This wording sounds remarkably similar to quantum mechanics. I wonder how far you could take the idea of building a game out of state vectors and linear transformations.
State vectors and linear transformations are by no means unique to quantum mechanics. A lot of dynamic systems can be described this way: robot arms, chemical plants, airplanes, even network dynamics.
Naively I can guess how robot arms and networks could be spoken of in terms of states (and perhaps even chemical plants), but airplanes? Do you have any more information on the topic?
The technique is called a state space model [0]. A complete airplane might have been a bit hyperbolic, but as long as the assumption of linear dynamics is allowable, extremely large systems with multiple inputs and outputs and thousands of states can be simulated. What's more, there are some elegant and practical ways to find controllers with mathematically proven performance (like LQG control, or Model Predictive Control). This field of study has lead to the Kalman filter, which might ring a bell.
> This wording sounds remarkably similar to quantum mechanics. I wonder how far you could take the idea of building a game out of state vectors and linear transformations.
That's an interesting idea (and might fit in with "math / science gamification" software). Terry Tao used the opposite point of view, describing quantum mechanics in terms of video games: http://terrytao.wordpress.com/2007/02/26/quantum-mechanics-a....
