geometry, i.e., black and white cells. In the real world of living things, we have atoms, molecules, macromolecules, cells and organisms. Thus the challenge in today's biology is to understand the rules of molecular interactions and how these interactions play out in real time and how all molecules inside (genetic programs) and outside (environment) influence each interaction.


December 10, 2005 (2012)/  © 2005 Lukas K. Buehler / go back to Book Review Home