David,
My opinion is that Sheldrake, while a small dog in popular science today, has his jaw clamped down on the big bone in the yard.
I am not certain what that means - but maybe it means that you think Sheldrake is reasonably close to the truth.
I am open to correction, however the idea the maths are mechanistic is due only to subjective feelings about how we practice it. The solid ontological term in my worldview of IR (informational realism) is probability. Randomness is a subjective expression about open possibilities (real-world probabilities) in certain environments. Math handles a probabilistic environment with equal skill in terms of meaningful relations of quantities; as does math handle a construction's site leverage of mechanistic processes.
Well lets explore that a little further. Let's just start with the standard time dependant Shroedinger equation:
(getting the equation in here is just too much trouble - unless there is an easy way - but you know the one I mean!)
The wave function simply evolves in a perfectly deterministic way - start with the same wave function over and over again, and it will evolve in the same way. At that stage there are no probabilities, but then you make an observation, and the resultant wavefunction is supposed to be one of a set of possible eigenfunctions (randomly picked according to state of the wavefunction at the time of the collapse).
The observer can influence the system by choosing what to observe and how often the observations occur.
Now I guess I like to think about the problem in this way, because I am sure of how it all works. Other equivalent formalisms can make the problem more abstract! Abstract formalisms can allow for more hand waiving!
The point to me, is that yes, the observer can control physical matter within reason (and Stapp now seems happy with the possibility that consciousness might act more directly by simply biassing the probabilities without the need for the Quantum Zeno effect). However explaining that control does not explain consciousness itself.
I have had a similar discussion with Neil, which unfortunately got rather heated.
My feeling is that QM can only provide some sort of interface with a mental realm, but that it is impossible to derive the mental realm from it. In particular, mind is not just information or information processing,
at the very least it has to involve qualia.
We also have to think about the NDE evidence that suggests that the mind can exist without a functioning body, and presumably without wavefunctions to collapse!
Put rather crudely, the most detailed book on dental caries, doesn't feel pain - consciousness simply cannot be equated to information!
David