Recently, the non-dynamical nature of computational systems has come under attack. Specifically, van Gelder [16] has argued that what is essential to computation is the notion of an effective procedure, and essential to that is the notion of discrete steps in an algorithm. He then claims that this discreteness, in both its temporal and non-temporal aspects, prevents computation from explaining many aspects of cognition, which he claims to be a fundamentally dynamical phenomenon.
The transparent reading of computationalism can be invoked here: if, in order to explain actual computers, it turns out that we need a more general notion of effective procedure, one which encompasses non-algorithmic, non-digital systems, then explaining cognition non-digitally will be a possibility for the computationalist.
But do we have reason to include non-discrete systems into the pre-theoretic class of computational systems, as phenomena which computational theory should account for? I think so, and one need not appeal to some hypothetical Watt machine in order to make this point. The fact is, current computers do much of the work they do by virtue of their non-formal, temporal properties. In any real-time computational system, correct performance depends on the computer getting the timing just right. Consider two computational systems intended to perform the complex task of landing a plane. The two systems could have identical algorithmic or Turing machine characterisations - from the perspective of current computational theory, or at least the theory that philosophers use as their target when criticising computationalism. And yet one could have perfect timing, and be ideal for the computational task, while the other could be hopeless, having little or no correlation between the timing of its steps and the timing required to successfully land the plane. The difference between computational success and computational failure is completely beyond the non-dynamic version of computational theory. Since we need a time-involving theory in order to explain extant computational systems anyway, it is no real objection to computationalism to point out that we need the same to understand cognition.