It's amazing how much you can learn about an animal's mind by a simply watching it.
In the late 1980s, a researcher named Jennifer A. Mather wondered about octopuses' use of spatial memory. This researcher and some volunteers did some skin-diving near Bermuda and observed octopuses going out in search of food. They noticed that sometimes after catching a tasty bit of chow, the octopuses ate out, but sometimes they'd take their snack to go and eat at home. And not only that, but it turned out that there was a correlation between the decision to eat out and the distance from home. When they were farther away from home, they tended to eat out; when they were closer, then took the catch home.
So what? This finding suggests that octopuses have at least a crude mental map of the space surrounding their homes: that they know their location in the environment relative to home, and they use that information to make a decision about where to dine.
What else did she find out about octopus navigation? You'll have to check back next week!
Mather, J. (1991). Navigation by spatial memory and use of visual landmarks in octopuses Journal of Comparative Physiology A, 168 (4), 491-497. DOI: 10.1007/BF00199609