Complexity_ A Guided Tour - Melanie Mitchell [100]
FIGURE 14.1. The traditional division of science into theory and experiment has been complemented by a new category: computer simulation. (Drawing by David Moser.)
Models are ways for our minds to make sense of observed phenomena in terms of concepts that are familiar to us, concepts that we can get our heads around (or in the case of string theory, that only a few very smart people can get their heads around). Models are also a means for predicting the future: for example, Newton’s law of gravity is still used to predict planetary orbits, and Einstein’s general relativity has been used to successfully predict deviations from those predicted orbits.
Idea Models
For applications such as weather forecasting, the design of automobiles and airplanes, or military operations, computers are often used to run detailed and complicated models that in turn make detailed predictions about the specific phenomena being modeled.
In contrast, a major thrust of complex systems research has been the exploration of idea models: relatively simple models meant to gain insights into a general concept without the necessity of making detailed predictions about any specific system. Here are some examples of idea models that I have discussed so far in this book:
Maxwell’s demon: An idea model for exploring the concept of entropy.
Turing machine: An idea model for formally defining “definite procedure” and for exploring the concept of computation.
Logistic model and logistic map: Minimal models for predicting population growth; these were later turned into idea models for exploring concepts of dynamics and chaos in general.
Von Neumann’s self-reproducing automaton: An idea model for exploring the “logic” of self-reproduction.
Genetic algorithm: An idea model for exploring the concept of adaptation. Sometimes used as a minimal model of Darwinian evolution.
Cellular automaton: An idea model for complex systems in general.
Koch curve: An idea model for exploring fractal-like structures such as coastlines and snowflakes.
Copycat: An idea model for human analogy-making.
Idea models are used for various purposes: to explore general mechanisms underlying some complicated phenomenon (e.g., von Neumann’s logic of self-reproduction); to show that a proposed mechanism for a phenomenon is plausible or implausible (e.g., dynamics of population growth); to explore the effects of variations on a simple model (e.g., investigating what happens when you change mutation rates in genetic algorithms or the value of the control parameter R in the logistic map); and more generally, to act as what the philosopher Daniel Dennett called “intuition pumps”—thought experiments or computer simulations used to prime one’s intuitions about complex phenomena.
Idea models in complex systems also have provided inspiration for new kinds of technology and computing methods. For example, Turing machines inspired programmable computers; von Neumann’s self-reproducing automaton inspired cellular automata; minimal models of Darwinian evolution, the immune system, and insect colonies inspired genetic algorithms, computer immune systems, and “swarm intelligence” methods, respectively.
To illustrate the accomplishments and prospects of idea models in science, I now delve into a few examples of particular idea models in the social sciences, starting with the best-known one of all: the Prisoner’s Dilemma.
Modeling the Evolution of Cooperation
Many biologists and social scientists have used idea models to explore what conditions can lead to the evolution of cooperation in a population of self-interested individuals.
Indeed, living organisms are selfish—their success in evolutionary terms requires living long enough, staying healthy enough,