MODELLING PROCESSES IN A FRACTAL
NETWORK:
A POSSIBLE SUBSTRUCTURE FOR CONSCIOUSNESS.
Richard Dryden
16 January 1996
Abstract: It is proposed
that consciousness does not emerge from a single level of biological
organization (for example: from computational activity at the
synaptic level in networks of neurons), but is a consequence of
interdependent modelling activities by networks at different levels
of organization including the molecular, organelle, and cellular
levels, in some way entrained to produce consciousness. Fractal
stacking and intercommunication of networks at different levels is
proposed as a substrate that may be required for consciousness,
either natural or machine-based. Adoption of this conceptual
starting point may overcome some of the difficulties encountered
when reductionist strategies are applied to the study of
consciousness.
Introduction
Contemporary discussions of consciousness tend to draw
upon the most deeply held features of our individual world-views, be it
quantum theory, information theory, chaos theory, parapsychology, or
spiritualism, in the hope that some combination of these will provide
enlightenment. There is clearly a problem of self-reference here in that
consciousness is both the tool and the object (Miller, 1962): consciousness is trying to understand itself, and has
no reserve of modelling capacity to aid simplification or to step back
and view itself from a more sophisticated metasystem. If we try to model
consciousness by making simplifying assumptions or using reductive
methodologies, it is in danger of slipping away in the process -
consciousness seems to be a product of ‘wholeness’ rather than 'partness'.
However, that is not to say that any attempt to understand consciousness
is without merit or that progress cannot be made - there are sufficient
regularities in the observable universe to allow us to extrapolate from
things we can know more readily to those which are less accessible, such
as consciousness.
In the proposal that follows, I shall combine ideas
from general systems theory and neural network theory to prepare a
conceptual framework from which to view consciousness. Essentially, I
shall suggest that consciousness does not emerge from activities at a
single level of biological organization (for example: from computational
activity at the level of synaptic interconnection in networks of
neurons), but is a consequence of interdependent modelling activities by
networks at different levels of organization, in some way intermittently
entrained to produce consciousness.
General systems theory
I have found the ideas incorporated into general
systems theory (GST) very helpful in developing an understanding of the
biological realm. GST identifies recurring patterns of organization in
systems of different types. There are several variants of this theory,
but I shall take the concepts developed by Bertalanffy (1968) as a
starting point. Central to GST is the concept of partially-bounded open
systems interacting with their environments by way of inputs and
outputs.

Figure 1
A
selected part of the environment 'flows through' an open system over
time, being changed by it - 'transformed' - in the process. Although
some system boundaries have an observable reality, for example: the
outer membrane of a cell, we must also appreciate the role of an
observer in 'drawing' boundaries: this separation of our world into
systems is still a reductionist approach.
Open systems are made of interdependent parts, each of
which can be thought of as an open system in its own right. Open systems
at a given level of organization can interact with each other to produce
systems that 'emerge' at the next higher level of organization: for
example, atoms and molecules interact to form cells, cells interact to
form multicellular organisms, and the organisms of some species interact
to form societies. Within a given level of organization, there can be
recognizable patterns of interaction such as hierarchy.
For me, the strength of GST lies in the recognition of
patterns that recur in systems at different levels, and I find it
provides a framework for incorporating reductionist scientific
observations into a more holistic worldview. For this reason, I feel
that GST can contribute to the debate about consciousness.
From my studies of embryos and other biological
systems, I would add another feature to this generalized conception of
an open system: a capacity for the system to 'model' its environment in
some way. That is, over a period of time the system develops a changing
representation of its environment through its two-way interactions and
as a consequence of its internal organization and functions.
I have chosen the word 'model' for this discussion in
the belief that it has a more neutral feel to it than the more
commonly-used alternatives such as 'consciousness' and 'awareness' (see
Velmans, 1995, for a discussion of the difficulties in using these
latter terms). No attempt will be made to pin down the exact meaning of
'model' at this stage; rather, it will be used to stand for
representational activities in general, sentient or otherwise.
