Commentary 02 on
Karl Jaspers Forum, Target Article 5, 14 December 1997
FROM SIMPLICITY TO HYPERCOMPLEXITY: THE G, Q, C FACTORS
by Varadaraja V Raman
HIERARCHICAL REALITY AND CONSCIOUSNESS
by Paul Jones
18 December 1997
Abstract
The ideas presented by V.V.Raman are akin to hierarchical logic and
the formula suggested might reflect some important features of
triads. However, the relevance of chaotic dynamics to consciousness
studies seems doubtful, and the distinction of the levels of reality
requires more specification.

V.V.Raman's short article presents a selfcontained model which
may be of value without associating it with any one of the possible
interpretations. This is a formal scheme deserving careful
investigation on itself; its feasibility for consciousness studies
could be considered separately. Still, the both aspects will be
concerned in this commentary.
The fundamental observation that classical and quantum physics
refer to different levels of reality lead Raman to the assumption
of multiple levels of reality, comprising both classical and quantum
behavior, as well as the level of chaos. This idea is sound enough,
even if some Raman's assertions may seem disputable. Thus, the
distinction of classical and quantum mechanics can hardly be
reduced to predictability and stochasticity. Both classical and
quantum mechanics are strictly causal, and it is the kind of
prediction only that differs: while classical mechanics traces
the changes in the position and momentum of a body, quantum mechanics
quite precisely treats the evolution of the quantum state vector,
or the density matrix in an alternative approach. On either level,
the basic quantities of the formalism are calculable for all times,
thus being completely predictable. The difference is in the additional
procedure of constructing the observables required in quantum mechanics
and absent in classical mechanics. However, the necessity of such
an averaging procedure cannot make quantum mechanics any more
probabilistic than classical mechanics, since, for instance, cross
sections get commonly extracted from intensity measurements,
which is principally the same as measuring mass, or position,
with the same statistical processing of the results. Probabilistic
interpretations are external to quantum mechanics, and classical
thermodynamics can be quite consistently developed without any
reference to quantum states, as many wellknown scientists of the
past used to believe.
The important characterization of the levels of reality suggested
by V.V.Raman is that every level of reality should be governed by
its specific laws. Inversely, any qualitative differences
in the observable behavior indicate the presence of different levels
of hierarchy, and it is the illegal mixture of different levels
that leads to apparent contradictions and paradoxality.
However, Raman's suggestion needs one important clarification:
the levels of reality are governed by different laws, but they
are the levels of the same reality. The same object can be
treated differently, according to the chosen level of consideration,
and all the objects combine quite different features requiring
much diversity in description. Thus, one can study the quantum
properties of macroscopic media, as well as the classical motion of
microscopic particles; the statistical description of a gas may
be well complemented by the purely thermodynamic treatment of weak
nonstationarity and nonlocality, etc. That is, all the levels of
reality are intrinsic to any object, but their hierarchical
ordering, with the dominance of certain kinds of behavior and
relative negligibility of other aspects, may only refer to the
object's interaction with the subject. In other words, what the
object is for us is determined by what we do with it. Evidently,
the roots of this impregnation of the object by subjectivity
lie in the nature of any interaction, which modifies the behavior
of the interacting systems so that they are not exactly like
the isolated systems of that kind. Commonly, the realization of
this fundamental circumstance is attributed to quantum physics – but
the simplest example of two balls with and without a spring
connecting them shows that the situation is quite the same in
classical physics too, with only the type of constraint changing.
Chaos has become an article of fashion in the end of the XX century.
The properties of chaotic behavior seem so fascinating to many
scientists (and especially to philosophers) that they are tempted to
attribute all the complexity observed at different levels of reality
to chaos – just like the uncommonness of the quantum picture of the
world lead people to attributing everything unusual to quanta
several decades ago. However, the very universality of chaos
speaks against its determinative role in distinguishing life or
consciousness from the "coarse matter". As V.V.Raman indicates,
chaotic behavior is equally typical for both biological systems and
manyphase physical media like clouds etc. – consequently, it is
not enough to mention chaos to specify the difference of a rabbit
from a snowflake, or Einstein from a rock intrusion. In Raman's
article, the level of consciousness differs from the level of life
just quantitatively, assuming that there is more chaos in the
"hypercomplex" reality of human reason than in merely "complex"
reality of a biological system. Such an approach raises two
principal objections: first, making chaos the measure of complexity
is somewhat problematic, and second, reason does not seem to be
chaotic – rather, too much chaos could be intuitively attributed to
the lack of reason, consciousness or will.
