What must a global theory of cortex explain?

At present there is no generally accepted theory of how cognitive phenomena arise from computations in cortex. Further, there is no consensus on how the search for one should be refocussed so as to make it more fruitful. In this short piece we observe that research in computer science over the last several decades has shown that significant computational phenomena need to circumvent significant inherent quantitative impediments, such as of computational complexity. We argue that computational neuroscience has to be informed by the same quantitative concerns for it to succeed. It is conceivable that the brain is the one computation that does not need to circumvent any such obstacles, but if that were the case then quantitatively plausible theories of cortex would now surely abound and be driving experimental investigations.