In my trip to Reed a few weeks ago, I was asked a very clever question after my talk on my SIMPLE model (a general model of social behavior that I developed for first chapter of my dissertation, downloadable from my research page). Greg Jenson, Allen Neuringer’s very smart Research Assistant, asked me “Have you ever thought about this model as a turing machine with multiple heads?” The answer was then no, but I have since thought about this almost daily and have been speculating that SIMPLE might be even more general than I had previously thought. In addition to being a general model of social interaction, it builds on the most general principles of computation.
In SIMPLE (Simulation of agent Interaction through Movement and Production in a Local Environment), agents move along a ring made up of several hundred unique cells, changing the energy level on those cells as they produce and consume energy. This is analogous to a turing machine which has a tape (in SIMPLE, the environment) with multiple squares containing information (energy), a head that can read the tape and alter it (adding or taking away energy) , a table which specifies how the tape is altered and how the head should move based on what is read and current state of the head (decision rules for movement, production and consumption), and a state register which tracks the present state of the head (read more about turing machines on Wikipedia).
It can easily be demonstrated that a turing machine with multiple heads is equivalent to one with just one head. I suspect that the ability of heads to replicate, mutate and terminate themselves (as they can in the SIMPLE model) leads to surprising dynamics that might be difficult to intuit from considering a turing machine with just one head (even though they are analytically equivalent).
