Paper here, "Informal Concepts in Machines", Kurt Ammon. Argues that algorithms exist which can perform computations beyond the limits of Turing machines. This is one answer to the problem of how, if humans are machines, we can definitively decide non-computability (one of Penrose's challenges).
"...there is good and bad speculation, and this is not an unparalleled activity in science...Those scientists who have no taste for this sort of speculative enterprise will just have to stay in the trenches and do without it, while the rest of us risk embarrassing mistakes and have a lot of fun." - Dan Dennett