> BTW, there are quite a few limitations placed on you by nature: uncomputable numbers, NP-completness, ...
Not really, NP-completness is only important if you want perfect solutions, which aren't necessary. Uncomputable numbers have no usage in real world scenarios.
Finally it is important to note that while a physical turing machine cannot exist due to lack of infinite tape, real machines are also more powerful than turing machines, for instance by having a real time clock and communication abilities.
For these reasons saying what we can and cannot do is quite complicated. For almost every situation possible, the only answer that is negative about capabilities is "it will take a while".
