Ramin replied me back and wrote:
Every program could be considered as an automata which gets a string input and outputs a string output of codes. I think the robustness of algorithms can be interpreted as “redundancy” in this messaging framework. Thus, I recommend this, as an alternative strategy, to bring robustness to computer algorithms from the communications view point.
The idea of translating computer algorithms to dynamical systems is fascinating but first, we should reconsider the “dynamic” properties of our algorithms.
And I wrote him:
You mentioned a very good and interesting point. I wonder if there is a relation between dyamical properties of the system and information content of the message. I guess that the fractal dimension of a trajectory of the system’s output has a relation with output signal’s entropy. Consider this: a stable system converges to a single point in the state space (or output space) (fractal dimension = 0) and the entropy of the output signal converges to the zero as knowing the system is stable is equivalent to knowing what its future would be. A limit cycle leads to a finite fractal dimension (e.g. in 2D state space, it is between 1 and 2), and the entropy of it is finite depending on the length of its descriptor string, and etc.
Properties like robustness may be considered as cross-entropy between source (disturbances) to destination (output signal). hmmm … it is interesting in my mind. Maybe we are reinventing cybernetics!
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