Therefore, at the human level, 'model' would include both conscious and
subconscious activities. For the sake of simplicity, I have placed the
'model' (‘m’)within the boundary of the open system illustrated in
Figure 1 - this is not necessarily to imply a physical presence
within the system, simply a close interrelationship between modelling
activities and the other systemic structures and processes at that level
of organization.
Although at the human level conscious experience gives
us direct access to modelling processes, the suggestion that we should
extend the idea of modelling capacities to systems at other levels may
appear particularly speculative. However, evidence in support of this
view is beginning to accumulate, and recently there have been several
publications proposing that cells, organelles, and even molecules have
the capacity for computational and representational processes as a
consequence of their organization (eg: Albrecht-Buehler, 1985; Hameroff,
1994; Bray, 1995).
This suggestion that open systems in general,
regardless of level, might possess a faculty for modelling echoes
panpsychism - the idea that all matter contains some quality that may be
called 'mind' or 'consciousness'. Panpsychism has often been classified
along with vitalism as being both unscientific and unnecessary (see for
example Popper and Eccles, 1990), although panexperientialism and
panpsychism have recently reappeared as discussion topics (de Quincey,
1994; Seager, 1995). However, it will be suggested below that modelling
can be achieved by processes familiar to contemporary science,
specifically those occurring in natural and artificial neural networks,
and do not require that we formulate additional properties of matter.
This is not to say that the experiential aspect of consciousness
will necessarily emerge from the modelling processes being proposed here
- rather that we need a suitable conceptual framework from which to
begin to tackle the ‘hard question' of consciousness delineated by
Chalmers (1995).
An internal model would impart a degree of autonomy to
a system over its environment, or at least that would be the impression
given to an observer, since stimulus-response loops will be buffered and
modified by the computational activities of the model. The result will
be that the system's responses show variation over time: the response
elicited by a particular input pattern may not be the same when the same
input is tried again after the system has gained other experiences in
the interim. De Quincey (1994) summarises it like this: "A
'compound individual' is a hierarchical society of suborganisms each of
which has its own level of experience and capacity for
self-determination (for instance, an animal compounded of living cells,
or a cell composed of organic molecules)" (page 223).
If this is the case, it allows the possibility for
more subtle behaviour of individual systems as they interact with their
environments and each other. In the case of a developing embryo, we can
envisage the growing community of cells forming a network of social
interactions (Dryden, 1991), each cell continuously harmonizing its
intrinsic drives and gene selection with the environmental cues
impinging upon it. At the same time, the embryo as a whole seems
to have an identity or model, since perturbations to the normal flow of
development can be coped with and responded to, even though particular
cells are lost or damaged. Thus, when open systems interact socially, it
seems that a new potential for creativity is produced.
Limitation of GST
There is, however, a shortcoming in this way of
looking at the world and the systems within it. The stratification of
the observed world by GST into levels of organization seems innocuous
enough in the sense that it recognizes the apparent ‘wholeness' of a
molecule, cell, or person, and identifies repeating patterns at each
level, but the problem then arises of understanding how events at one
level impinge upon events at another - for example, do events at a
higher level determine what happens at lower levels (‘top-down'
causation), or do events at lower levels dictate what happens at higher
levels ('bottom-up' causation)? Or can both occur? Interestingly,
scientific disciplines seem to be stratified in a similar way, each
focusing on a particular level of organization, and a similar problem
arises: a discipline that works well within one level (eg: cytology) may
not have an obvious explanatory value for a discipline at the next level
'up' (eg: psychology). It is as if we have a good ‘within level'
science but have need of a better 'between level' science (interscience?)
to link the levels. Given that we consider the universe to be an
interconnected whole, and science to be a consistent methodology for
learning about it, this is quite surprising, and gives us cause to
re-examine the way we observe the world and make subdivisions. Part of
our current difficulty in understanding consciousness may result from
inappropriate separations being made.
The problem of linkage also applies to the proposal
that models may exist in systems at different levels: how would those
models interact?

