Gustav von Hertzen

**I posit that consciousness is brought about by incessant
cerebral self-reference which fractally transcends our four-dimensional
existence. Thus we gain a restricted overview of all reality, including
ourselves, and can regard the world from the outside as it were. Our
consciousness knows no bounds; it expands inexorably with the accumulation of
external and internal experience but, like our physical universe, we can only
watch it from the inside. Still, in rare moments, we may somehow conceive the
connection of all things and capture a glimpse of the vision of God.**

Our self-awareness is coupled to brain activity, an incredibly complex
physico-chemical process. The brain’s self-programming requires interaction with
the environment; the neonate is barely aware of itself although all the brain
cells are in place. Without a stream of sense impressions the brain cannot
exploit its potential, explore reality, identify patterns, work out the rules of
the game. Devoid of social contact the “I” cannot become aware of itself; our
latent identity, entrenched in the cerebral processes, remains closed within its
objectively four-dimensional actuality.

Speculating about computer consciousness is a fascinating exercise, and not the
sole reserve of science-fiction writers. The description and adequate
programming of an activity always presupposes a higher intelligence than is
involved in direct implementation. Consciousness is an excessively dense
language game transcending even the high cardinality of the vernacular. Thus the
construction of ‘beings’ with genuine self-awareness calls for superhuman
overview and insight as well as a hypothetical hyper-language, which removes
conscious computers to a far-off and perhaps unattainable future.

Reality can be adequately surveyed only from the outside: to immediately
comprehend a two-dimensional existence calls for three-dimensional creatures.
Similarly the validation of mathematical truth requires a meta-mathematical
value frame which provides the indispensable superior perspective. Consciousness
implies that we possess a certain overview of our own four-dimensional
existence, as the mind plays with itself in ever-changing self-reference. Thus,
we must postulate a higher dimension to which man and possibly also other
advanced species have some access.

We may speculate casually about higher dimensions, but such loose ideas must
be set within a tangible framework. The fractals – dimensional quantities
intervening between the integers – offer an attractive mathematical model for my
present purpose.

The concept of fractals derives from the infinity mathematics of Georg Cantor
(1845–1918). In 1890, Giuseppe Peano (1858–1932) could demonstrate that an
‘infinitely complex’ curve can fill a plane if it is extended without limit. The
Brownian, thermally randomized motions of microscopic particles represent the
physical equivalent of a Peano curve. But a curve may also be constructed such
that its dimension is a fractal, something between one and two.

A fractal dimension presupposes infinite continuation of the convolutions of the
curve or the irregularities of the surface, as the scale approaches zero. This
is in accordance with the modern conception of the nature of reality. The
elementary particles are not well-defined points, where the grainy nature of
matter comes to an end; instead they can be described in terms of statistically
prescribed processes. Heisenberg’s uncertainty principle excludes exactly
defined positions and trajectories; even the vacuum is far removed from
absolutely unstructured emptiness.

The wealth of variety in the world does not disappear as space and time scales
approach zero. Material interfaces are therefore qualified for interpretation
according to the fractal principle; they are always somewhat ‘wrinkled’ and
possess a certain ‘sense’ of a higher dimension. Any real surface is not only
irregular down to the last atomic detail; the ambiguity is further enhanced by
the creativity of empty space. A three-dimensional particle has, by virtue of
its process nature, an analogous depth contact with the fourth dimension of
time; pure being appears to be a metaphysical impossibility.

Imaginative computer simulation has brought forth a whole hierarchy of fractals
from the relative simplicity of the Peano curve over the multi-fractals
characteristic of turbulent flow to the completely non-repetitive superfractal
of the Mandelbrot interface. I postulate that human consciousness is coupled to
an intense cerebral variability which conceives a hyperfractal, capable of
penetrating into a fifth dimension. Four-dimensional space-time can then, to
some extent, be surveyed and embraced by the incessantly scanning brain
function. In cybernetic terms consciousness is an ultra-ergodic system; the same
state is never repeated. Not only does every brain diverge, but every conscious
moment of a single human brain generates a new and unique experience unlike
anything that has gone before. Only thus is there a guarantee of continuing
‘ruggedness’ in the boundary of space-time, providing contact with a higher
dimension.

Strange attractors are fractal structures, which embody the implicit rules of
quasi-chaotic play in the appropriate hyperspace. Accordingly, consciousness
could be interpreted as a superstrange attractor, emerging out of incessant
self-simulation at the hyperfractal intersection of concrete and abstract
actualities. Our mental processes thus become the metaphysical proof of the
fuzzily quantified structure of the world. A hyperfractal state is not
compatible with a completely deterministic machinery. Its prerequisites are an
infinite wealth of variety, self-repetition without self-similarity, a
meaningful unpredictability, or in other words individual freedom.

The brain operates in a meta-stable state of dissipative biochemistry, and
the mathematical treatment of analogous physical phenomena may therefore further
illuminate our subject matter. Dissipative and chaotic states are relatively
indeterminate. A minimal and almost imperceptible move in the micro-dimension
can make the whole macroscopic system change course in a cascade of cumulative
self-realization.

The minutest difference between the starting points of a chaotic process can
cause significant macroscopic bifurcation. Computer simulation of one realistic
mathematical model started with an initial difference of 10 exp -12 and yielded
an amplification of 10 exp 13 after only 50 iterations. Quantum mechanical
uncertainties can thus easily create completely different outcomes for the same
game, given that the process is charged with dissipative energy. There is no
lower limit for the proximity of the points that predestine divergent
developments; it is not a distance in the usual sense since it has a fractal
dimension of less than 1.

We are certainly not supreme autocrats in our own spiritual kingdom and yet we
do enjoy a restricted autonomy. The internal, hologram-like self-representation
of the brain constitutes a marvelously rich dissipative system. Consequently,
the choice between myriads of available moves can, to a certain degree, be
directed from a self-referential platform, fractally penetrating into a fifth
dimension. Consciousness and free will are inseparable concepts, part and parcel
of joy as well as tragic bereavement. A totally determined but sentient being is
a metaphysical self-contradiction, if not a logical impossibility.

In the typology of physical state equations, a characteristic entity is the
number of dimensions in which changes must be taken into account. The
interesting point is that if the dimensionality should exceed four, it would be
possible to avoid the complicated renormalization procedure, and the much
simpler classical field theories would apply. We can take this to mean that the
slightest transgression of four-dimensionality generates a general and
comprehensive juxtaposition of the elements within a system. Bypassing infinity,
all its several parts are brought into continual and immediate contact with one
another; they, as it were, ‘feel’ one another.

The oceanic experience of the mystics springs to mind. Cut off from everyday
trivialities, human consciousness occasionally enters an abnormally high fractal
dimension and for one blissful moment of concentrated introspection experiences
the connection of all things, beholds the meaning of existence and captures a
glimpse of the vision of God.