Using the Godel incompleteness result for leverage, Roger Penrose has argued that the mechanism for consciousness involves quantum gravitational phenomena, acting through microtubules in neurons. We show that this hypothesis is implausible. First the Godel result does not imply that human thought is in fact non-algorithmic. Second, whether or not non-algorithmic quantum gravitational phenomena actually exist, and if they did how that could conceivably implicate microtubules, and if microtubules were involved, how that could conceivably implicate consciousness, is entirely speculative. Third, (...) cytoplasmic ions such as calcium and sodium are almost certainly present in the microtubule pore, barring the quantum-mechanical effects Penrose envisages. Finally, physiological evidence indicates that consciousness does not directly depend on microtubule properties in any case, rendering doubtful any theory according to which consciousness is generated in the microtubules. (shrink)