explained using specific shapes of the basins of attractors of
neural dynamics, but it is much easier to understand it repre-
senting these attractors and the decision boundaries between
them in the P-space. Thus the same event may be seen from
psychological and from the neurodynamical point of view.
Learning of the base rates changes synaptic connections in
the neural models, creating larger and deeper basins of at-
tractors - in the P-space objects (high probability values)
corresponding to these attractors are large. Inverse base rate
effects result from deeper, localized attractors around rare
categories, or smaller, localized objects in P-spaces.
Processes acting on representations in feature spaces de-
fine certain physics of mental events, with forces reflecting
the underlying neural dynamics. The state of the system,
called “the mind state” [7], is a point moving in the P-space.
Base rate effects influence the size of the basins of attrac-
tors, represented by the size of objects in the P-space. They
also influence transition probabilities: specifying value of
a feature that frequently appears in combination with other
features gives momentum to the mind state in the direction
parallel to the axis of this feature, initiating a search for a
category completing the missing features (for application of
the searches in feature spaces see [17]).
IV. Summary and related work.
The need for psychological space treated as an arena for
psychological events is evident in recent psychological lit-
erature. The static picture of P-spaces with probability den-
sity functions defined on them is useful not only for cate-
gorization but also object recognition [18]. In psycholin-
guistics problems such as the word sense disambiguation
and learning the semantic contents of new words by children
are solved placing categories (words) in P-spaces. Landauer
and Dumais [19] analyzed a dictionary of 60.000 words and
using the Latent Semantic Analysis model estimated effec-
tive dimension of the P-space that is needed to preserve
similarity relations to be about 300. Linguists use also the
idea of non-classical feature spaces, calling them “mental
spaces” (cf. [20]).
Static version of the Platonic model should be sufficient
for description of a short-term response properties of the
brain, “intuitive” behavior or memory-based responses, but
understanding behavior in the time frame longer than a few
seconds must include dynamical aspects. The dynamic Pla-
tonic model, introduced in [7], goes in the same direction
as Elman’s “language as a dynamical system” idea in psy-
cholinguistics and “mind as motion” ideas in cognitive psy-
chology (cf. [21]). Stream of thoughts forming a sentence
create a trajectory of visited (or “activated”) objects in psy-
chological space. General properties of such trajectories
reflect grammar of the language. Further simplification of
the Platonic model lead to the Bayesian networks and Hid-
den Markov Models in which the dynamics is completely
neglected and only the probability of transitions between
states/objects remains. Reasoning in symbolic models of
mind, such as SOAR, is based on problem spaces, which are
metric spaces rather than vector spaces. It is not yet clear
what are the precise restrictions of modeling psychological
spaces using vector space structure.
A unified paradigm for cognitive science requires elu-
cidation of the structure of psychological spaces, search
for low dimensional representations of behavioral data and
for connections with neural dynamics. Linking neural dy-
namics with psychological models based on feature spaces
leads to a complementary description of brain processes and
mental events. The laws governing these mental events re-
sult from approximations to neural dynamics, similarly as
the laws of classical physics result from approximations to
quantum mechanics. These modified feature space mod-
els are useful in analysis of psychological experiments, ex-
plaining data on judgments of similarity between objects
and abstract concepts, as well as results of experiments on
categorization. Perhaps at the end of this road a physics-like
theory of events in mental spaces is possible?
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