Indiana University Bloomington

Letter Analogy Problems

CRCC's love affair with letter analogy problems goes back years; Hofstadter came up with the domain starting as early as 1980, in an attempt to distill out the essence of analogy. To the uninitiated this love can seem an arcane love indeed. The basic idea is simple:

I change efg into efw. Can you "do the same thing" to ghi?
(This example is taken from Hofstadter's book FCCA, page 202.) There are a great number of possible answers to the question, but consider these two: whi and ghw. In the first answer, we've construed the change as being "change 'g' into 'w'", but in the second we've seen it as "change the rightmost letter to 'w'". Each is a valid answer, but the second has something of the feel of a higher-level answer, since it's not a blind search-and-replace of the letter 'g'.

A closely related analogy is

I change efg into wfg. Can you "do the same thing" to ghi?
Here, the same two answers, whi and ghw, remain -- but now they can be seen as construing the problem in different ways. The first can be seen as "change the leftmost letter to 'w'", but the second now looks more like a rather elegant solution, noting that the two strings are mirror images of one another in the sense of moving away from 'g', and replacing the "far end" with the letter 'w'.

The letter analogy domain is thus an attempt to define a very, very small domain (just the twenty-six letters of the alphabet, the concepts of "left" and "right", the notions of "successor" and "predecessor", small numbers for grouping letters, and so forth) that still admits the possibility of expressing elegance, creativity, comparisons, even a mild form of humor if you've spent enough time with it. We don't know of anyone who's managed a belly laugh over a letter analogy, but miss enough sleep and you can certainly get a chuckle. The point is that this tiny domain allows us to model all kinds of cognitive phenomena without getting bogged down in either the attempt to compile an encyclopedia of all human knowledge or the trap of thinking that a reduced domain is somehow equivalent to such an encyclopedia.

Here are a few more letter analogy problems. See if you can come up with various answers to them and compare their qualities. It's a subtle aroma you're looking for, but it's worth the effort.

abc --> abd; ijk --> ?
abc --> abd; ijkk --> ?
abc --> abd; mrrjjj --> ?
abc --> abd; xyz --> ? (Note: the alphabet does not wrap around!)
abc --> abd; ydq --> ?