The dictionary contains definitions for the word "chaos" that have little to do with the actuality of chaos. Various definitions
1. complete disorder and confusion.
2. the formless matter supposed to have existed before the creation of the universe.
or even more elaborately,
1. (obsolete) chasm, abyss.
2. (often capitalized) a state of things in which chance is supreme; especially the confused unorganized state of primordial
matter before the creation of distinct forms.
3. the inherent unpredictability in the behavior of a complex natural system (as the atmosphere, boiling water, or the beating
4. a state of utter confusion.
5. a confused mass or mixture.
Only certain of these ideas fit with the modern mathematical and scientific definition of chaos. Our definition utilizes
the concepts of unpredictability, statistical behavior, but not necessarily of disorganization or formlessness. It also relies
upon a notion of some underlying pattern that is being followed though not in a strictly cause-and-effect mechanical fashion.
It is better developed in the formalized subject known as Chaos Theory, first put forth in that version by Henri Poincaré
in 1890 and later more fully developed under the label "ergodic theory". Numerous contributors followed over the next three
quarters of a century until Benoit Mandelbrot successfully characterized all such phenomena in terms of geometric patterns
that were closely reproduced at all scales of size. This characteristic, called statistical "self-sameness", was caused by
the occurrence of fractional dimensionality in the equations describing the phenomena. Such patterns were ultimately labeled
"fractals". When viewing a fractal pattern, one can change the scale to either smaller increments or larger magnitudes and
continue to find the same or very similar patterns of plotted functions geometrically repeating over and over.
This property is also found in the real world and is present when one looks at dynamic natural systems ranging from clusters
of galaxies all the way down to atoms and below. Such self-sameness implies that in the real universe, there can always be
something smaller as well as larger than anything we presently think is a final definition of physical reality and the matter
it contains. This suggests that we will find smaller particles than the current crop of elementary particles as well as even
larger interacting structures besides galactic clusters. It is the author's conclusion that all such structures are behaving
this way because of a basic set of physical elements they have in common.
If one could find the master equation that would fully describe all dynamic behavior within the universe at any scale of size,
virtually all of the mathematical development of different scientific disciplines would literally become unified. It is anticipated
that when these master equations are finally discovered, each of the current scientific descriptions will be seen as special
cases, limits or boundary conditions of the master equations. Further, these master equations will incorporate all of the
known types of force and particle property characteristics or determinants.
A more detailed elaboration of the etymology of the word "chaos"