Physicists (or those with strong physics backgrounds) have often gotten into the biology game with wonderful results, e.g. Francis Crick, Linus Pauling, George Gamow. Before the nature of the gene had been worked out, though, many physicists jumped onto the bio bandwagon because, without falling inwittingly into full-blown vitalism, they expected to discover “new physics” associated with Life. What they found is live pretty much boils down to hydrogen bonds and complexity, neither of which is all that interesting from a theoretical standpoint. Hydrogen bonds are very well described. Complexity is an ever-evolving field, but the foundations are firm, and while quantum weirdness does have its place in it, many of the classical consequences of chaos theory are, if anything, mitigated somewhat by quantum phenomena; they tend to smear things out and make the basic unit of a complex interaction, a collision, softer than what would be expected of the interactions of infinitessimal, hard objects.
The weirdest consequences of quantum theory, which have been proven to exist, are entanglement and non-locality. I am struck, though, whenever I read about experiments to probe these phenomena, both by the astounding precision of the measurements being made, and by the extraordinarily well-controlled conditions that are necessary to tease out quantum weirdness from the decoherent background. Everything to do with quantum computing seems to rely, ideally, on supercold vacuums. The human brain is anything but. Brains are made of atoms and molecules, which do exist in quantum superpositions, and do contain particles that may be in entagled states with other particles. But these weird quantum states would probably last for picoseconds or less in the hot, dense environment of the brain. Particles are flying about furiously in there, interacting at a stupendous rate. It is well known that interactions destroy quantum coherence and break superpositions (an interaction is equivalent to an observation, a la the Copenhegan Interpretation).
The speed of impulses in the human nervous system is about 200 m/s. So the fastest a signal could travel from your foot to your brain, assuming you are two meters tall, is about about 10 milliseconds. The restoration of neuron action potentials can also be measured in milliseconds. That’s two orders of magnitude, at the very least, greater than what one could expect the abosolute longest conherent state to last in a brain. So, when it takes signals so long to go anywhere, and it takes neurons so long to refire, I just can’t see how the non-local/FTL and massively parallel consequences of the weird interactions of entagled particles could be of any importance to human cognitive processes. The brain is amazingly complex, but as far as I can tell, it’s a classical machine. One shouldn’t evoke quantum weirdness until they have come fully to grips with the daunting complexity of the brain, and found classical explanations to be lacking, beyond all reasonable doubt.
We’re a long way off from that. Penrose, beyond ignoring some basic physical limitations of the intracranial environment, is really jumping the gun, if you ask me.