wise, your brain can compute the direction from which a sound arises according to a particular trigonometric rule, even if it sometimes makes errors that are incompatible with that rule. We expect these errors in anyone, and we find greater errors among those of us who are hearing-impaired. But why think that most people’s auditory systems are solving the same trigonometric problems in error-prone ways rather than solving their own personally tailored problems in an error-free way?
It isn’t as arbitrary as it seems. The reasonable thing to say is that something performs a computation if it would normally perform that computation. Abnormal and non-ideal circumstances – having a head cold while walking through an organ-grinding festival – can lead to errors. This causes surprisingly few difficulties in cognitive science. Cognitive scientists are able to identify, in testable and motivated ways, which behaviours are the result of abnormal or interfering factors. But even though we have a stable, usable empirical concept of what computation a system ‘would normally perform’, it is wildly unsettled what it actually is for something to ‘normally perform’ one computation rather than another.
That’s just the beginning of our problems. In saying which problems could be solved by rule-bound calculations, Church and Turing defined models in which a set of symbols expressing the problem (the line ‘21 x 3 = ?’ in your notebook) is transformed into a set of symbols expressing the solution (‘63’). But the very same models could be used to convert meaningless gibberish (‘j&^@’) into other meaningless gibberish (‘•¡ø∂’). Would those transformations then count as computations? Turning back to the natural world: does it really matter that the firing of a neuron means that a sound came from thataway, or does it just matter that when this neuron here starts firing (whatever news or information that neuron might have about the world), it triggers those neurons over there to start firing?
If our brains are computers, our mental lives must be rich with meaningful information
In fact, the question of whether computation involves meaningful representation can bear on the question of what it is for a system to ‘normally perform’ a computation. If the Arabic numerals ‘1’, ‘2’, ‘3’, … represent the numbers one, two, three and so on, and if some machine or organism takes any two of those numerals and typically churns out a numeral denoting its sum, then there’s good reason to think that this thing normally performs addition, even if it occasionally hiccups out the wrong sum when it is tired or distracted. If the system is just swishing around meaningless symbols, it is much more difficult to say what should determine that the system normally performs one computation rather than another one.
Many have thought that computation must involve meaningful representation or information. Far from saying that we are meaningless machines, the claim that our brains are computers would require that our mental lives are rich with meaningful information. Yet if computation requires giving meaningful answers to meaningful problems then, in order to say what it would be for the brain to be a computer, one must also say what it would be for activity in the brain to be meaningful. One difficult question begging another. There are a number of dissenting and intermediate positions about whether computations must be meaningful.
It’s not so clear that there is any single answer to what a computer is. Computation might not be a uniform kind of thing in nature. Many things are said to compute: household PCs, analogue machines, looms, brains and even DNA and quantum-mechanical systems. These are quite different pieces of nature (or, in the case of PCs, looms and analogue machines, human artifice – itself a piece of nature). What it is for one sort of thing to compute might turn out to be quite different from what it is for another sort of thing to compute. The features of a Navy fire-control system that make it distinctively computational might differ from the features of the