An aspect of cognition that is receiving a growing level of attention
from many researchers concerns the properties of the mind as a
dynamical complex system, placed at the border between complete order
and complete disorder. From the seminal work of Zipf (1949), it is
known
that linguistic units exhibit power-law frequency distributions. More
recently it has been shown that, within a text,
linguistic units also exhibit long range, fractal style, correlations
(see,
e.g.,
Ebeling & Pöschel, 1994).
In recent work, I have explored in much detail the
multi-fractal
properties of written texts, and their implications for cognitive
processing (
Moscoso del Prado,
submitted).
Among other things, one finds that the frequency and informational
spectra of text follow multiple fractal regimes, which correspond
directly to traditional linguistic levels of description: lexicon,
syntax, pragmatics,
etc.
Furthermore, the analyses of corpora make it clear that the traditional
stationarity assumption is a dangereous one to make when dealing with
human language; the statistical properties of language change along
discourse. Importantly, this non-stationarity follows a regular
multi-fractal pattern. In recent research (
Moscoso del Prado and Dunn, in prep.), we have modelled the process of
diversification and extinction of human languages
along history. We find that the dynamical fractal patterns present in
linguistic utterances, also arise in the statistics of the historical
evolution of languages.
Interestingly, similar fractal properties have been found in the
dynamics of human behavioral sequences (Gilden, Thornton, &
Mallon, 1995). In recent research I have shown that
reaction times also exhibit power-law properties, in a very similar
way to language
(Moscoso
del Prado, 2009).
This power-law property of reaction times is universal: Independently
of the task
subjects perform, the power-law tail is identical. This provides a
direct link to the measures of cognitive cost mentioned above,
cognitive processing is reflected in the transient deviation from the
power-law distribution, which represents a sort of baseline or "resting
state" of the system in its natural state. In terms of
cognitive models, the power-law is directly predicted by an extremely
simple, yet very powerful model of human reaction times
(Moscoso del
Prado, submitted). In recent research I have shown how this theory
outperforms
most current theories of reaction time distribution.
The fractal properties of human behavior are not necesarily a
generalized property. In a recent methodological paper, I have shown
how information-theory can be of use in locating the sources of fractal
scaling in concurrent sequences of behavioral responses
(Moscoso del Prado, 2011).
In addition, the information theoretical model of behavior can itself
predict whether responses will or will not follow a fractal pattern:
Fractal properties arise when the system is placed close to a
phase-transition between different cognitive mechanisms
(Moscoso del Prado, submitted).
Finally, I have also developed a statistical method (and the
corresponding R library implementing it) to test detailed hypotheses on
the fractal scaling properties of time series (which is used in the
studies above). The method, the
Bayesian
Assessment of Scaling, is based on an analytical Bayesian
formulation, and does not require Monte Carlo simulations (
Moscoso del Prado, 2011).