We are interested in all of these phenomena. Note that they are a very diverse bunch: some are states (to be in pain is to be in a certain state), some are events (calculations are events), some are processes (planning a party is a process), and some are properties (it is a property of me that I know the capital of Rhode Island).
This is not the sort of question a scientist can answer. We don't need to learn more about thermometers and how they work - the question would remain even if we knew all of that. What we need to learn about is what it is to have a mind - what it is that we are looking for.
This is something that we might be able to do from an armchair (contentious), perhaps because it is a matter of learning about our concept MIND (contentious), or about what we mean by the word 'mind' (contentious).
Accounting for this is a problem for substance dualism and property dualism: how can anything which is non-physical causally interact with something which is physical?
Necessarily: for all x and y: if x and y have the same physical properties then x and y have the same mental properties.
(If the variables range over objects within worlds then we have local supervenience; if they range over worlds then we have global supervenience.)
Necessarily: for all x and m: if m is a mental property and x has m then there is a p such that p is a physical property and x has p and necessarily: for all y: if y has p then y has m.
(p is called a supervenience base for m. Note that it is a supervenience base and not the supervenience base - there might be others. Strong supervenience has local and global readings too.)
Strong supervenience entails supervenience (proof?). What about the other way around?
Supervenience is just a claim about covariance, so in this respect it is quite weak. Observe that mathematical properties supervene on physical properties. Also observe that supervenience is compatible with substance dualism. But it might entail that there can be at most one kind of Cartesian mind: any two Cartesian minds are alike in all physical properties (they have none), so they are alike in all mental properties, so they are alike in all properties. This might render Cartesian dualism implausible, and push us towards physicalism.