This reversal of boundary roles (inclusive Q vs. exclusive
h) arises from a differing perspective on the complementary
pair. In the case of Q, a self-moment is being 'observed'
(or conceptualized) as a whole from the outside. In the
case of h, our observation of the quantum event takes place
from the inside.[2] According to
Bohm, the phenomena of the explicate universe are derived from
an implicate order of reality that underlies and transcends the
explicate order.[3] In this sense, the
implicate order lies 'outside' (or beyond) the explicate one.
Therefore, the apparently micro level of quantum events nevertheless
is a larger (or deeper) level of reality than our phenomenological
perceptions of physical objects-including supercolliders and electron
microscopes. In a context of their own, the complementary pair
of position and momentum can represent both sides (A and
O); however, in a larger context the pair are explicate
expressions (both A) from an implicate reality (O)
related in this context to Q and the area of uncertainty.
Let's now examine the concepts discussed so far with an example.
Consider a person as a conscious being. On some level, the person
is a unified whole -- let's refer to this wholeness as 'Andy'.
Although the identity of Andy may seem obvious for those who know
Andy, the truly singular Andy is difficult to define because Andy
is constantly changing and expressing a myriad of different characters
depending on particular contexts and roles. We might define Andy
as the material expression (i.e. body) of Andy, and there is some
obvious truth behind the assertion -- the two are related in some
manner. However, Andy's body undergoes continuous change as well,
and this definition ignores consciousness as one of Andy's significant
properties. There does live a singular identity behind Andy's
many faces but this identity is implicit. Who is Andy? The subjective
truth is rather difficult (and logically impossible) to express
objectively. Andy lives within the complementary limits presented
by an inexpressible inner reality and diverse expressions of outer
reality (including the dynamic expression of a body and its various
sensory relationships -- visual, tactile, etc.). Each side of
the dialectical coin affects the other.
Andy explodes upon further examination. If Andy's outer expressions
are examined more closely -- whether physiological or psychological
-- each individual part becomes a whole existing in a complementary
relationship with its individual parts ad infinitum. And
if the implicit identity known as Andy could be examined more
closely, quantum resonance theory predicts that we'd find the
same phenomenon moving in the other (more expansive) direction.
Andy is also a part within many levels of deeper collective --
or more inclusive levels of mind. Thus, Andy may be potentially
defined relative to collective human consciousness, collective
primate consciousness, collective animal consciousness, collective
global consciousness, etc.
The preceding analogy is a bit misleading. 'Andy' never really
exploded. 'Andy' is a name that refers to a contextual identity
-- and there is certainly a measure of validity behind the reference.
However, in this case the identity being examined (i.e., Andy)
explodes from the endlessly recursive perspective of the reader.
It's all a matter of perspective -- and this raises some very
significant questions regarding the nature of self-definition
(both in an individual and a collective sense)! For example, self-definition
influences whether one identifies more as a particular individual
rather than as an identity within a given collective. Furthermore,
the theory also implies that as one identifies oneself so one
becomes. Self-definition becomes behavior.
Let's return to Andy (who never really exploded). Speaking psychologically,
Andy behaves according to many differing 'personalities'. For
example, Andy manifests a diverse range of emotional states and
recognizable personalities become associated with each of these.
There are differing roles for Andy according to context -- consider
Andy's relationships with environments (e.g. home or work) or
with types of people (e.g. family members or coworkers). Andy
may develop relationships with increasingly specific environments
(e.g., a room in the home, or a piece of furniture) and specific
people (e.g., a person, or a personality of a person), and this
recursive phenomenon holds on more inclusive levels wherein Andy
may develop relationships with deeper levels of Andy's own implicit
collectives (such as ancestors or gods). Furthermore, each and
every such relationship itself lives as a quantum resonance self-moment.
