CSH Workshop “Computation in Dynamical Systems”

Abstract:

Scientists view many real-world dynamical systems as performing computations, even if we did not construct those systems. Examples range from individual cells to brains to turbulent flows to societies. Even systems like off-equilibrium spin networks have been viewed as computers. However, the same physical system can often be viewed as performing different computations, depending on how we choose to define its computational variables (sometimes called its “information bearing degrees of freedom”). How should we identify the computation done by such a system, if we don’t have a pre-specified way of mapping its degrees of freedom to computational variables? Is there a principled way to identify what computation (or set of computations) is performed by an arbitrary physical system without pre-specifying its computational variables? More precisely, if I give you a dynamical system (either in discrete or continuous space and/or time), what is the set of all computational machines that are conjugate to that dynamical system?

Going further, can we enrich physics in a nontrivial way by reformulating it in terms of computational systems? In particular, can we gain insight into the dynamic behavior of spatially distributed, heterogeneous physical systems by reformulating them in a first-principles way as performing computation? All physical systems we construct to behave as computers crucially rely on there being at least two additional physical systems that they interact with i) An input system to determine the initial state of the computer and the input (or stream of inputs); ii) An output system to observe the outputs of the computer. We can restrict attention to input and output systems that are useable by humans. (So for example, an input system that requires fixing an infinite number of digits in a real number would be ruled out.) How does the problem of identifying computation in the real world change if we expand it to involve such triples of systems? How does the problem change if we combine (i) and (ii) into a single system, an external environment that interacts with the computer’s outputs and determines its inputs?