Pair the two sets of paths into a joint path zn ≡ (xn, yn),
and invoke some inverse coupling parameter, K , between the
information sources and their paths. By the arguments of
Wallace (2005a) this leads to phase transition punctuation
of I [K], the mutual information between X and Y, under
either the Joint Asymptotic Equipartition Theorem, or, given
a distortion measure, under the Rate Distortion Theorem.
I[K] is a splitting criterion between high and low proba-
bility pairs of paths, and partakes of the homology with free
energy density described in Wallace (2005a). Attentional fo-
cusing by the institution or machine then itself becomes a
punctuated event in response to increasing linkage between
the structure of intereest and an external signal, or some
particular system of internal events. This iterated argument
parallels the extension of the General Linear Model into the
Hierarchical Linear Model of regression theory.
Call this the Multitasking Hierarchical Cognitive Model
(MHCM). For individual consciousness, there is only one gi-
ant component. For an institution, there will be a larger, and
often very large, set of them. For a useful machine, the giant
components must operate much more rapidly than is possible
for an institution.
This requirement leads to the possibility of new failure
modes related to impaired communication between Giant
Components.
That is, a complication specific to high order institutional
cognition or machine distributed cognition lies in the neces-
sity of information transfer between giant components. The
form and function of such interactions will, of course, be de-
termined by the nature of the particular institution or ma-
chine, but, synchronous or asynchronous, contact between gi-
ant components is circumscribed by the Rate Distortion Theo-
rem. That theorem, reviewed in the Mathematical Appendix,
states that, for a given maximum acceptable critical average
signal distortion, there is a limiting maximum information
transmission rate, such that messages sent at less than that
limit are guaranteed to have average distortion less than the
critical maximum. Too rapid transmission between parallel
global workspaces - information overload - violates that con-
dition, and guarantees large signal distortion. This is a likely
failure mode which appears unique to multiple workspace sys-
tems which, we will argue, may otherwise have a lessened
probability of inattentional blindness.
8. The dynamical groupoid
A fundamental homology between the information source
uncertainty dual to a cognitive process and the free energy
density of a physical system arises, in part, from the formal
similarity between their definitions in the asymptotic limit.
Information source uncertainty can be defined as in equation
(1). This is quite analogous to the free energy density of a
physical system, equation (5).
Feynman (1996) provides a series of physical examples,
based on Bennett’s work, where this homology is, in fact,
an identity, at least for very simple systems. Bennett argues,
in terms of idealized irreducibly elementary computing ma-
chines, that the information contained in a message can be
viewed as the work saved by not needing to recompute what
has been transmitted.
Feynman explores in some detail Bennett’s ideal micro-
scopic machine designed to extract useful work from a trans-
mitted message. The essential argument is that computing,
in any form, takes work. Thus the more complicated a cogni-
tive process, measured by its information source uncertainty,
the greater its energy consumption, and our ability to provide
energy to the brain is limited: Typically a unit of brain tissue
consumes an order of magnitude more energy than a unit of
any other tissue. Inattentional blindness, Wallace (2007) ar-
gues, emerges as a thermodynamic limit on processing capac-
ity in a topologically-fixed global workspace, i.e. one which
has been strongly configured about a particular task. Insti-
tutional and machine generalizations seem obvious.
Understanding the time dynamics of cognitive systems
away from phase transition critical points requires a phe-
nomenology similar to the Onsager relations of nonequilib-
rium thermodynamics. If the dual source uncertainty of a
cognitive process is parametized by some vector of quanti-
ties K ≡ (K1 , ..., Km), then, in analogy with nonequilibrium
thermodynamics, gradients in the Kj of the disorder, defined
as
S ≡ H (K) - ∑ Kj ∂H∕∂Kj
j=1
(6)
become of central interest.
Equation (6) is similar to the definition of entropy in terms
of the free energy density of a physical system, as suggested
by the homology between free energy density and information
source uncertainty described above.
Pursuing the homology further, the generalized Onsager
relations defining temporal dynamics become
dKj /dt = ∑Lj,i∂S∕∂Ki
i
(7)
where the Lj,i are, in first order, constants reflecting the
nature of the underlying cognitive phenomena. The L-matrix
is to be viewed empirically, in the same spirit as the slope and
intercept of a regression model, and may have structure far
different than familiar from more simple chemical or physi-
cal processes. The ∂S∕∂K are analogous to thermodynamic
forces in a chemical system, and may be subject to override by
external physiological driving mechanisms (Wallace, 2005c).