> A computation is just an implementation of a function `f: {0,1}^N-> {0,1}^M`... if not, what is the meaning of the word at all? Sure, that's a definition. It

> A computation is just an implementation of a function `f: {0,1}^N-> {0,1}^M`... if not, what is the meaning of the word at all? Sure, that's a definition. It happens to be mathematically equivalent to the calculation of any observable signal in the real world, because there exist isomorphisms between {0,1}^N and the set of functions of maximum frequency f over time t, for example. > All these phrases "manipulates data", "computation", and so on... they dont mean anything They are certainly meaningful. > A kettle "manipulates data". Yes, it does, but in a very trivial and uninteresting way. Crucially, it does more than just manipulate data, but manipulating data is one of the things a kettle can do. > You think you're saying something empirically significant about the brain using this language, but this language has no empirical content. It is a language of pure mathematics. We certainly can say empirically significant things about the brain, since facts about the way in which it performs computations can be inferred, and from this we can infer information about how the brain must be structured. Trivially for example, we can infer that the brain must be able to have a minimum amount of outgoing total neuronal bandwidth by analyzing the makeup of outputs in can compute, and indeed we can do more. > All of these claims are true of any system. Of course, they are. But for some systems they can provide more insight than for others. The computation a kettle can do is insignificant and largely irrelevant to what interests us kettle-wise, so we don't really care. However, the way in which the brain manipulates data is much more interesting and intricate (and we can of course place lower and upper bounds on how intricate it is), and correspondingly we can learn much more. > If you can provide a logical model of the algorithm the brain is performing, and a model of how the brain implements it, then we learn something. I don't need to provide a model of the algorithm the brain is performing nor of how it is implemented to learn things. Thanks to various interesting results in computer science (in conjunction with results in the hard sciences), we can learn things about the brain without needing at all to know which algorithm it is implementing, and without knowing much of how it is implemented. At the extreme of knowing little about the implementation, we have physical lower bounds of physically possible implementations of any given computation, regardless of the algorithm. CS theory allows us to infer facts about algorithms by knowing the computation. For example, if I have a black box that inputs a list and outputs a sorted list, since I know that it is impossible to sort a list in the general case faster than n log n, and since it is impossible to know the original list from the sorted list, knowing the Landauer limit, I can infer for example a minimum power consumption. I don't need to know anything about the implementation or algorithm.