(Talk formerly titled "An epistemic problem for implementation")
Many accounts in philosophy of computation distinguish between abstract notions of computation and physical systems computing concretely. Ontologically this distinction seems plausible. As many engineers can attest, one needs to arrange matter in highly contrived ways to coax it into computing. The relation between abstract and physical computation is called implementation. We rely on the implementation of boolean logic in solid-state circuitry for our everyday computing needs. But we should be careful not to generalize the success of solid-state circuitry to other physical systems. For implementation poses an epistemic problem. To make matter compute, one needs to know how to arrange it and one needs to be sure that it will compute correctly - at least in most of the cases. I will discuss a case of analogue electronic circuitry, namely an op-amp based analogue equivalent of certain system of ordinary differential equations, where it is unclear if the circuitry implements the differential equations it was set up to implement. There are two reasons why we cannot be sure of the implementation: 1) We do not have analytic solutions of the differential equations in question. 2) The numerical solution of the discretized version shows a different behaviour than the analogue circuitry. We now face the epistemic problem of which computation we should believe. Do we vouch for the analogue circuitry because we suspect problems with the discretization, or do we go with the numerical solution blaming noise and unaccounted errors in the analogue electronics? Rather than trying to come up with a philosophical answer to this question, I will discuss how it has been answered historically in the case of digital and analogue computer engineering and argue that the current renaissance of analogue and hybrid computers might shake the old consensus.