I remain baffled that anyone thinks dragging brains into discussions of these things does anything but make everyone more confused. This kind of thing is exactly what I'm getting at—that it's common for even people in the computer technology field to think the comparison is apt, or illuminates anything, is a wild indication of how inclined we are to be tricked by computer programs that happen to operate on language.
You are baffled because of your own ignorance of the underlying principles under discussion. Do you believe in a dualist interpretation of reality, that the process of thinking is somehow nonphysical? That these programs operate on language is besides the point. The fact you think this is why it's interesting shows you don't even understand the argument.
Are you familiar with the physical church turing thesis?