Question: Is there a relationship between the formal, mathematical foundation of virtual spaces and chaos theory?
Answer: It depends, of course, on how the programs for the virtual spaces are written. One research area that has some structural similarities with chaos theory is artificial life. The goal of artificial life programs, as you know, is to get emergence to emerge--a reflexive procedure that Luc Steels has called "second-order emergence." First order emergence refers to properties that emerge when the parts of a system interact. Emergent properties typically cannot be found in any of the parts by themselves; they arise at the global level only and are not present at the local level. Mob behavior is an example of first-order emergence. Taken separately, the members of a mob would not act as the mob does, but something in their interactions with each other causes new and different behavior to come about. Second-order emergence refers to emergent properties that have the capability to change the structure of the system itself, especially the way the system processes information. Daniel Dennett and others have argued that human consciousness is a second order emergence, in the sense that it emerges from the interactions of the parts of the mind and, through its emergence, changes how the system processes information.
The similarities with chaotic systems can be seen when we consider how programs that demonstrate emergence are structured. Typically, to get emergence and especially to get second-order emergence, the program's structure has to be highly recursive. The system's output is fed back in again as input and is put through a nonlinear algorithm. As a result, small changes in input can cause large changes in the system's response, just as with chaotic systems. This rapid magnification of small uncertainties or perturbations implies that the programmer cannot know how the program will evolve, just as people dealing with chaotic systems (the weather, for example) cannot predict very far in advance how the system's behavior will evolve over time. An important point about this inability to predict future behavior is that it is *in principle* impossible. It comes about because of how the system is structured, not because of a given person's ignorance.
Emergence opens virtual spaces to the unknown. It is an attempt to import into the computer environment the aconscious cleverness, astonishing variety, and adaptive capacities of evolution as the driving force of life. Emergence, like chaos, is the reservoir of the new.
Some further thoughts we might want to explore in discussion: What happens to consciousness, itself an emergent biological phenomenona, when it interacts with other emergent phenomena in a computer environment? Does third order emergence result--that is, behavior that comes about from the interaction of second-order emergent structures? If second-order emergence changes the way a system processes information, what does third-order emergence do? I look forward to hearing what others think about these ideas.