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This is a note from Paul Prueitt to New England Complex Systems Institute Forum , October 22, 1999.
To New England Complex Systems Institute Forum
It is my understanding of the work done by Stu Hameroff, that the mechanisms of objective reduction (OR) are control parameters that act on a gravitational artifact.. to bind otherwise separated (in space time) quantum states. As such, the theory is somewhat incomplete, given that the theory does not impart any type of differential structure, to the artifact, having a pragmatic grounding in a present moment ("as if" time where causal due to differential channels of potential extending into a future (Bohm's idea of implicate order I think)). This notion of differential channels is THE foundational notion to Peircean existential graphs (in my humble opinion), and thus we may have a means to lay down situational logics in this regard (I think that this is what Pospelov was in rout to doing in the years before the Soviet Union collapsed and his research group dissipated.)
The computing that Stu uses is state switching in protein metastable states, so is not computing as defined by von Neumann.
and Stu's wonderful book, Ultimate Computing.
I will say that society often forces innovators such as Penrose, Hameroff.. and (the specific case history is interesting to me...) Steve Grossberg.. into defining a position.. often making unfortunate intellectual steps to find a closure in this defense.
Clearly, in my opinion, Hameroff's presentation and theory would benefit from the Rosen type category theory.
I will also note a brief discussion at a conference in 1992 or so, when Penrose attended Pribram's conference and meet Stu (if I remember this correctly). I suggested to Sir Penrose that the presentation he made did not seem to account for Prigogine's notion of how one gets out of Godel paradoxes through the use of deterministic chaos during self organization. He said to me, "This is not what I am doing".
It is difficult for me to bias my whole view of Penrose's work based on this brief exchange. But I no longer saw him as having a solution to the "binding problem". He merely defined what was wrong with the current paradigm. This definition was in a real way historic - due to the fact that one could now point to Penrose's argument and say "go read this".
Rosen and Penrose both dealt with non-computability. Rosen's point is deeper as his position was that the formation of a categorical homomorphism between natural systems and formal system just could not be done. I. E. formal systems are not natural systems.
Penrose address a more narrow issue, having to do with the logical requirement for a non-computational aspect to the phenomenon of awareness. Of course, this is not the generic problem.