The behavioral influence of self-definition bears relevance to
the issue of self-regulation. How can a living system so complex
regulate itself? Although the problem seems complicated, the answer
is relatively simple: each collective self-moment regulates its
own relative parts. How is this done? The parts of a collective
live within the complementary limits of cooperation (i.e., identification
with the collective) and conflict (i.e., identification with an
individual), and the health of an entire self-moment depends upon
maintaining a homeorhetic balance between complementary limits
for all involved. This tendency toward homeorhesis manifests in
all areas of life through two common principles: Central Tendency
and the Golden Mean. These two principles correspond with the
complementary perspectives of a self-moment discussed earlier
-- whether defined (or perceived) from the 'outside' as an inclusive
whole (an omega perspective) or from the 'inside' through a diversity
of explicit perceptions (an alpha perspective).
The Central Tendency principle corresponds to the alpha perspective.
In the case where explicit perceptions manifest complementarity,
the complementary expressions are exclusive -- it's one or the
other to some degree depending upon the circumstances. Let's examine
a simple example of this: when the proverbial coin is tossed and
lands on its side, it will land on only one of them. Consequently,
the favored side is explicitly perceived while the other is hidden.
(Incidentally, the 'moment of truth' when the coin lands on one
favored side corresponds to a quantum wave collapse when the quantum
event is simultaneously perceived and decided.) Curiously, as
the coin is tossed repeatedly, it will tend to land on both sides
equally (or with equal 'fairness'). This is the Central Tendency
principle in action--and there is no empirical explanation
for why this should necessarily be the case.
This is a puzzling predicament. Consider this opening scene taken
from a play by Tom Stoppard.[4] We join
the main characters, Rosencrantz and Guildenstern, who have been
betting on coin tosses, and there's a troubling problem: the two
of them can only throw heads. (This is a foreshadowing of the
main characters' inevitable demise -- refer to Shakespeare's play
Hamlet.) Guildenstern becomes increasingly troubled by
the absoluteness of the result: heads.
G: (Flips a coin.) The law of averages, if I have got this
right, means that if six monkeys were thrown up in the air for
long enough they would land on their tails about as often as
they would land on their--
R: Heads. (He picks up the coin.)
G: What about the suspense?
R: (Innocently.) What suspense?
Small pause.
G: It must be the law of diminishing returns...I feel the spell
about to be broken. (Energizing himself somewhat. He takes out
a coin, spins it high, catches it, turns it over onto the back
of his other hand, studies the coin--and tosses it to Rosencrantz.
His energy deflates and he sits.) Well, it was an even chance…if
my calculations are correct.[5]
Guildenstern's rationalization (i.e., and again it was just an
even chance) provides a sharp assessment: if a coin is repeatedly
tossed in independent throws, why can't it land heads all the
time? Or tails? Why are the independent coin tosses even expected
to behave dependently? Regardless of contrary logic, observable
results display this principle in all areas of life.
The abstract principle of Central Tendency manifests as the standard
probability distribution, also known as the Normal (or Bell) Curve.
The standard probability distribution may be expressed mathematically
as "the expansion of a binomial with any complementary pair of
values raised to the power n"[6]
(i.e., the binomial expansion) -- as a formula:
(A + O)^n
The Normal Curve arises from the interaction of exclusive probabilities
(represented above as A and O). The phenomenon seems
straightforward -- the members of the pair tend toward mutual
balance as n increases. Also, the complementary values
of the binomial are additive because "in general, the probability
of alternative outcomes is the sum of the probabilities of the
outcomes taken separately."[7] It is significant
here that the statistical conceptualization behind this operation
presumes the interactions of probabilities rather than objects
-- corresponding well with the interaction of quantum resonance
identities.
According to a quantum resonance interpretation, the Central
Tendency principle provides a living example of homeorhetic balance
(or fairness) between complements. In the interests of healthy
self-regulation, a living collective tends toward a balance of
expression for all its parts. The healthy game, so to speak, behaves
fairly for all concerned. In addition, the Normal Curve reveals
an oft overlooked quality of life: unlike the exclusive dualism
of the simple coin, identities generally express themselves as
spectrums of possibility. Complementary identities live within
an identity as a symbiotic relationship. The pair provides limits
for a probability distribution of expression -- rather than inevitable
choices between one or other.
