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
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
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.