By a complex system I mean one made up of a large number of parts that interact in a nonsimple way.
— Herbert Simon, 1962
Bottomless wonders spring from simple rules, which are repeated without end.
— Mandelbrot, ~1980
When we talk about complex systems in time, we often used the term complex dynamical systems.
Examples of complex systems
- The economy (Anderson 1996)
- Boolean networks
- Cellular automata
- Neural networks
- Many physical systems
Understanding complex systems
There is an interesting series of articles that are about how different scientific disciplines approach the same problem of understanding an incredibly complex system that we initially don’t know anything about:
- The story of Doug and Bill (Sullivan 1993)
- Can a biologist fix a radio? (Lazebnik 2002)
- Could a Neuroscientist Understand a Microprocessor? (Jonas, Kording 2017)
These articles challenge the very notion of “understanding”, which may mean different things from one scientific discipline to the next. Interestingly it seems that such understanding is neither necessary nor sufficient for constructing a replica of the complex system being studied. Evolution doesn’t understand the complexity of the human body, and although we understand a microprocessor very well, actually constructing it requires a whole different range of technologies.
What does it mean for artificial intelligence? We could take the path of the microprocessor, jointly developing a blueprint for an intelligent system and the technologies that enable it in order to construct an AI. Neural networks are interesting because we don’t understand them fully despite having a clear description of each of its small component. For this reason, they might end up being parts of very large complex systems that we barely understand like the human body.
Can complex systems evolve?
The biosphere is a striking example of very large and intricate complex system. One of its most impressive feature is the fact that it has allowed for intelligent life to develop through evolution. Like many complex systems, Earth is capable of emergent behavior.
Can this kind of incredible events happen within other complex systems such as cellular automata?
- Phillip W. Anderson. . The Economy as an Evolving Complex System: The Proceedings of the Evolutionary Paths of the Global Economy Workshop, Held September, 1987 in Santa Fe, New Mexico. Edited by Phillip W. Anderson. Evolutionary Paths of the Global Economy Workshop. Santa Fe Institute Studies in the Sciences of Complexity 5. Reading, Mass.: Addison-Wesley Publ. Co.
- William T. Sullivan. . "The Salvation of Doug". Generations 1 (3):1439–43.
- Yuri Lazebnik. . "Can a biologist fix a radio?—or, what I learned while studying apoptosis". Cancer cell 2 (3). Elsevier:179–82. DOI.
- Eric Jonas, Konrad Paul Kording. . "Could a Neuroscientist Understand a Microprocessor?". PLOS Computational Biology 13 (1). Public Library of Science:e1005268. DOI.