Physics and Mathematics on the Nature of Reality
by Dana Gaynor
The
subject of cosmology is broadly understood as the study of the universe
as a whole while typically
focusing on its nature and origins. Over
the last 100 years physics has offered us two competing cosmological
orientations, Steady State and Big Bang (Hawking, 1988; Prigogine,
1996). The Steady State theory
proposed by Bondi and Gold, developed further by Hoyle (Bondi, 1960) suggested
that the universe always was and always will exist in a state of expansion while
the Big Bang theory developed by Alpher, Bethe, and Gamow in 1948 suggests that
the universe began from subatomic zero mass point, a singularity, and literally
exploded into existence. Based in part on the work of Russian mathematician Friedman
completed in 1922, Hubble (1929) discovered that the universe was expanding.
Over time, celestial expansion rates were eventually modeled and reversed
suggesting a starting point for the universe.
The first proof of such a starting point occurred in the early 1960’s
through the phenomena of microwave emanations.
The Big Bang was expected to have produced radio waves in the microwave
range. Wilson and Penzias (Hawking, 1988) stumbled on this
very phenomenon while trying to trouble shoot noise from a satellite
communications antenna. Later
Penrose (1965) showed that a star in infinite space must eventually collapse
into a zero mass singularity. By
1970 Hawking and Penrose had demonstrated that this could be applied to the very
origins of the universe because based on Penrose’s work there must have been a
time in the beginning of the universe when it was so small it constituted a zero
mass singularity. This meant that
general relativity theory of Einstein was inadequate to fully explain the nature
of the universe. Further it
meant that quantum physics, addressing the subatomic aspects of existence, was
required to explain it (Hawking, 1988). In
essence their work integrated the two most significant and yet partial theories
of the nature of reality developed this century; Einstein’s general theory of
relativity (accounting for cosmic activity) and Quantum mechanics (accounting
for subatomic activity).
Quantum
physics: a dualistic reality
You will recall that Atomism suggested that all things are made of
fundamental finite units called atoms. With
the publishing of Newton’s Philosophiae Naturalis Principia Mathematica
(1687), Atomism developed into what today is referred to as classical physics.
Over the last 100 years or so systems theorists and physicists alike have
observed that application of this Newtonian-mechanistic to the world of atomic
physics is wrought with problems (Bertalanffy, 1968; Gleick, 1987; Heisenberg,
1971). There are levels of
significant irregularities and unpredictabilities that are not parsimoniously
accounted for with a purely classical model.
Beginning with the premise that reality is composed of fundamentally
separate atoms, classical physics discovered that things just didn’t add up.
At the subatomic level, boundaries that were supposed to be finite
didn’t act as if they were. Electrons
did not function in finite orbits. At
the macroscopic level, planetary orbits didn’t track exactly with what
classical physics would expect. There
appear to be additional influences affecting their journeys.
Fluids and gases demonstrate complex dynamic qualities that cannot be
predicted by classical Newtonian means. Even
light demonstrates behavior which has warranted a dualistic model, both wave and
particle in nature. Everywhere, there is irregularity and uncertainty or
built-in error. In short, when the
empirical evidence is modeled by classical Newtonian science it does not lead to
exact predictability (Bertalanffy, 1968; Gleick, 1987; Haisch, Rueda, &
Puttoff, 1994; Heisenberg, 1958; Zohar, 1994).
Reality appears irregular by comparison. In fact, Heisenberg (1958)
observed that it is impossible to predictably resolve any phenomena into
discrete local events because the observer and the observed interact effecting
each other in the moment. Heisenberg’s
observation thus reiterates the fundamentally interrelated nature of
consciousness and reality that we have begun to observe.
It is helpful to note that Heisenberg and his audience were contemporary
physicists addressing the issues associated with physicalist modeling.
As a result of this inability to track and predict reality exactly,
classical physics has given way to two significant and alternate views on the
nature of reality. Possibly the
most prevalent view is quantum physics.
