E.10.INT:5 - Archetypal Grounding

E.10.INT:5.1 - An informative controller query

A controller must choose an input that gives output 5. It has two equally plausible candidate relations, y=x and y=-x, and can first query input 0 or input 1. “Choose the more surprising query” leaves the criterion unclear.

At input 0 both candidates return 0. At input 1 they return 1 and -1 respectively. The second query distinguishes the candidates: after observing 1, command 5; after observing -1, command -5. The recovered instruction is “query input 1 to distinguish the relations, then choose the command.”

A separate fair coin produces an outcome with one bit of surprisal, but its outcome is independent of which relation holds. Querying input 1 yields one bit of information about that relation under the stated equal prior. Tossing the coin yields none. If the controller is already given the relation, it can select the command immediately.

The example constructs an information-seeking policy. Whether a particular controller can execute it is a further capability question.

E.10.INT:5.2 - Progress and a stepping stone

In a constructed example, a compressor learns a dictionary entry for a repeated substring in a fixed data block. Its total lossless description of that block, counting the dictionary and encoded data under the same convention, falls from 100 bits before the update to 80 afterwards. “The second version is more interesting” can now be recovered as “this dictionary update reduced the total description by 20 bits for this block.” If the team is choosing more training, it considers the likely further improvement and the work required.

Another construction may deserve attention even though that measure has not improved. In Stanley and Lehman’s Picbreeder example, a participant retained and developed an image resembling an alien face; a car-like image appeared through later changes. The first participant could act on the available image and its variation possibilities before knowing that destination. The practical result of this recovery is to retain the construction and its means of variation for exploration. C.18 governs an archive used for that purpose.

These cases permit different choices: improving a known performance measure and preserving a possible starting point for new work.

E.10.INT:5.3 - Choosing an interesting rhythm

A workshop needs music for listeners who are familiar with 4/4 and are beginning to work with 7/8. “Choose moderately complex rhythms; they are the most interesting” hides both the response sought and the listeners’ preparation.

Recover the request as “choose material that helps these listeners maintain the beat and want to move while encountering 7/8.” The facilitator can start from simpler 7/8 material and adjust from the listeners’ response. If the purpose is instead to exercise a skilled drummer’s coordination, that practice question needs its own choice of material.

This distinction is supported by Spiech and colleagues’ study: Western listeners’ groove ratings peaked at moderate complexity in 4/4, while simpler rhythms received the highest ratings in the less common meters tested. Here groove means the pleasurable urge to move. The study supports adapting the comparison to listener and meter; the workshop’s teaching method supplies the exercise.