Figure 2
For example,
how would models within cells possibly interact with or in some other
way contribute to consciousness at the human level? In the context of panpsychism, Seager (1995) calls this the 'combination problem':
"how the myriad elements of 'atomic consciousness' can be combined
into a new, complex and rich consciousness such as we possess"
(page 280). Reductionism is an approach which requires dismantling a
system and studying its parts, or studying the behaviour of a system in
an artificially simplified and controlled environment. However,
consciousness appears to be a property emerging from an intact system,
from ‘wholeness' rather than 'partness', and may not be reducible in a
conventional sense without risking losing the very insight being sought.
Neural networks
Although GST stumbles at this point, it is possible to
make progress with the idea of interacting models at different levels by
bringing in and modifying the concept of neural networks.
The term 'neural network' is rather loosely used and
may refer either to a network of biological neurons forming part of a
nervous system (natural neural network) or a computer simulation
of a network composed of interconnected units with neuron-like
properties (artificial neural network). In both cases, each node
in the network has one or several inputs of variable 'strength' (usually
both excitatory and inhibitory) and summates the inputs, giving rise to
an output or outputs when a stimulus threshold is crossed. (For a review
of neural networks and a discussion of some of their limitations, see
Crick, 1989.)
Artificial neural networks are often simulated with
three layers of units: an input layer, an intermediate 'hidden' layer,
and an output layer.

Figure 3
The connections between units are changed during periods of
'training' or 'learning': connections that contribute towards correct
behaviour become strengthened, while connections that contribute to
aberrant behaviour are given less weight, with the result that a
distributed 'memory' of the task is established across the network in
the pattern of different-strength connections. A trained network
contains information about associations, categories, and algorithms in
its pattern of connection strengths and operational rules, and in the
sense used above, therefore embodies a 'model' of its task.
The neural network concept provides an explanation for
modelling capacities in networks of interconnected units, and is playing
a significant role in developing our understanding of biological
systems. As noted above, the concept can be applied not only to studies
of neuronal assemblies, but also to individual cells and parts of cells
such as organelles and macromolecules (Albrecht-Buehler, 1985; Hameroff,
1994; Bray, 1995).
Combining GST and the neural network
concept
The 'units' which form the nodes of a given network
share most if not all of the properties already delineated for open
systems: inputs, some kind of inner transformation or function, outputs,
and interactions with other units. Therefore, we can redraw a neural
network with open systems as the units.

Figure 4
But by building on our experience with GST, we can
take the analysis further. If we are considering a natural neural
network, the units are the neurons. Each neuron is a complex and living
assemblage of interacting parts, and those parts can also be viewed as
open systems. So we could model the neuron itself as a network with, for
example, its organelles forming the units. Similarly, we could model
organelles such as the mitochondria as networks, with their constituent
molecules forming the units. This process of identifying network
characteristics could probably be extended further to include molecules
such as proteins which are known to respond to environmental cues. We
begin to see an interconnected pattern of networks within networks.

Figure 5
Looked at in this way, biological organization appears
as nested sets of networks, with the units in a network at one level
being networks in their own right at the next level down, and the units
at that lower level are also formed from networks, and so on. A suitable
term for this arrangement would be fractal network, since it
captures the quality of self-similarity or recurring patterns at
different levels (ie: nets-within-nets). The term 'fractal' is being
used here in a slightly different way from Merrill and Port (1991) and
Globus (1992), who describe fractal network patterns while considering a
single level of organization rather than linking different levels,
although clearly these two uses of the term 'fractal' are complementary.
Hameroff (1994) also hinted at the pattern of organization outlined
above: "the cytoskeleton within each of the brain's neurons could
be viewed as a 'fractal-like' subdimension in a hierarchy of adaptive
networks" (page 114).
Discussion
Consciousness is widely believed to be the result of
physiological processes in the brain: the 'stream of consciousness'
perhaps being a product of changing patterns of nerve impulses flowing
through an incredibly complex network of neurons communicating by way of
synapses. By this view, consciousness 'emerges' from computational brain
activities at the neuronal-synaptic level. However, not everyone is
convinced that this approach will ever provide a sufficient explanation
of consciousness, particularly its experiential aspects. As Hameroff
(1994) points out: "the mechanism of consciousness may depend on an
understanding of the organization of adaptive ('cognitive') functions within
living cells" (page 97). Others propose the need for
intervention by non-computational processes (Globus, 1992; Penrose,
1994), or even the introduction of novel properties of matter or
information at a fundamental level of scientific description (Chalmers,
1995; Seager, 1995).