Using theories of probability and a philosophically dualistic
wave/particle orientation, quantum physics has provided for much more accurate
predictions. In it’s widest
focus, a quantum physical reality is thought to be a holarchy composed of
embedded holistic systems each having wave like qualities which allow for
blending between systems, and particle like qualities which have a finiteness or
separateness to them. With the
quantum “world view”, the formerly finite boundaries of a classical
Newtonian atomistic universe have given way to the notion of an interactive
universe of dualistic nature. Contiguous systems are now understood to interact
at their boundaries forming new boundary systems in which systemic
characteristics blend and fade into one another.
Through interaction additional new properties emerge.
Systems cease to be defined as either/or states resolving rather into
both/and states.
Originally Niels Bohr (1963) developed a model of the atom that placed
electrons orbiting discretely around the nucleus and depicted electrons jumping
from one energy state to the next in discontinuous Quantum leaps.
Today Quantum physics suggests that quantum particles typically shift
state for no "apparent" reason.
As atoms become unstable, the paths of their electrons are thought to
make unpredictable discontinuous shifts from orbit to orbit.
The shifts are unpredictable as are the new orbits.
Each possible journey and destination is associated with a probability
alone. Further quantum physics hypothesizes that the electron may
actually follow all these possible paths at once. Each is thought to behave as though it were “smeared” out
over time and space and was everywhere at once.
In the quantum model, electrons are thought to put out
"feelers" in the form of their wave aspects to identify which path is
best suited for them. These feelers
are known as virtual transitions. Their
existence suggests the simultaneous existence of multiple virtual realities.
Quantum physicists call these virtual realities superpositions. One
quantum reality is thought to be layered on another and so forth.
The moment of observation or measurement is the moment that the
superposition collapses into one reality. This
is called the collapsing-the-wave function described by the now famous Shroedinger
wave equation (Shroedinger, 1935).
Using Shroedinger's work, physicist John Von Neumann (1955) visualized
the act of measurement as broken into small steps creating a chain of events and
demonstrated that the collapsing of the wave could occur anywhere between the
event and consciousness. He did
however, feel forced to theorize consciousness was the site of occurrence
because it was the only link in the chain that was unique in that it was not
mere molecules in motion. The direct intervention of consciousness collapsing
infinite virtual realities into one singular reality supports the observations
of Heisenberg and characterizes a reality inseparable from consciousness. Reality and consciousness, for the quantum physicist as well,
comprise one irreducibly interrelated system.
If this is the case then quantum reality, like subjective reality is
self-referential. Both exist only
through interrelationship with consciousness.
When quantum systems interact, the particle aspects are thought to stay
relatively separate while the wave aspects overlap and blend giving rise to an
emergent wave encompassing all of the particle aspects.
As the systems interrelate they evolve into complex integrated systems
with new wave and particle aspects. A
quantum universe is characterized by the overlapping of wave aspects that have
come into contact in what is called phase entanglement or quantum phase
connection. If each quantum entity
is smeared out across the universe infinitely in all directions in potentia with
wave aspects overlapping, their separateness is an illusion because all systems
in a quantum universe must be phase connected.
Hence they affect each other and therefore in a quantum reality all
things are interrelated and interdependent. This interaction is self-directing
or recursive because the actions of any one moment effect the next and
theoretically all other moments as well.
Fostered by the notion of the quantum interconnectedness of everything,
Einstein was the first to show that quantum mechanics implied a kind of
instantaneous connectedness between apparently separate things (Einstein,
Podolsky, & Rosen, 1935). Non-locality
or correlation in the absence of any locally observable force is the term used
to describe this phenomenon. Einstein
was uncomfortable with this notion and theorized that some basis for non-local
interaction was omitted from quantum theory that would demonstrate local
interconnectedness and causal influence. Irish
physicist John Bell (1964) developed his now famous theorem of
interconnectedness as proof that, about this, Einstein was incorrect. It states roughly that no local, linear model of reality can
explain the results of a particular experiment because polar processes,
demonstrate nonlinear interrelatedness. Bell’s
theorem was largely theoretical at the time but since then has been proven on
numerous occasions by many physicists, Clauser & Shimnoy (1978) among them.
