The important word is : formal. I, too, think that the brain is 'a computer'. But the formal definitions of computation we have today require the computer to b

The important word is : formal. I, too, think that the brain is 'a computer'. But the formal definitions of computation we have today require the computer to be left alone for some time between the moment the input is given and the moment the output is due. The brain does not work like that, ergo we lack a formal model of how the brain operates, and thus the definition of 'computable function' -which is based on our model of computation- is less general than what the brain can do. e.g. We have no proof that the only way neurons communicate with one another is via the synapses.