This encompasses a fully interpenetrating biopsychosocio-
cultural structure for individual consciousness, one in which
Baars’ contexts act as important, but flexible, boundary con-
ditions, defining the underlying topology available to the far
more rapidly shifting global workspace (Wallace, 2005a, b).
This result does not commit the mereological fallacy which
Bennett and Hacker (2003) impute to excessively neurocentric
perspectives on consciousness in humans, that is, the mistake
of imputing to a part of a system the characteristics which
require functional entirety. The underlying concept of this
fallacy should extend to machines interacting with their en-
vironments, and its baleful influence probably accounts for a
significant part of the failure of Artificial Intelligence to de-
liver. See Wallace (2006) for further discussion.
6. Punctuation phenomena
As a number of researchers have noted, in one way or an-
other, - see Wallace, (2005a) or Wallace et al., (2007) for
discussion - equation (1),
H ≡ lim ''' (n>],
n→∞ n
is homologous to the thermodynamic limit in the definition
of the free energy density of a physical system. This has the
form
F (K >= lim K ,
V→∞ V
(5)
where F is the free energy density, K the inverse tempera-
ture, V the system volume, and Z(K) is the partition function
defined by the system Hamiltonian.
Wallace (2005a) shows at some length how this homology
permits the natural transfer of renormalization methods from
statistical mechanics to information theory. In the spirit of
the Large Deviations Program of applied probability theory,
this produces phase transitions and analogs to evolutionary
punctuation in systems characterized by piecewise, adiabati-
cally stationary, ergodic information sources. These biologi-
cal phase changes appear to be ubiquitous in natural systems
and can be expected to dominate machine behaviors as well,
particularly those which seek to emulate biological paradigms.
Wallace (2002) uses these arguments to explore the differences
and similarities between evolutionary punctuation in genetic
and learning plateaus in neural systems.
7. Multiple Workspaces
The random network development above is predicated on
there being a variable average number of fixed-strength link-
ages between components. Clearly, the mutual information
measure of cross-talk is not inherently fixed, but can contin-
uously vary in magnitude. This we address by a parametized
renormalization. In essence the modular network structure
linked by mutual information interactions has a topology de-
pending on the degree of interaction of interest. Suppose we
define an interaction parameter ω , a real positive number,
and look at geometric structures defined in terms of linkages
which are zero if mutual information is less than, and ‘renor-
malized’ to unity if greater than, ω . Any given ω will define
a regime of giant components of network elements linked by
mutual information greater than or equal to it.
The fundamental conceptual trick at this point is to invert
the argument: A given topology for the giant component will,
in turn, define some critical value, ωC , so that network ele-
ments interacting by mutual information less than that value
will be unable to participate, i.e. will be locked out and
not be consciously perceived. We hence are assuming that
the ω is a tunable, syntactically-dependent, detection limit,
and depends critically on the instantaneous topology of the
giant component defining, for the human mind, the global
workspace of consciousness. That topology is, fundamentally,
the basic tunable syntactic filter across the underlying modu-
lar symmetry groupoid, and variation in ω is only one aspect
of a much more general topological shift. More detailed anal-
ysis is given below in terms of a topological rate distortion
manifold.
There is considerable empirical evidence from fMRI brain
imaging experiments to show that individual human con-
sciousness involves a single global workspace, a matter lead-
ing necessarily to the phenomenon of inattentional blindness.
Cognitive submodules within institutions, - individuals, de-
partments, formal and informal workgroups - by contrast, can
do more than one thing, and indeed, are usually required to
multitask. The intent of this work is to suggest the possibil-
ity of constructing machines which work on similar principles,
but much more rapidly.
Clearly multiple workspaces would lessen the probability of
inattentional blindness, but, we will find, do not eliminate it,
and introduce other failure modes examined in more detail
later.
We must postulate a set of crosstalk information measures
between cognitive submodules, each associated with its own
tunable giant component having its own special topology.
Suppose the set of giant components at some ‘time’ k
is characterized by a set of parameters Ωk ≡ ωk, ...,ωkl.
Fixed parameter values define a particular giant component
set having a particular set of topological structures. Sup-
pose that, over a sequence of ‘times’ the set of giant com-
ponents can be characterized by a (possibly coarse-grained)
path xn = Ω0, Ωι,..., Ωn-1 having significant serial correla-
tions which, in fact, permit definition of an adiabatically,
piecewise stationary, ergodic (APSE) information source in
the sense of Wallace (2005a). Call that information source X.
Suppose, again in the manner of Wallace (2005a), that a
set of (external or internal) signals impinging on the set of
giant components, is also highly structured and forms another
APSE information source Y which interacts not only with the
system of interest globally, but specifically with the tuning
parameters of the set of giant components characterized by
X. Y is necessarily associated with a set of paths yn .