light wavelength, sound intensity, or sound frequency. Derived alphabets, on the other hand, depend for their ordering properties on learning. Thus, the letters A, B, and C are without order as symbols -- until the student learns in kindergarten or the first grade the utterly arbitrary order in which they occur in the Roman alphabet. Similarly, the set of digit names and the names of the set of notes comprising the musical scale of C major acquire their ordering properties through learning. In the latter case, learning is based on a direct correspondence between a derived alphabet (the names for the notes of the C major scale) and a direct alphabet (the set of frequencies for the pitches of the C major scale).
A serial pattern is formed by rules operating on either a direct or derived alphabet Thus, given an initializing stimulus, B, on the derived alphabet of Roman letters, the pattern BCDE can be generated by three successive applications of a NEXT rule to the alphabet. The pattern could be extended, BCDEBCDE, giving it a hierarchical structure, by applying a REPEAT rule to the subset BCDE ( Simon & Kotovsky, 1963; Restle, 1970; Jones, 1974). In another domain, such as music, the sequence beginning with middle C, C-D-E-F#, defines a four-tone sequence on a scale, the whole-tons scale in particular, in which an octave is divided into six equal intervals on a log scale of frequency.
Thus, serial patterns are described in terms of explicitly defined formal structure. The behavioral consequences of variations in that formal structure can then be explored. For example, in studies with human subjects, it has been found that people (a) find patterns with formally complex as compared with formally simple rule structures more difficult to learn; (b) have a predilection to extrapolate patterns, inducing a rule from a sample of a pattern and applying the rule to supply the next stimulus in a pattern sequence; (c) tend to make errors in anticipating the next stimulus in a pattern at those points where structural rules change in the pattern; and (d) find patterns easier to learn if they are "chunked" or grouped into subunits by temporal pauses or other cues located, similarly, at those points where structural rules change in the pattern ( Bower & Winzenz, 1969; Deutsch & Feroe, 1981; Jones, 1978; Kotovsky & Simon, 1973; Restle, 1970; Restle, 1972; Restle & Brown, 1970; Vitz & Todd, 1969).
In a recent series of experiments, we have been able to show that rats learn to anticipate the elements of direct and derived alphabets based on food quantities according to many of the some principles demonstrated by humans ( Hulse, 1978; Hulse & Dorsky, 1977; Hulse & Dorsky, 1979; Fountain & Hulse, 1981; Hulse & O'Leary, 1982). Thus, rats find formally complex patterns harder to learn than formally simple patterns, extrapolate patterns, and so on. Terrace and his associates (e.g., Straubet al., 1979; Straub & Terrace, 1981) have been pursuing a similar line of research with pigeons with notable success. Thus, there appear to be many functional parallels between the way in which people and animals process serial information.