Voyage to Serendip: The Moral?
In a word? Exploring is fun (see "To seek whence cometh a sequence" in Fluid Concepts and Creative Analogies by Douglas Hofstader et al, Basic Books, 1995). But even more importantly: aimlessness, playfulness, random movement without knowing where you are going sometimes pays. Serendipity is much more than an oddity, or a cover story for ignorance as to how something actually happened. Its an expression of the reality, intuitively understood by animals, children, and some adults, that orderly processes are limited in their capabilities, that some things may be found only by restless and undirected searching.
At the lower levels of the Voyage, Serendip's movements are orderly, and the movement patterns can be fairly easily detected (see Hofstader), making it possible to predict Serendip's future locations and so to find Serendip relatively quickly. At the Hard level, Serendip is moving randomly from location to location. Because of this, any of a variety of search strategies will, on the average, do equally well at locating Serendip. Among the equally good strategies are repeatedly looking at the same location and picking search locations randomly.
The interesting case is the hardest level. Here, Serendip is using different movement patterns each time you restart the game. Sometimes Serendip is using one or another orderly movement pattern and on other occasions it is using a random movement pattern. If you try and anticipate movements based on a pattern detected in your previous experience, you may never find Serendip, since it may be using a movement pattern which never overlaps with your search pattern. The same is true for any orderly search pattern, including repeated searching at a single location since Serendip's movement pattern may not include that particular square. In the situation of an unknown movement pattern which may be either orderly or random, the only search strategy which can assure success is one that is itself random.
The existence and significance of random, or at least "ill mannered", processes in behavior and its underlying brain function is further considered here .