Page 432 - Deep Learning

Notes to Pages 79–82 415

the strategies of one domain seem to be unrelated to those of other domains,
has discouraged a search for a general theory of problem-solving strategies (but
see Lenat, 1983, for a promising start). Perhaps due to the difficulty of finding
anything general to say, research that primarily aims to identify and analyze
problem-solving strategies has waned as a basic research enterprise, but con-
tinues to be of interest in applied contexts; see, e.g., Schraagen, Chipman and
Shalin (2000). For a strategy-oriented application of search concepts to under-
standing creativity in Artificial Intelligence, see Buchanan (2001): “Search at the
meta-level gives us a means for identifying the choices that are most effective for
performing a specific task” (p. 23). This top-down view of (artificial) creativity
is almost the opposite of the psychological theory proposed in Chapter 4 of this
volume.
52. Hayes and Simon (1974) and Simon and Hayes (1976) did empirical work on the
comprehension of problem instructions, but their conclusions fell far short of a
theory of the origin of problem spaces. Buchanan’s (2001) concept of meta-level
search is one vision of such a theory.
53. For a history of Gestalt psychology, see Ash (1995); for many of the original
papers, see Ellis (1967); and for a reconstruction of their theory of problem solv-
ing, see Ohlsson (1984a).
54. The Gestalt laws are summarized in Goldstein (2008, pp. 72–80). The original
texts are Koffka (1922) and Wertheimer (1923).
55. The Necker Cube was first published by the Swiss crystallographer Louis Albert
Necker in 1832 in the London and Edinburgh Philosophical Magazine and Journal
of Science (Necker, 1832) and again the following year in Annalen der Physik.
While studying line drawings of crystals Necker discovered the tendency of such
drawings to flip between two alternative three-dimensional (3D) percepts. How
the Necker Cube passed from these science journals into Gestalt psychology I
do not know, but it is mentioned in an article on the physiology of vision by
Wheatstone (1838, pp. 381–382). The closely related figure-ground distinction and
the use of reversible figures to illustrate it are due to the Danish psychologist
Edgar Rubin, whose Danish-language book Synopslevede Figurer (Copenhagen,
Denmark: Gyldendalske, 1915) appears not to have been translated into English.
Reversible figures were discussed by the Gestalt psychologists and passed into
common knowledge, but knowledge of the original sources was lost along the
way. The reversions of the Necker Cube and its relatives continue to serve as
symbols or metaphors for representational change in general. For example, Kuhn
(1970) drew an analogy between reversible figures and paradigm shifts in sci-
ence (pp. 111–114). The features of the Necker Cube that continue to fascinate
are that a 3D perception of the line drawing is clearly a cognitive construction,
and that a shift between the two possible 3D constructions is just as clearly non-
monotonic: It is impossible to see the two 3D interpretations of the drawing at
the same time. The Necker Cube continues to interest researchers in visual per-
ception as well, now absorbed into a wider research program on “multistability”
and “binocular rivalry” (Pearson & Clifford, 2004).
56. Wertheimer (1959/1968, pp. 170–171).
57. Köhler (1972, p. 134).