[ouid]

last clarifications, sorry.

Some manifold has a goodness function defined on it, described by a (totally ordered?) relation provided by the observing scientist.

The goodness function is assumed to be (continuous/differentiable/continuously differentiable?) with respect to some metric, and the computer picks a random coordinate within some small distance of the last coordinate in the metric, and then asks the human to order them?

I don't think this is hill climbing, and my simple reasoning for that is that I don't believe the first assertion. The expert is almost certainly behaving non-deterministically. In fact, I believe that each time the expert is presented with the "same" pair of coordinates, he is more likely to yield a different ordering.

That said, I could be reading this wrong.