We intend to show in this paper that the two fundamental concepts of t
he 'Grand Unification' and the 'Chaos Theory' are essential constituen
t elements of a 'theory of everything' and appertain, in fact, to the
overall domain of complexity in space, time and gravitation. The autho
rs hope that the present paper may offer suggestions for the necessary
methodology in the analysis of complex problems. Following a short re
view of the main concepts describing conventional complexity, we intro
duce as an example of a possible development in standard paradigms, a
new type of Rayleigh-Benard instability which may be generated in the
interior of a gravitating body and may be the cause of earthquake phen
omena. We define the new terminologies of constructive and destructive
resonances es in relation to the stability of the solar system. We at
tempt to find a physical argument in support of the invariant characte
r of a gravitational chaos. Within the frame of a Riemannian spacetime
we obtain also a mathematical formulation of El Naschie's conjecture:
gravity is caused by an average deviation of fractal time from linear
uniform time. We study also in some detail the physics of black holes
because black holes offer perfect laboratories for all manifestations
of complexities and simplicites. We stress that singularities as well
as chaos demonstrate an invariant character. Even the Schwarzschild r
adius, which was initially considered to be merely a coordinate singul
arity, is found to retain or deepen its physical significance by diffe
omorphisms. Symmetry principles in particle physics and continuous att
empts to find a fundamental and unique constituent (strings, p-branes,
etc.) of matter are reviewed and their link with complexity, dimensio
nality of spacetime and chaos is indicated. Particular attention is pa
id to spontaneous symmetry breaking and the Higgs mechanism in the con
text of a cascade of concepts: classical lattice gas, Ising, model, or
der-disorder transition, inflationary scenario, and the universe as a
lattice. This cascade tends to confirm the universality of the lattice
structure of the universe. In the final section of this first part of
the paper we propose a novel multi-spherical cosmic fractal as a mode
l of homogeneous and isotropic cosmologies. If chaos is generated at t
he level of a background-arena in spacetime, then additional chaotic m
anifestations generated in this arena represent chaos on a higher leve
l or scale. The suggestion is offered that a chaos on a higher level c
alled 'superchaos' interlaces with chaotic effects at different lower
levels. The two other prospective parts of the paper will refer to the
subjects: Part 2. Chaoticity of Anisotropic Cosmologies. Part 3. Elem
entary Particles, Dark Matter and Information Aspects in Relativity. (
C) 1998 Elsevier Science Ltd. All rights reserved.