In a quantum universe all aspects are interrelated.
While particle aspects maintain generally observable boundaries, wave
aspects merge in varying degrees. At
the extreme high level of unity are Bose-Einstein condensates generally
thought of as supercooled quantum structures that are so highly ordered all wave
fronts overlap sharing one identity and acting as one.
The name stems from the fact that these structures are made of quantum
particles called bosons. Bosons
are "particles of relationship that bind the four fundamental forces of the
universe...electromagnetic, gravitational and nuclear forces both weak and
strong” (Herbert, 1985). Their
wave fronts are thought to overlap, tending to bunch up or self-organize.
Further they are thought to possess what is called causal agency meaning
they appear to possess attributes having the vague beginnings of volition and
conscious activity. They appear (if
we were to anthropomorphize for a moment) to make choices.
These structures are unlike anything in classic physics and we will speak
of them later with regard to consciousness.
For now it may be said that quantum physics has suggested that the degree
of unity available within a quantum system can be so high as to make the system
appear a single entity in identity and action.
This type of structure demonstrates activity that appears behavior-like
suggesting the possibility of volition and the attributes of choice (Zohar &
Marshall, 1994). They offer the
possibility that at a fundamental level the fabric of existence is aware. Penrose
(1989) among others has extended this notion creating a quantum model of
consciousness based on this unifying principle.
Quantum Physics describes a universe in which the wave aspects of systems
merge into ever-larger waves of ever-larger systems through the process of phase
entanglement. Through the
merging of wave aspects, the particle aspects transmute into ever changing
structures. At this level the
universe is thought to be clearly impermanent.
But if waves and particles manifest in impermanence, of what are they
manifestations? This question
spawned the branch of physics known as quantum field theory as well as
the notion of the quantum vacuum from which quantum fluctuations emerge. According to quantum field theory, all manifestations of
existence, all waves and particles, emerge from and exist in relationship with a
background against which they stand out and through which they operate.
This background or universal context is referred to as a vacuum though it
is not empty. It has an energetic nature.
Quantum waves operate atop the vacuum.
Quantum particles stand out against the vacuum in a similar way.
For contemporary quantum physics reality emerges from, returns to, and
always exists in relation with a universal background field of energy within
this void. The process is ongoing
occurring moment by moment and understood to have a flickering aspect, as
quantum particles seem to appear and disappear spontaneously.
It is the notion of patterns of interrelationship emerging and returning
to a field of pure energetic potential within a greater void that ultimately
transcends quantum physics as we shall see and we will return to it many times
in this discussion.
The idea of an energy field from which existence manifests is referred to
in quantum physics as the ground state or minimum energy state of the
universe. It is considered a perfectly coherent boson state and considered a
Bose-Einstein condensate. Excitations
of this fundamental state are thought to produce the various manifestations of
the physical universe. If as
suggested earlier Bose-Einstein condensates exhibit behaviors which appear
volitional then there is at least the possibility that this universal sea of
potential itself is conscious in some fashion.
This would constitute what could be called a fundamental universal
consciousness. Out of this
universal backdrop (ground state), all existence might be understood as quantum
fluctuations, excitations or self-organizations of this coherent boson state. Hence quantum physics provides the possibility that a
universal field of conscious wills itself into the various forms of existence.
In this light, individual consciousness may be considered a localized
self-organization of universal consciousness.
Finally this universal ground state is measurable because it provides a
subtle push or inertial resistance on all fluctuations within it and that is
everything. Inertia is an important
characteristic of existence because it suggests physicality.
We will return to it shortly.
The
problems with a quantum model
In a quantum universe particle aspects form systems of local interaction
while wave aspects merge and overlap creating dualistic systems and a
probabilistic reality. Though
providing increased functionality over Newtonian physics, there are several
significant problems with this model. The
first is that quantum physics is counter-intuitive; a quantum universe does not
match one’s experience. For
example, quantum particles are considered to not have trajectory and yet we
experience moving objects as having trajectory.
A second point is that dualistic particle/wave hypothesis also does not
match experience. Quantum
physics’ probabilistic nature is cumbersome as well.
