Definitely no apologies necessary. That's essentially what I meant below when I said numerical solutions can't really be described as correct. They can be useful approximations sometimes for some problems, given reasonable assumptions and well built difference equations. That said, there is certainly no such thing as an "analytic solution" to the brain. And given that numeric solutions depend wholly on good assumptions, there will never be a working brain model (maybe biochemically modeled, but certainly not 'conscious', in the sense we understand it). The Blue Brain Project has already wasted a billion dollars. Now the NIH (who is close to broke) is spending something like $50,000,000 to figure out the 'connectome', the set of all synaptic connections in an average brain ("a map of the mind," they like to call it--laughable, IMO). Maybe you can send your back of the napkin calculations to someone in power and help them realize the futility of their work.