Chaos may have something to do with complexity, though this relation
is far from having been investigated in any detail. The contraposition of
chaos to classical and quantum physics seems most doubtful, since
both classical and quantum systems can exhibit both chaotic and
regular behavior, so that there is no contrast to stress. Rather,
chaos can be considered as a specific level of description different
from either functional ("deterministic") or statistical ("stochastic")
description, combining the aspects of them both. These are the
levels of reality (in only one of the possible dimensions) that could
be associated with the factors G, Q, C introduced by V.V.Raman.
In this sense, the traditional term "chaos" might be put in line with
such words as "ramification", "polymodality" etc., so that the
sequence "statistics" → "functionality" → "chaoticity" would
form a complete triad of hierarchical logic [1].
The formula GQ + GC + QC = k suggested by V.V.Raman (the constant k
might be set to unity without any loss of generality) could express
the structural aspect of the triad (G, Q, C), so that the weights of
the possible links between the elements of the triad would
be defined by the weights of the respective elements in some
hierarchical structure (arising through the interaction of the
system with the observer), and the constancy of the sum would
reflect the integrity of the system as described by this triad.
Of course, to make the formula quantitative, one would have to
either define G, Q and C as dimensionless values, or make them
have the same dimension sqrt([k]), or introduce a unit conversion
factor somewhere in the formula (since if [Q] = [C] = [k]/[G] then
[QC] = [k]^{2}/[G]^{2}).
Recalling the cyclic unfolding of any triad, one could observe that
Raman's equation might express the development of the system in the
cycle ... → Q → G → C → Q' → ..., with the constant k being a kind of
"grow factor", which may be either universal or characteristic for
a particular system.
It should be noted that Raman's formula is not the only possibility.
A simpler expression GQC = 1 would allow for exactly the same limit
cases, if one takes into account that there are no zeros and infinities
in Nature, and hence one may speak about very large and very small
values only. This triadic formula can also be rewritten as
GQ = 1/C = X, with X being "inverse chaos" – order?
Now we can turn to the questions posed by V.V.Raman in the end of
his article:
(a) "Can C be tracked by physics and chemistry?"
(b) "Is C is intrinsic or extrinsic to the system?"
If C represents a level of reality qualitatively different from G and Q
(with any possible interpretations of the letters), C cannot be reduced
to G and Q, as well as G or Q cannot be reduced to Q and C, or G and C,
respectively. As for intrinsic and extrinsic properties of the system,
there is no rigid boundary between them, and what is intrinsic in one
respect may well become extrinsic in another. This refoldability
of the hierarchy is due to the nature of any development converting
the external interactions of the system to its structural peculiarities.
Finally, I would like to once again question the relation between
chaos and consciousness. Unlike a chaotic system, consciousness tends
to smoothen fluctuations, regularize them. Yes, the goals can be
arbitrary, and the will is free – but once a goal has been set,
a conscious being can move towards it despite of any variations
in the initial conditions or parametric noise. Raman himself
noted that "an important characteristic of the human brain is
its capacity for complex logical reasoning" [2]. Even considering
that we can never draw a perfectly straight line, one should admit that
our "lines" are straight enough in most cases when our reason has
a chance to reveal itself. Raman's note that any chance occurrence
may result in dramatic long range consequences in the course of one's
life is not relevant here, because it is the uncontrolled passive
development that is meant; as soon as the significance of an event
has been realized by a conscious person, its influence on the person's
life becomes far from chaotic.
One should distinguish chaotic behavior from pseudochaotic behavior
observed in dynamic systems. Thus, no finite sequence of trials can
distinguish a chaotic system from a complex ergodic system obeying
the usual Lagrange dynamics. Computer simulations of chaos are in fact
pseudochaotic due to the finite accuracy of calculations. Also,
a divergent Lagrange flow can manifest the same property of amplifying
small variations in the initial conditions that is often considered
as a typically chaotic behavior. So, if human reasoning is observed
to draw very distant conclusions from minor circumstances, it says
nothing about the chaotic, deterministic, or statistical character
of the process.
If we assume that there is no direct relation between consciousness
and chaos, Raman's questions 7a, 7b become irrelevant to the study
of consciousness. There is no need to think that free will is a property
of the brain, or admit any teleology otherwise. Rather, any physical
or biological system may have some relation to consciousness, and
the task of science is to specify the kind of this relation. The other
side of it is that no physical or biological system can represent
subjectivity in full, and hence the human body may be not unique
to house reason and there may be other implementations possibly of
a quite different kind.
References
[1] P.B.Ivanov "Hierarchy of Logic" http://unism.pjwb.org/arc/1997hl/hle.htm
[2] V.V.Raman BRAIN MODES, ILLUSIONS, PERCEPTION. KJF, Commentary 1 to Target article 3.