These three issues reflect, among other things a lack of parsimony in
quantum physics. Though an
extremely effective and functional model, if an alternate model was developed
that could address these issues in a more parsimonious way and yield the same or
better predictability then that would be preferable.
In the next section we will explore more deeply the construct of inertia,
and begin to identify an alternate model of reality utilizing a more
parsimonious approach than quantum physics.
Latter, we will extend the possibility this alternate line of thought
offers to consciousness and psychospiritual transformation.
Notes
Quantum physics models consciousness/reality as a complex dynamic system
in which irregularity is implicit. With
wave or field like aspects interconnecting all manner of existence the universe
is highly interrelated. Implicit in
this model is the irreducible interconnection of consciousness and reality.
At the lowest and highest levels consciousness and reality may be viewed
as dual aspects of a singular process. With
quantum physics reality can be modeled as a conscious energetic field in which
patterns of interrelationship manifest in increasingly complex thresholds of
differentiation.
Inertia
Poincaré and Lorenz, in the nineteenth and twentieth
centuries respectively, suggested that inertial mass might arise from an effect
called electrostatic self-energy. Though
this theory was destined to fail, the groundwork was laid for the latter
development of stochastic electrodynamics that addresses these issues in depth.
Even Einstein, while showing the functional reality of a relative frame
of reference, was uncomfortable with the notion of no absolute frame of
reference. He spent much of his
later life working on a unified field theory that would resolve this dissonance.
Stochastic
Electrodynamics
Haisch, Rueda & Puthoff (1994) working in the field of stochastic
electrodynamics (SED) identified a possible model for inertia.
SED is derived from the work of Poincaré
whose efforts led to the development of dynamical system theory often called chaos
theory. SED is therefore
a chaos model. Chaos theorists
typically apply dynamic systems models to a variety of real world phenomena and
analyze apparently random activity for implicit patterns.
Haisch et al. applied one such approach in their model of inertia.
This model accepted the existence of fluctuations in the universal
vacuum, a priori (as implicit) and then applied an entirely classical (i.e., non
quantum) approach to inertia. It
was fundamentally different from quantum physics’ explanation of inertia which
utilized the hypothesis of a wave/particle duality.
Rueda (1990), among others, demonstrated that SED offers a perfectly
accurate account for the bizarre quantum effects without resorting to the
complex hypothesis of quantum theory.
The SED model focuses on a part of the universal vacuum called the
zero-point field. It is a sea
of background electromagnetic radiation, within the universal vacuum, which is
both uniform and isotropic (i.e. the same in all directions).
Reminiscent of the residue of the big bang, the ZPF is thought to be a
sea of radiation that spans the entire universe. "It is a highly energetic emission whose spectrum.
. . continues to rise sharply with the frequency of the radiation." (Haisch
et al., 1994. p.29). Every
time the frequency doubles, the energy increases by a factor of eight.
It is unclear at this time whether there is a limit to the spectral range
and what that might even be. For
now we can say that it contains an enormous amount of energy.
The ZPF is understood to be a ground energy state as well as a Bose-Einstein
condensate. It is eternally present
and like the quantum ground state and is considered at least potentially
volitional or conscious.
In assuming the a priori existence of the ZPF, as originally
proposed by Andrei Sakharov (1968), Haisch et al. demonstrated mathematically
that what we think of as inertia may in fact be described equally well as a
Lorenz type force (detectable only during acceleration or deceleration) created
by motion through the medium of the ZPF. They
were able to show that when an electromagnetically interacting particle is
accelerated through the ZPF, a force is exerted on the charge that is directly
proportional to the acceleration but acts in the opposite direction. "The charge experiences the electromagnetic force as
resistance to acceleration. Using
Einstein's general theory of relativity (based on the assumption that
inertial and gravitational mass are equivalent and indistinguishable) as a
foundation, we can apply this orientation to both gravity and inertia" (Haisch
et al, 1994, p. 30).
Puthoff (1989) formulated a non-relativistic representation of Newtonian
gravity in which all charges in the universe fluctuate in response to
interaction with the ZPF emitting secondary electromagnetic fields.
