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paradigmatic linguistic system for studying the difference between look-up ta-
bles for exceptions and rules for common verbs (64). Joanisse and Seidenberg
(24) constructed a simple neural network model in which output units represent
a sequence of phonological features—ordered lists of vowels (V) and conso-
nants (C). Thus, each word can be aligned with a basic template: CCVVCCC-
VC. Tasted might read "C0V0CC0VC," in which "0" denotes wildcards or
empty slots not filled by a given verb.
Each verb is represented by a unique hidden unit in the network. In addi-
tion, the network contains semantic units to render verb meanings. Input units
encode basic phonology as with the output units. Thus, inputs connect to hidden
units that connect to output units. Semantic units also connect to hidden units
recurrently. One of the tasks of the network is to take a phonological input and a
tense marker and generate an identical output (autoassociative mapping), while
another required a semantic input to be mapped onto an appropriate phonologi-
cal unit.
Perturbations to the network involved severing a proportion of connections
or by adding Gaussian noise to semantic units or phonological units. "Lesions"
to 5% or less of the connections had almost no effect on performance (as meas-
ured by proportion of correct outputs given a target vector—the Hamming met-
ric). Perturbations of over 5% and higher led to a roughly linear reduction in
system performance. Perturbations to the phonological units tended to produce
"irregularization" errors, whereas damage to the semantic units tended to pro-
duce regularization of irregular verbs.
Thus, this network was able to preserve its basic function over a small range
of perturbations, above which it degraded gracefully. This linear reduction in
system performance is a result of the distributed nature of the computation.
Moreover, the way in which the model lost robustness reflected, in some way,
the pattern of language deficit observed in Alzheimer's or Parkinsonian patients.
4.7. The Extended Phenotype of Human Culture
The derivation of human culture from genetic processes remains a contro-
versial and often poorly posed enterprise. However, it is possible to ask whether
there are universal tendencies among human populations to institutionalize rules
that minimize the impact of perturbations. In other words, are there rules, norms,
and procedures that serve to make human populations more robust? The mathe-
matical study of the stability of human culture to social perturbations is in the
domain of game theory.
One area in which the human species has been stated to be unique is in the
possession of arbitrary symbols combined with a combinatorial grammar. An
essential early step in the evolution of language has been the evolution of pho-
nological rules, in which phonemes are combined into words. Why should this
transition take place? Why use compositional signals rather than expanding the
number of phonemes? Nowak and Krakauer (27) as well as Nowak, Krakauer,