Central Tendency corresponds to an alpha perspective in which
the complementary expressions are exclusive. The Golden Mean,
on the other hand, corresponds to an omega perspective wherein
the 'expressions' are inclusive (and one of them is an implicit
'expression'). In the case of Andy, the principle of Central Tendency
applies to complementary relationships among Andy's many explicit
parts. If considered as an inclusive identity (i.e. the whole
Andy), the Golden Mean applies to the relationship between the
implicit Andy and Andy's explicit parts--and provides the basis
for Andy's healthy (or homeorhetic) recursion.
Any identity defined in relation to itself is recursive. Andy's
individual parts are each defined in relation to the implicit
Andy who is defined in relation to deeper collectives, etc. It's
analogous to a picture with a mirror showing a picture with a
mirror showing a picture with a mirror, leading the viewer into
infinity. Recursive identities are common in nature and generally
possess the curious characteristic that each level of recursion
embeds itself within the greater one according to the ratio of
the Golden Mean.
Although the term is often used with a meaning like 'a tempered
approach, or the avoidance of extremes', the Golden Mean refers
to a ratio discovered and coined by Pythagoras. Picture a stick
divided into two unequal parts with a line. The Golden Mean ratio
determines the division--let's bypass the mathematical explanations
and simply use approximate values of 2.618 for the stick
with values of 1 and 1.618 for the segments. Let's assign Q
to represent the entire stick (2.618), A to represent the
smaller segment (1), and O the larger segment (1.618).[8]
With these variables, the Golden Mean implies that the ratio of
Q to O equals the ratio of O to A.
This may be expressed as: Q/O = O/A. Each explicit A
is a part of an implicit O in the manner that the implicit
O is itself part of a transcendent collective Q.
As expressed by Nigel Reading, "The Golden Mean then, is an archetypal
fractal in that it preserves its relationship with itself … in
the most mathematically robust, economical but also elegant, way.[9]
In a quantum resonance perspective of living identities, the Golden
Mean is also considered a healthy form of recursion --
just as Central Tendency is considered a healthy (or fair)
manner for the distribution of exclusive probabilities.
The opening paragraph of this paper asked the question, "How
does a single collective identity exist simultaneously as many
diverse (and potentially conflicting) individual identities?"
There are no solutions for logic's difficulties with this vicious
circle -- life defies the limitations of logic.[10]
However, an exploration of the question has been useful nonetheless.
Quantum resonance theory may provide a new perspective on Heisenberg's
Uncertainty Principle; furthermore, a quantum resonance interpretation
suggests a provocative explanation for the principle of Central
Tendency and the Golden Mean as expressions of healthy self-regulation.
This is provocative insofar as it posits living consciousness
as the necessary basis for reality -- and this is indeed a significant
conclusion implied from the discussion. So while more questions
are provided than answers, evidence suggests that life may be
the mechanism behind all of it.
____________________
1 Keener,
Matt (1999), The Quantum Resonance: A Theory of Life, http://www.xmission.com/~mkeener/document.html
(visited June 19, 2000).
2 Perspectives
from the outside or inside correspond to omega or alpha representations
in quantum resonance theory; ibid., pp. 26-27.
3 Bohm, David
(1980), _Wholeness and the Implicate Order_, London: Routledge.
4 Stoppard,
Tom (1967), _Rosencrantz & Guildenstern Are Dead_, New York: Grove
Press.
5 Ibid., p.
13.
6 Guilford,
J. & Fruchter, B. (1973), _Fundamental Statistics in Psychology
and Education_, New York: McGraw-Hill Book Co., p. 106.
7 Ibid., p.
103.
8 The alpha
being a reduction of the omega; cf. Keener (1999), p. 17.
9 Reading,
Nigel, Dynamical Symmetries: Autopoietic Architecture, http://www.giant.co.uk/phimega.html
(visited June 19, 2000).
10 Keener (1999),
p. 4.