These secondary electromagnetic fields give rise to a force that Haisch
et al. (1994) propose may be identified with gravity.
While the fluctuations occur at near light speed and in this way are
relativistic, the ZPF, as a uniform frame of reference, is absolute. While not
generating gravity or inertia by itself, they appear to be manifest during
interaction within the field. The
parsimonious conclusion would be that there is no mass only charge and that
apparent mass is a byproduct of a localized excited state interacting with the
ZPF. This would even apply to
neutrons typically considered electrically neutral because, at the most
fundamental layer, they are thought to be composed of quarks, which are
electrical in nature. The absolute
frame of reference of the ZPF, in conjunction with a universe composed entirely
of energy; provide us with a new purely energetic model of the nature of
reality. Einstein’s formula “E
= mc2”, appears, in this
context, to be a statement “about how much energy is required to give the
appearance of mass. Indeed if this
view is correct, there is no such thing as mass - - only electric charge and
energy, which together create the illusion of mass. The physical universe [could
be modeled as] ... massless electric charges immersed in a vast, energetic, all
pervasive electromagnetic field. It is the interaction of those charges with the
electromagnetic field that creates the appearance of mass.”(Haisch et al.,
1994, p. 26).
To sum up, the ZPF is photonic electromagnetic radiation distributed
evenly through the supercooled vastness of space, it is therefore a Bose-Einstein
condensate, which as we have noted may exhibit volitional behavior and therefore
possess some form of consciousness. Volition
is possible in two ways. Most
importantly a field of photonic energy suggests to physicists the continuous and
apparently random shifting of subatomic particles into and out of existence.
The nature of this flicker may be volition.
Secondly, the localized excitations or self-organizations of this
photonic energy within the ZPF produce the various aspects of the universe.
Hence this process of self-organization suggests a certain level of
volition. In both quantum physics
and SED we can conjecture that manifest existence may represent volitional
excitations of, and state changes within, a universal field of conscious energy.
With the SED model, individual consciousness would represent a
self-organized and self-referencing holarchy of energy patterns within a
potentially conscious and uniform energetic source/medium.
Since everything would be explainable as energy and charge, the construct
of a material universe would be a subtle illusion.
Ultimate reality might then be thought to consist of a potentially
conscious universal energetic field and all existence would represent localized
excitations within this uniform medium.
To be fair, problems exist around the question of whether the ZPF also
produces what is called the cosmological constant, “best known as an add-on to
Einstein's equations of general relativity that endows free space with extra
energy and gives it a gravitational effect...” (Mathews, 1994, p. 613). This theory implies a greater constant than what is currently
considered acceptable. Haisch’s
response when I asked about it was that one possible consequence of the Sakharov
theory of gravity is that vacuum energy can’t generate and therefore create a
gravitational field. In this way it
would not create the constant. There
might be alternative frames for dealing with this issue.
For instance, only motion or excitation might create the constant.
Notes
We have seen that SED offers a model for reality, which is functionally
equivalent to quantum physics yet more parsimonious.
Like quantum physics, SED suggests the existence of a universal energetic
field within which all aspects of reality, including individual consciousness,
are necessarily localized excitations. Whether
SED proves to be correct or not, the notion of a massless universe in which the
illusion of mass is created by motion through a uniform medium is too elegant to
simply ignore. In future chapters
we will see connections between many of the great spiritual traditions and all
the views we have discussed especially this one.
Using a massless model, nothing prevents us from thinking of individual
consciousness as a localized change in oscillation, a localized alteration of
the frequency patterns within a universal and potentially conscious energetic
medium. This type of
conscious reality would clearly form a complex dynamic system composed of
self-organized energetic patterns interacting within a uniform energetic medium.
With this type of model the chaotic irregularities observed with
Newtonian and quantum physics disappear. Following
the lead of SED we now turn our attention directly to the study of chaos.
