I've never been able to see why one would give the lookup table any credence. It's just kicking the can down the road one step in terms of abstraction.

The second you assert that the lookup table can pass a turing test with, eg. a gigabyte of exchange, then the table of every single one gigabyte number in it becomes your state space and program, the page number becomes the state, and you've got just as much complexity as any other simulation with one gigabyte of state. You haven't changed the parameters of the problem at all.