1. The system under scrutiny is not purely deterministic.
It always has a statistical aspect built into it. One could
incorrectly state that a billiard ball aimed at another billiard ball is strictly determinate when all the angles and forces
are exactly known. But statistical mechanics, quantum theory and an imperfect knowledge of an event coming from outside
of the real room with its real pool table can always possibly introduce a real factor to interfere with the cue
ball's trajectory. Whether it is an earthquake, crashing airplane or pet cat suddenly bounding onto the pool table,
the certainty of the cue ball hitting its target ball in a true and exact fashion is never quite 100.00000%.
2. Most if not all systems are non-linear.
Even a theoretically straight line or linear function, if recreated in our physical universe, actually has some
bending due to gravitational gradients always present in all of known space. And when one looks at real
world motion of any kind, from swirling air masses to cars driving on a straight highway that is applied to the surface of
a large, curved globe, then it must be concluded that curvature and non-linearity is a basic universal feature.
3. When one looks mathematically at any kind of fractal image or pattern, the equations more often
than not contain the property of fractional dimensionality. Thus
a fractal equation describes the structure and formation or growth of a tree, a colony of cells, or the varying length
and feature size of the perimeter of an island like Oahu in the Hawaiin Islands.
Let us ask, what the true perimeter of Oahu is. Is it the value that is given by cartographers and almanacs?
Or if you go down to the scale where you also include all the irregular and constantly moving water that flows into and out
of the sand, rocks and other non-linear features of the boundary between the land and wave-filled ocean? Then again,
could it not be even larger if you add the increased distance caused by water percolating into the porous parts of the rocks,
sand and soil at the ocean's edge? The perimeter must be even longer when one also includes the spaces between molecules
and atoms at the boundary. In fact, the perimeter seems to be ever-changing, but randomly oscillating around some average
value as waves wash onto and off of the shoreline and at each smaller scale, it tends towards an astronomically large value,
if not a particular value in a set of Cantorian infinities. Again we see a dynamic, turbulence-caused, non-linear,
statistically based metric present in our real world. Such a metric, if one could find the exact set of equations to
describe it, would have to possess a fractional dimensionality to account for the differences in scale.
4. When one looks at the plethora of chaotically-linked fractal phenomena, the equations that describe them all
have the principle of self-sameness embedded in them. This has to
be a fundamental property of chaos-based descriptions of the real world. Though self-sameness is usually ascribed to
the fractional dimensionality feature, it is useful to list this as an independent characteristic because one oftens observes
the real world in visual patterns before recognizing their chaos basis. The main way that self-sameness is elicited
is to look at the pattern, identify some key feature and then look for this type of feature at ever-decreasing or increasing
scales of size. If the pattern repeats or nearly repeats at different scales of size then the phenomenon under study
is fractionally dimensional, chaotically associated or generated and non-linear in nature.
With these concepts understood, we can enumerate the repeated patterns of nature and define how they behave within the
context of chaos theory. Take for example, the chaos-like connections between elementary particle physics,
quantum mechanics, atomic and molecular theory, planetary fluid dynamics, solar system structure and dynamics, and galaxy
structure and dynamics. The scale of sizes go from the extremely submicroscopic to the massively astronomical.
Each can be explained within its own definable frames of reference.
Circulating with positive kinetic energy around a more massive central object, smaller particles are attracted
and captured by one or more kinds of fields and the self sameness of this pattern is readily understood. It
has been noted since the time of Niels Bohr that the structure of the Bohr atom, with a large, central nucleus and smaller
"orbiting" electrons is highly reminiscent of the structure of the solar system and its planets. This paradigm is again
mimicked when one takes note of the structure, motion and forces at play in well-developed galaxies such as our
own Milky Way and the Andromeda galaxies. The structures of galaxies appear to be controlled by the presence of a supermassive
black hole object that captures passing matter in its gravitational well and then over time slowly distributes itself in a
common rotating plane normal to the central object's rotatonal axis. Only through friction or collision do the orbits
of the circulating stars and other matter decay and ultimately merge with the central object. Such a central object,
whether an atomic nucleus or a galactic nucleus, can be viewed as a chaos theory "strange attractor". In an atom, we
know from modern quantum theory that we do not have a flat planar distribution of the electron orbitals as Bohr had initially
analogized. But chaos theory is rife with examples of a non-identical but similar pattern repeating itself
at an infinite number of scales of size. Fractal images viewed in various computer programs that can plot these functions
allow one to magnify such non-linear plots many orders of magnitude and beautifully demonstrate this behavior. We might
very well accept this basic behavior of self-sameness into our re-examination of the Theory of Everything (TOE) and the cosmological
model that we are trying to construct. If we do that then it only makes sense following Occam's Razor to expect the
arrangement of particles in an atomic nucleus and the arrangement of elementary particles composing even smaller particles
to have such similar structure and motion. Perhaps after more obsevational data becomes available, we will find that
super-galactic clusters follow a similar pattern with most of their masses concentrated nearer the center of gravity of the
When one looks at the range of physics paradigms that are found best to describe the behaviors at these different
scales of size, it gives a sense of continuity and a tying together of the different disciplines of physics. Chromodynamics,
nuclear physics and quantum physics at the smaller end of the size spectrum transitioning into Newtonian or classical
physics at our everyday scale of magnitude and again transitioning into general relativity for the larger scales and
most intense of environments and events. Here lies the promise of a TOE but it has not yet jumped out and bitten
our collective noses.
Currently we have encountered serious flaws in our ability to describe certain classes of objects and their behaviors
with the present state of our scientific disciplines. Astrophysicists and astronomers keep discovering objects
that do not fit neatly into the present physical frameworks. Observational (experimental) science is always needed to
"keep theoretical science honest" to its founding principles. Without a continual cross-fertilization and cross-check,
theoretical science becomes a runaway horse headed for a cliff. Without a well-oiled theoretical science establishment,
experimental science becomes a meaningless collecting of facts and observations with no enlightenment. The present day
view of cosmology appears to this author to have some major blindspots that have headed it for a bottomless cliff. To
rescue it, we must all agree to allow a broader range of proposals, experimental work and interpretations to be explored
without pre-conditions. But skepticism and rigorous application of the basic tenets of the scientific methods should
be paramount in each scientist's approach. We really do not make any real advancements in knowledge without a lot of
exclusionary work and negative experimental results. Thus the experiments that don't work as expected and the observations
that don't quite fit can be considered equally important to uncovering the ultimate view of physical reality.