"That classical mechanics is not capable of integrating consciousness into science is manifest. Classical mechanics is an expression of Decartes's idea that nature is divided into two logically unrelated and noninteracting parts: mind and matter..."
Of course, it is often debated whether or not it might be a fruitful idea that there be a quantum aspect to the functioning of the brain! In his textbook on quantum theory David Bohm (Bohm, 1951) pointed out several interesting parallels between conscious experience and the qualities of quantum systems. On the other hand, large scale quantum effects have been typically known to happen only in special circumstances (such as low temperature or very high pressure): from this point of view the burden is on the advocates of a quantum brain perspective to show how their view is not unreasonable. (A step in this direction is of course the model of Frohlich.) Our task in this regard is to broaden our understanding of how coherence manifests, but also especially to enlarge our understanding and appreciation of the solid-state entity that is the organism.
One can begin the other way around and assume a quantum view based on general priciples. This, in different versions, is the path followed by Stapp, Marshall, Umezawa, et. al...
My view, that evolution is wily, subtle and integrative and likely quantum coherent to the core, was spelled out several years ago in a posting to psyche-d.
How does the brain maintain dynamical coherence? One idea is that there is a quantum coherent state underlying this, as has been articulately argued by Ian Marshall.QBD: Quantum Brain Dynamics
Marshall,I.N."Consciousness and Bose-Einstein Condensates." New Ideas in Psychology, v.7, n.1 (1989)"Combining the two ideas so far - long-range order and a sharing of the identities of constituent units - leads to the notion of Bose-Einstein condensation..."
"Quantum field theory (QFT) has been proven in recent years to be the conceptual framework able to explain how ordered structures could emerge from a set of elementary components with symmetric interactions. The relevant mechanism is spontaneous symmetry brealing..."Microtubules and the mind
Del Giuice, Doglia, Milana, Vitiello (1986)
The "Quantum Brain Dynamics" paradigm goes back to Ricciardi and Umezawa...
L.M. Ricciardi and H.Umezawa, Kibernetik 4 , 44 (1967)
The interested seeker might well wish to read Dissipation and Memory Capacity in the Quantum Brain Model by Giuseppe Vitiello (available here with interpolated comments by Jack Sarfatti), or Gordon Globus' Consciousness is Cybernetic.
G. Vitiello sent an extended abstract on quantum memory models to quantum-d.
There is various evidence linking neuronal microtubules with learning and perhaps even the basis of counsciousness.Stapp's quantum paradigm
Hameroff, S.R. (1994) Quantum coherence in microtubules: A neural basis for emergent consciousness? Journal of Consciousness Studies 1(1):91-118.
A model of 'top level control' by a quantum state has been discussed by Henry Stapp, who argues generally that the quantum description is appropriate to consciousness in a way the classical one cannot be."The conscious act is represented physically by the selection of a new top-level code, which then automatically exercises top-level control over the flow of neural excitations in the brain through the action of the quantum-theoretic laws of nature. The unity of conscious thought comes from the unifying integrative character of the conscious creative act, which selects a single code from among the multitude generated by the causal development prescribed by quantum theory."
Henry Stapp, 106