(Also, I love how you define “not having sufficient resources in our universe” as a “circumstantial engineering problem”. )

If a table is possible in the math sense, and the only thing that prevents us from building one is the circumstantial engineering problem that our universe has no sufficient resources, then the only thing preventing us from solving the Turing test is a complexity-theoretical issue. Therefore complexity theory is cool. QED.

Jochen’s observations are quite interesting. I agree that we’re definitely talking about something analogous to the “reductions that do all the work”; indeed, what’s missing here is exactly the complexity-theoretic analysis of the question, as the problem is essentially solved from a purely computability-theoretic standpoint.

I don’t think the question related to machines having tables of different sizes is relevant, though. It is usually assumed that a Turing test session has a pre-defined duration, so beyond a certain size that won’t make a difference any more. (At the moment I don’t recall if the issue of duration is addressed by Turing’s original paper.)

Then there’s the issue of how these lookup-tables are created in the first place. It’s easy to create a table of all possible conversations of a certain length, but to pick out the ‘meaningful’ ones, which will be a small subset, the majority being largely gibberish, additional input is needed — so in Turing-testing these machines, who is really tested: the machine itself, or who- (or what-)ever supplied the additional input to weed out nonsensical dialogue histories? This seems somehow akin to one of those ‘reductions that do all the work’.

In analogy, one could put the requisite lookup table into a book that follows the style of these ‘choose your own adventure’-books; a ‘reader’ thinks of a certain dialogue part, then looks up the next one in the book. Should one consider the book to be ‘Turing-conscious’, i.e to pass the Turing test?

Perhaps one should consider a ‘strong’ Turing test somewhat like the following: an entity is judged to pass the strong Turing test if it passes the Turing test as administered by any other entity that passes the Turing test. This would exclude lookup-table machines, since there always exists another lookup-table machine with a larger lookup table that exhausts the first one’s table, and thus, which could administer a Turing test the first lookup machine could not pass, but would leave humans in the running (barring unfortunate practical issues such as age and death).