into local strategies for derivations is called problem reduction. It is based on
the idea that whenever one has a long-range goal, there are usually subgoals
whose attainment will aid in the attainment of the main goal. Therefore if
one breaks up a given problem into a series of new subproblems, then
breaks those in turn into subsubproblems, and so on, in a recursive fashion,
one eventually comes down to very modest goals which can presumably be
attained in a couple of steps. Or at least so it would seem ...
PrQblem reduction got Zeno into hot water. Zeno's method, you recall,
for getting from A to B (think of B as the goal), is to "reduce" the problem
into two subproblems: first go halfway, then go the rest of the way. So now
you have "pushed"-in the sense of Chapter V-two subgoals onto your
"goal stack". Each of these, in turn, will be replaced by two subsubgoals-
and so on ad infinitum. You wind up with an infinite goal-stack, instead of a
single goal (Fig. 115). Popping an infinite number of goals off your stack
will prove to be tricky-which is just Zeno's point, of course.
Another example of an infinite recursion in problem reduction occur-
red in the Dialogue Little Harmonic Labyrinth, when Achilles wanted to have
a Typeless Wish granted. Its granting had to be deferred until permission
was gotten from the Meta-Genie; but in order to get permission to give
permission, she had to summon the Meta-Meta-Genie-and so on. Despite
610
FIGURE 115. Zeno's endless goal tree,for getting from A to B.
Get from
A to Elea
Get from
A to B
Get from
Elea to B
Artificial Intelligence: Retrospects