If we are to take into account the levels of
organization that underpin the synaptic level of brain activity, we need
some effective way of linking activities at the different levels. In the
hypothesis outlined above, the behaviour of an open system at any given
level of organization is considered to be the result of social
interactions between partly autonomous components which are each capable
of modelling aspects of their environments. Modelling is considered to
be a fundamental property of open systems, allowing them to interact in
subtle and creative ways. It is suggested that the modelling and social
activities at each level are integrated to produce the emergent
properties recognized at higher levels, including consciousness.
Interaction, together with the presence of individual
capacities for modelling, can be a source of new complexity in open
systems. Structures, specializations, processes, and institutions emerge
in a way that presumably would not be possible without interaction
between individual members with social potentials. Communities of cells
build organisms; communities of ants build complex anthills. In the
human social context we are familiar with systems of government,
justice, education, health care and so on which arise as emergent
properties of individual social interactions. If we form a conceptual
link between these creative activities of social systems and the
adaptive behaviour of neural networks, then we begin to have a better
understanding of emergent properties, including consciousness.
To bridge between levels, I have suggested that it is
helpful to integrate the open system concepts of GST with the concept of
neural networks, giving rise to a fractal arrangement of adaptive nets.
This approach has two advantages:
The fractal network concept provides the potential for
more 'depth' when discussing consciousness in the sense that it links
activities at more than one level of organization. However, by simply
adding more layers of networks we are not necessarily going to feel much
closer to answering the 'hard problem' of consciousness (Chalmers, 1995:
what is the source of the experiential aspect of consciousness?), since
doubts have been expressed about the ability of monolevel networks to
exhibit understanding of their computational activities (eg: Searle,
1990), let alone have subjective experiences.
Nonetheless, the interconnected nature of the
hypothesized fractal network may help us to understand how proposed
lower-level influences might interact with consciousness. For example,
there is considerable discussion about the possible involvement of
quantum coherence in consciousness. Penrose (1994) suggests that
"coherence could be part of what is needed for
consciousness" (page 408), and with Hameroff (1994) believes that
cytoplasmic microtubules might provide a suitable location for a
'dithering' between quantum and classical realms. Seager (1995) agrees
with Penrose that "only coherent multiparticle systems will
preserve the peculiar quantum mechanical properties that underlie the
appropriate 'summation rules"', and continues "only systems
that can maintain quantum coherence will permit 'psychic combination' so
that complex states of consciousness will be associated only with such
systems" (Page 285).
The fractal network concept appears to accommodate the
possibility of between-level coupling, but at this stage it is not clear
how this might be achieved or maintained. The concept has the advantage
that all parts of the network remain interconnected and therefore
represent a single entity, so although at the synaptic level of brain
function there may be shifting patterns of activity, there could still
be continuity and intercommunication in a more global sense at
sublevels, perhaps allowing extensive coherence.
There is reason then to believe that conscious
experience requires some form of 'entrainment' or resonant coupling of
activities at different levels. Since conscious alertness cannot be
sustained continuously for long periods; and is punctuated by periods of
reduced alertness including sleep, this may be an indication of a
periodic need to uncouple activities at different levels, perhaps to
allow restorative processes to be carried out. In the absence of
coherence, it could be envisaged that computational processes would
still be possible within a given level, but perhaps without the full
experiential accompaniment.
Although speculative, the fractal network hypothesis
is open to testing by currently-available methods. Fractal networks are
amenable to computer simulation (Merrill and Port, 1991), giving an
insight into their computational properties. The effects of blocking
communication between networks at different levels of organization could
then be studied - this may illuminate the suggestion that anaesthesia
operates by blocking normal microtubular action and thus uncoupling
quantum coherence effects (Hameroff, 1994). It would also be interesting
to test the suggestion that modelling at the molecular and organelle
levels influences the modelling capabilities of individual cells:
extrapolation from these lower and less complex levels might help us to
better understand the emergence of human consciousness.
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