In the early 1980s, Douglas Hofstadter introduced the “Copycat” letter-string domain for analogy-making. Here are some sample analogy problems:
If the string abc changes to the string abd, what does the string pqr change to?
If the string abc changes to the string abd, what does the string ppqqrr change to?
If the string abc changes to the string abd, what does the string mrrjjj change to?
If the string abc changes to the string abd, what does the string xyz change to?
If the string axbxcx changes to the string abc, what does the string xpxqxr change to?
The purpose of this “microworld” (as it was called back then) is to model the kinds of analogies humans make in general. Each string in an analogy problem represents a miniature “situation”, with objects, attributes, relationships, groupings, and actions. Figuring out answers to these problems, it was claimed, involves at least some of the mechanisms of more general analogy-making, such as perceiving abstract roles and correspondences between roles, ignoring irrelevant aspects, and mapping the gist of one situation to a different situation. In Chapter 24 of his book Metamagical Themas, Hofstadter wrote a long, incisive analysis of human analogy and how the Copycat domains captures some key aspects of it. The letter-string domain is deceptively simple — these problems can capture a large range of complex issues in recognizing abstract similarity. Hofstadter and his students (myself among them) came up with thousands of different letter string analogies, some of them extraordinarily subtle. A small collection of examples is given at this link.
To continue reading this article, click here.