You're talking about his quantum tubules theory of consciousness. Honestly, I think it's coming from the same emotional agenda that made Geocentrism and later Vitalism so popular. It's just the latest philosophical secret sauce.

Besides, that's just trying to explain qualia. Pretty sure no one thinks memories are quantum phenomena.

Actually Penrose isn't so much interested in qualia as he is in things mathematicians can do, but which Turing machines cannot (from http://en.wikipedia.org/wiki/Quantum_mind - "Penrose is not interested in explaining phenomenal consciousness, qualia, generally regarded as the most mysterious feature of consciousness, but instead focuses mainly on the cognitive powers of mathematicians").

If I have closed timelike curves, an oracle for the halting problem, or the ability to perform arbitrary computations on real numbers in my brain, I would certainly like to know how to use them.