Possibility of Analogue Computation
Overview
Consciousness might require functions that are not replicated exactly in a digital simulation, even if they can be simulated to arbitrary input/output accuracy, e.g. numbers whose exact value cannot be calculated digitally (pi, e, phi, etc.) and non-computable mathematics (e.g. certain non-constructivist proofs).
In particular, we might look to certain physical phenomena which are invoked in contemporary theories of consciousness, e.g. continuous physical phenomena (e.g. certain interpretations of physical fields, such as electromagnetic fields or space-time in general relativity) or quantum phenomena non-simulable in practice (e.g. large entangled systems may require prohibitively long simulation times), etc.
Responses
Adjust CF to require analogue computation.
Reject the claim that human capabilities are beyond Turing Machine equivalence. For instance, human creativity is at risk of adequate duplication in current generation AI (at least relative to low percentile human performance, who are presumably conscious in relevantly similar ways to the most brilliant). Interpretations also exist in which non-computable proofs by human mathematicians are not evidence that we infallibly compute non-computable functions, but rather that we are deploying specific forms of representational reasoning and heuristic inference that could also be implemented on a machine subject to similar limitations.
Reject the claim that any analogue features are necessary for consciousness (or place the burden of proof on CF critics to demonstrate the analogue claim).