Taking a standard reductionist view of science that everything can reduce down to physics, although it is often more useful to view things on a larger scale through the other sciences, science becomes primarily focused on matter and how matter interacts. It doesn't really consider the mind/consciousness within this (ok, this is questionable for sciences such as psychology, as it's questionable whether this is entirely about the functioning of the brain or whether an individual consciousness plays a role. Some would even say consciousness is entirely about the functioning of the brain and so this whole train of thought falls apart, but that would be less interesting, so I'll put that thought to one side).
If you want to consider things like psi scientifically, particularly for things like telekinesis, where there is a clear interaction between mind and matter, you need to consider the more general question of whether science can accommodate consciousness, which to me sounds a far more interesting topic to think about.
As a cosmologist, Carr, asked the question about this drive for a theory of everything, where we keep extending the theories to take into account other forces to the point where cosmologists are now considering things like M-theory (and we're now going well beyond my knowledge of physics with things like that). What if this could be extended further to include notions of consciousness? Would it be useful? What would it predict?
I'm fairly skeptical about the whole psi thing, although being able to move bottle tops with my mind would be quite a fun thing to do and if someone claimed it were possible and wanted to show me how I'd certainly be open to giving it a go. However, Carr, came up with the valid point that although a lot of scientists rule out this sort of stuff, some of the results predicted by string theory are equally bizarre and equally unproven and yet far more acceptable.
So, taking that further, this got me thinking (a not entirely new thought) that although scientific models at their core have a proven evidence base to show this is a good model in the scope that we're looking at, when you go beyond that scope and start making predictions outside of this, you start going into the realm of belief. Admittedly, in terms of science you then experiment and prove this belief right or wrong and adapt your model accordingly and this is how we progress.
This then gets me thinking about belief in general (particularly religion, which seems to keep cropping up in conversation lately - probably due to the time of year and the people I've been talking to) and the thought that these are just personal models of reality based on our own experiential evidence and predictions about the nature of reality based on those. In fact, I've heard a lot of very religious people say that these sort of things are beyond our comprehension and religion is just our way of understanding it, which fits this quite well. Then again, I was a mathematician and not a very religious one, so I probably would view it this way.
Whereas much of the scientific models of reality are experimentally verifiable, but only cover a narrow focus of the materialistic stuff, religious models cover everything, but generally appear less easily verifiable (after all, even if there was a god and he were to strike me down with a thunderbolt, I might just put it down to a freak weather occurrence).
So, in a way we already have several models for this sort of stuff, they're just not expressed mathematically. This doesn't mean they can't be. After all, talking to Newton about string theory would probably have confused the socks off him, he didn't have the mathematics for this.
So, whether science can accommodate consciousness, seems to me more of a question of what science is. Is it purely about the materialistic world or can it include theories on other aspects of reality?