When functionalists compare the relationship between the mind and the brain to the way in which computer software relates to hardware, they are thinking about the functional role played by mental states in the output of the brain.
The hardware of a computer system is visible and neutral. What it does depends on the software you run on it. Similarly, the brain is a physical system which, according to theorists such as John von Neumann, might be replicated mechanically. Although a brain, like a computer, may be more or less powerful, the output largely depends on the input of the mind.
It is often remarked that people who have created the greatest suffering in human history are highly intelligent (i.e., they have powerful brains). This is true of Adolf Hitler, Osama bin Laden, and Saddam Hussein, for instance. In each of these cases, one might describe the individual as running highly destructive software, in the form of ideologies and aspirations, on powerful hardware, in the form of their brains.
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