Page 445 - Deep Learning

428 Notes to Pages 175–184

involve multiple learners. Obviously, both types of effects have to asymptote at
some point, but the appearance of intermediate plateaus is more likely in tempo-
rally extended and complex cases.
12. The student was faced with a 5 by 5 matrix, with the letters of the alphabet ran-
domly distributed over the 25 cells. The task was to focus on 12 of the cells in a
specified order, notice the letter in each cell and write them down in the specified
order. The subset of 12 cells and the order in which they were to be visited were
the same from trial to trial, but the distribution of the letters varied.
13. See Notes 40–43, Chapter 7, for background references for the concept of
transfer.
14. Bloom (1984), Chi et al. (2001) and Cohen, Kulik and Kulik (1982).
15. See Warren (2006) and Willingham (1998) for theories of motor coordination
and motor skill learning.
16. Catrambone (1995, 1998).
17. Corrigan-Halpern (2006) and Corrigan-Halpern and Ohlsson (2002).
18. Empirical evidence for goal hierarchies has been provided by Altmann and
Trafton (2002), Anderson (1993, pp. 129–132), Catrambone (1995, 1998),
Corrigan-Halpern and Ohlsson (2002, Figure 2), Egan and Greeno (1974, Figures
4.20–4.22), Greeno (1974) and others. The fundamental reasons that complex
systems tend toward hierarchical organization have been laid out by Boulding
(1961, Chap. 2), Koestler (1972), Simon (1962) and von Bertalanffy (1968/1973,
pp. 25ff).
19. See Anderson (1976, pp. 116–119) and Winograd (1975) for early statements of the
declarative-procedural distinction, and Ohlsson (1994) for a summary.
20. The cognitive sciences have long pondered how the relation between the declara-
tive, descriptive aspect of knowledge and the action-oriented, prescriptive aspect
should be conceptualized; see Ohlsson (1994) for definitions and Ohlsson (2007b)
for a historical analysis of the relationship.
21. The term “production rule” stems from the fact that one can view such rules
as producing the symbol or symbol structures on their right-hand sides. This
notation for describing symbolic computations was invented by the American
mathematician E. Post (1943) for the purpose of proving theorems in automata
theory. It was imported into cognitive science via Noam Chomsky’s (1957/1972)
generative grammars. Newell (1966, 1972, 1973) and Newell and Simon (1972a)
extended it by implementing the first computer program that could execute a set
of production rules and thereby automatically derive the behavior of a set of rules
in a given situation or context. For the subsequent development of production
system models, see Neches, Langley and Klahr (1987) and for recent develop-
ments, see Anderson (2005) and Nason and Laird (2005). The production rule
format is as close as cognitive science has come to a lingua franca for describing
cognitive processes.
22. Newell (1972, 1973) and Newell and Simon (1972a).
23. Researchers working with the production rule formalism have published a vari-
ety of rule sets for tasks ranging from spatial reasoning to geometry; see, e.g.,
Anderson (1983, 1993), Newell and Simon (1972a), Ohlsson (1990a) and various
chapters in Klahr, Langley and Neches (1987). Very simple strategies might be