The
patterns of diversity are chaos for the Newtonian mind
The study of chaos as a contemporary discipline is generally thought to
have begun with Poincaré (Abraham, 1994; Gleick, 1987) who demonstrated
that classical Newtonian physics offered only an inaccurate means for modeling
the activity of our solar system. He
discovered that cosmic reality was not perfect in the way Newtonian physics
described. In fact it was rather
consistently imperfect. Linear
mathematics did not account for the consistent irregularities in the activities
of the solar system. The orbits of
planets, for instance, could not be accurately modeled using classic Newtonian
physics. Within the chaos of
dynamical solar turbulence however the consistency of irregularity offered a
deeper glimpse of reality. Poincaré developed a new form of mathematics to address the
nonlinear and unruly behavior of a complex dynamical solar system.
His work is the basis for what would later be called chaos theory (aka.
complexity theory or dynamical system theory).
Stochastic electrodynamics (SED) discussed in the preceding chapter is an
offshoot of this work.
In 1960, using this same form of mathematics and an ancient computer by
today’s standards, Lorenz had begun to explore the chaos of atmospheric
turbulence. Over time he was able
to model relatively simple weather systems using nonlinear differential
equations (Lorenz, 1976). His findings were significant because these turbulent
systems had previously been viewed as random and unpredictable.
Lorenz discovered they demonstrated highly complex innate patterns of
movement shifting between what appeared to be unstable and stable conditions.
In time, he established that these highly complex systems could be
modeled from relatively simple nonlinear differential equations.
His basic methodology was to load atmospheric qualities like air pressure
changes and air stream shifts as variables or control parameters in simple
nonlinear differential equations. He
then ran them in recursive iterations on his computer (feeding output into each
succeeding step or iteration as input).
The computer was programmed to print a simple character representing a
particular variable's result for each step.
The characters printed depicted spatial changes over time.
By connecting the characters in their order of occurrence, the various trajectories
of the system could be tracked. Over
many steps, the characters would self-organize in ways that mirrored observable
natural weather patterns. Because
these trajectories demonstrated a similarity and stability they would later come
to be referred to as attractors. We
could describe attractors as implicit limiting characteristics that draw
trajectories in particular ways. Said simply, they are systemic propensities for a
particular behavior determined by the systems parameters.
Lorenze discovered that restarting one of his runs in the middle,
effectively established different beginning points because of programmed
rounding of values by the computer. This
had the effect of yielding slightly different trajectories or patterns in time.
He found that trajectories starting from close yet non-identical initial
points or conditions diverged in the near future, yet all, obeying the same
forces of relationship, created similar patterns or attractors.
This divergence of trajectory, associated with the use of alternate yet
nearby starting points, is called sensitivity to initial conditions and
is a hallmark of chaotic attractors. By changing a “control parameter” in the equations used to
describe dynamical systems, like those Lorenze was concerned with, even more
dramatic changes in attractors are caused.
These dramatic changes are called bifurcations and can include;
both the appearance and disappearance of attractors, as well as changes in their
size and shape. The ability of
systems to bifurcate and to show chaotic properties is characteristic of only
nonlinear dynamical systems i.e. those systems that can be described by
nonlinear difference or differential questions.
At or near their bifurcations, attractors become unstable.
Eighteen years later, Feigenbaum (1978), using the same nonlinear
differential equations, spent time investigating control parameters and the
ratio of successive bifurcation points created by changing the constants in the
equations. He fed the results back into his equation and reran it
through long reiterative cycles, much like Lorenz had originally done.
Feigenbaum was looking for the exact point where mapping changed from
repetitive or periodic to chaotic. He
found that even small changes to control parameters can cause large qualitative
changes to the stable spatio-temporal characteristics or attractor thereby
altering the patterns they reflect.
Further he discovered an unexpected regularity in the ratio of successive
bifurcations. They converged to a
constant rate now known as Feigenbaum’s constant.
This bifurcation sequence demonstrated a fundamental scalability.
It was self-similar across multiple orders of magnitude. He tried various
difference equations and found that they all produced the same results and a
sequence of changes that was independent of scale.
His work offered hope that real-world systems would behave in similarly
recognizable patterns and that they would be measurable.
