 Any device or organ whose internal processes can be described completely by means of (what Church called) effectively calculable functions can be simulated exactly by a Turing machine (providing that the input into the device or organ is itself computable by Turing machine). But any device or organ whose mathematical description involves functions that are not effectively calculable cannot be so simulated. As Turing showed, there are uncountably many such functions. It is an open question whether a completed neuroscience will need to employ functions that are not effectively calculable.