Mind is necessarily physical?

We are so used to the way our minds work, it can be quite a surprise to realise what it has to do to work as it does.  Minds can make decisions, they can imagine, they can remember, they can reason.  Just looking at one of these abilities - memory - tells us a lot about what must be needed for a mind to work.

Memory needs some form of storage.  Retrieval of memory needs some sort of indexing of the storage so that the right memories can be brought to mind.  There also has to be some sort of categorisation of memory, so that the memory of something which is like another thing can be recalled.  It should also be apparent that whatever provides these memory functions can't itself be a mind, otherwise that would not explain anything - there would be a recursion.  From all this it seems clear that mind has to need some sort of physical substrate, some parts which can change state and which can interact in reproducible ways.  

So, mind seems to be necessarily something physical, because of the nature of the functionality that necessary for mind to actually do what a mind is expected to be able to do!