The equation he studied most is called the logistic equation and
has successfully modeled a number of natural processes.
About the same time Feigenbaum was exploring fluid turbulence, Mandelbrot
(1982) found that long-term changes in cotton prices followed a sequence or
pattern that was independent of unpredictable short term pricing.
Curves for monthly and daily pricing matched perfectly while the prices
themselves varied. These phenomena
should not have existed as they were considered by economists to be the result
of random fluctuations in the price index.
Mandelbrot discovered that though any particular price change was random
and unpredictable, the sequence had properties that remained constant over 60
years and through two world wars. This
sequence reflected the existence of an economic attractor, an inherent
propensity for cotton pricing to reflect a particular pattern.
Developing an interest in applications where such propensities to pattern
existed, Mandlebrot found patterns of irregularity in many things from the
shapes of clouds to shorelines to lightning.
He observed, for instance, that in geometric shapes and the coastline of
England, length could not be measured independent of scale. The position of the
observer, near or far, affected the measurement.
He found that variability in measures of mass or length meant a
dimensional constant was necessary for a measure independent of scale.
By utilizing this dimensional constant, mathematicians could recognize
such self-similarity across scales. Mandelbrot
created a new geometry to make this possible and developed the word
“fractal” to describe such phenomena. Over time increasing examples of fractals have been
found in the real world.
By definition, a fractal is a geometric object, a pattern created
by graphing expanding iterative difference or differential equations in a
specific way. Fractals
show remarkable interrelational similarities across different scales of
observation including a nesting or replication of the whole pattern, or its
parts, within its parts. In
other words, changing perspective, “zooming in and out, so to speak “, can
reveal the same pattern at different orders of magnitude.
We can see this quality in leaves, clouds, shorelines, snowflakes, stock
trends, and the list goes on. The
key point here is that these patterns represent spatio-temporal structures that
are independent of scale and derived from their nonlinear nature.
Further this nonlinear nature can be modeled with relatively simple
differential equations. Hence,
“simple chaotic dynamical systems possess fractal properties, and fractals
being generated by iterative processes are dynamical systems.
They share they same insights into the nature of reality.” (Abraham,
2000). The qualities of
fractals that make them extremely pertinent to our discussion of
consciousness/reality are recursion or self-direction, self-similarity
and scalability.
To the extent a system responds to information derived from its activity
it is self-directed or recursive. Said
another way, a system is recursive or self-directed if the value of its control
parameter depends on the state of the system.
Self-direction is a hallmark of dynamical systems like fractals.
As a result of self-direction systems are said to self-organize.
To the extent that this self-organization produces spatio-temporal
characteristics that are self-similar independent of scale the systems they
reflect are fractals. Finally, the
changing of control parameters by self-organizing systems (i.e. self-direction)
is determined not only by their response to external factors, but by their
response to their own internal conditions.
In this way, self–organizing systems are adaptive, because they react
to changes both within themselves and the environment dynamically.
Through self-direction, they can be extraordinarily flexible. Latter we will apply the characteristics of fractals to the
“intentional system” of individual consciousness. We will suggest that such systems appear to require less
stable states to make the non-characteristic choices (bifurcations) associated
with growth and innovation; expanding creativity and systemic flexibility in the
process.
As we consider the adaptive properties of fractals, marked by
self-direction and self-similarity independent of scale, we are struck by the
obvious connections to consciousness/reality described in the preceding
chapters. There are other
implicit considerations that make a dynamical system approach a good choice for
modeling consciousness/reality as well. With
dynamical systems we look for a set of complex and evolving interrelationships,
both subject and object. We have
seen that an evolving subject/object relationship is implicit in the operation
of consciousness/reality. Further
because dynamical systems reference multiple interrelationships, causality is
considered multivariate or multi-determinate.
This orientation matches experience as we have seen that complex
dynamical interrelationships are implicit in consciousness/reality.
Collectively these considerations offer a holistic approach to analysis that
makes intuitive sense. In the next
issue we will use this approach to explore individual consciousness and come
to see that it is well modeled as a dynamical system.