A theory of advice

Machine intelligence problems are sometimes defined as those problems which (i) computers can't yet do, and (ii) humans can. We shall further consider how much "knowledge" about a finite mathematical function can, on certain assumptions, be credited to a computer program. Although our approach is quite general, we are really only interested in programs which evaluate "semihard" functions, believing that the evaluation of such functions constitutes the defining aspiration of machine intelligence work. If a function is less hard than "semihard," then we can evaluate it by pure algorithm (trading space for time) or by pure lookup (making the opposite trade), with no need to talk of knowledge, advice, machine intelligence, or any of those things. We call such problems "standard." If however the function is "semihard," then we will be driven to construct some form of artful compromise between the two representations: without such a compromise the function will not be evaluable within practical resource limits. If the function is harder than "semihard," i.e. is actually "hard," then no amount of compromise can ever make feasible its evaluation by any terrestrial device.