If you mean mind as in qualia of mind or subjective mind, then I believe the following, assuming that causality exists (which I have heard it doesn't):
Mind and brain correlate, that is, their informational content is exactly identical but of a different nature, and neither of them could be said to have causal influence on the other. Instead, they correlate by some universal process that translates neuron-states into mind-states (and vice versa) for no reason.
However, the physical universe has causal influence on the brain. Causal influences on the mind cannot be said to exist because qualia cannot access themselves and thus cannot analyze their qualia-influences. Since the physical universe is causally closed, it shall be assumed that qualia have no causal influences on their own.
The illusion of free will is a result of several psychological factors which are (a) self-consciousness (as in the brain's capability to refer to itself in information processing processes), (b) emulating capabilities (imagination, memory etc.) and (c) reason.
Taking causality out of the calculation, I'd say that mind and matter are two sides of the same coin in that they correlate as described above. I would assume, without being able to prove this, that every set of connected neurons has a correlating set of qualia. I'm not entirely sure if something similar could be said about (a) cells that are not neurons, (b) one-cell organisms, (c) viruses and (d) dead matter.
I'm also arguing that the 'mind', as we perceive it, does not play a role in the evolutionary process and that it's just bad ass luck that we get a mind with our neurons, even though it doesn't have a point. Also, as I'm writing this, my brain, when using the word 'mind', thinks of a part of itself while in my subjective mind the term mind refers to my subjective mind itself rather than to the abstract concept that my brain uses. Did that make sense?
Furthermore I believe that it is impossible to investigate this problem on a scientific basis and that it is impossible to solve or even come close to a solution. I believe that the problem will not be solved as long as this universe with its current setup of mind/matter exists. And by 'solved' I mean solved in such a way that the solution can be put into words. I think the closest you can get is naming the subjective experience of solving the puzzle, a word that carries no meaning if you have not experienced it (look below for Zen).
The task of philosophy is to bring the mind/body problem into alignment with the natural sciences without explaining away human dignity or free will. I think that this is best done by looking at matter and mind as two sides of the same coin, as said above.
Another way to explain this is to assume a kind of substance that is totally different from mind and matter and that is a closed system. This substance would be the foundation to both mind and matter in that they are both equal representations (projections) of this substance into their respective dimensions. It would be the underlying principle of the universe, neither mind nor matter.
It could be argued that the process of spiritual enlightenment ('Satori' in Zen) enables both mind and matter to get in a state that is in total alignment with the guiding principles of this underlying substance. It would be for mind and matter to join in unity and for the mind to get access to this substance, to 'sneak a peak' on it. This alignment is given in at least all forms of dead matter, maybe even stupid animals. A stone is enlightened in that it does what it does. To become enlightened as a human being is to reacquire this type of alignment and to overcome the illusion of division of mind and matter. I have found that this analogy works decently to explain Zen. But I'm not the one to talk.
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