A Mathematical View of Consciousness

November 4, 1996

"Can we not see that this voyage is not what we need to be cured of, but that it is itself a natural way of healing our own appalling state of alienation called normality?"

R. D. Laing, "The Politics of Experience", 1967

speaking on pyschotic episodes.

Ronald Laing, a Scottish psychiatrist, defines a "person" (as opposed to a physical being), "in a twofold way; in terms of experience, as a center of orientation of the objective universe; and in terms of behavior, as the origin of actions." ... "My experience and my action occur in a social field of reciprocal influence and interaction."

This is a self-referential or "bootstrapped" approach in which a "person" is defined only through his/her relationships with others. The process for this definition is the recursive interaction between "experience" and behavioral response. Laing makes the point that we can never understand "people" using the mechanical causal logic of "things". We will only understand them by trying to see into their experiences. However, our modern western culture thinks almost exclusively in material-causal terms, hence the large red warning flag raised by Laing with respect to what we call "normality".

Goedel's theorem is a theorem which says that there is a limit to logical constructs, theorems etc. which can be built from material-causal (Aristotelian) logic, beyond which such linear tools cannot hope to securely expose self-consistent truths and where the tools can lead us deeply into false inference. The limit is inherent in the proposition that "all Cretans are liars". This proposition, the liars paradox of the Greeks, was the avenue of attack used by Goedel in formulating his proof.

The difference in the "all Cretans are liars" proposition from countless other material-causal propositions that we could make, such as "all Cretans have two legs", is that we have given the Cretans "consciousness" in this liars paradox. That is, they must be "conscious" of truth before they can lie. Thus in the attempt to prove that the liars paradox is provable or disprovable using material-causal logic, mechanical thinking comes into a direct confrontation with "consciousness", and can't deal with it.

Consciousness is thus beyond linear logic, but that does not say that it is beyond reasoning, As David Bohm says; "Rational law is not restricted to an expression of CAUSALITY." ... "... a rational explanation takes the form; 'As things are related in a certain idea or concept, so they are related in fact.'" This opens the door to an acceptance of a natural order between things which is essentially a "massless" phenomena. As Bohm argues, the full perception of gravity experienced by Newton, based on Newton's notes, could be expressed; "as with the order of movement of an apple in fall, so with that of the moon and so with all." The natural order characterizing the dynamic interrelationships between things was dropped out of this experience by Newton in framing gravity in terms of material-causal logic; i.e. F = g*m1*m2/d**2.

The inclusion of natural order in rational thought opens the door to concepts such as bootstrapping where a web of interrelationships can be used in a self-defining context. The bootstrapping concept makes use of this view of nature in which there is a natural "order" through which every subsystem consists of all other subsystems. This is consistent with Heraclitus' view of nature as being an unfolding dynamic "ordered" by the "logos", the inherent coherency underlying everything.

The bootstrapping principle implies a natural reality in which everything references everything else, a "holographic" situation. Bootstrapping, seen in this way, is about building a holographic (conscious) view of things.

As Ronald Laing pointed out, people ARE IN THEMSELVES holographic or "bootstrapped" constructs in that their "person" is defined by a self-referential recursion between the experience and behavior of themself and those with whom they interact. And Laing's lament is that people do not accept the role of complex experience (including fantasy and negation) as their self-engendering agent and are thus alienating themselves from nature; "What we call 'normal' is a product of repression, denial, splitting, projection, introjection and other forms of destructive action on experience."

It seems clear from the evolving history of scientific thought, which is just now opening its doors to nonlinear concepts such as bootstrapping; and, indeed, proclaiming that this technique is capable of unifying our view of the whole of nature, that we have heretofore tried to force-fit linear, material-causal explanations on all of our existence and experience. What has this meant? For one thing, it has meant all those things that Laing iterates above which are involved in the alienation of our own complex experience. It has meant the denial of our own consciousness.

Consciousness IS bootstrapping. So when science says that bootstrapping shall provide the ultimate understanding of nature, it is something of a tautology. It is like saying; Let's begin to accept and embrace our consciousness so that we, as an enfolded part of nature, can understand ourselves.

In mathematical terms, our mind has the ability to handle the imagery of extended self-referential relationships which mathematically, are expressible only in higher dimensional space. Linear, material-causal logic, which we insist on using to explain all experience, is UNCONSCIOUS AND LOW DIMENSIONAL. This is why the Artificial Intelligence people have been so confident that AI will be able to reproduce human consciousness. It is because the target we are setting for ourselves is not true consciousness at all but a bastardized mechanical surrogate which we have erroneously labelled consciousness. So, the AI folks are right, it is very likely that machines will be able to reproduce the kind of "consciousness" which will be able to leverage the self-alienation which plagues us today.

As Laing says, "the life I am trying to grasp is the me that is trying to grasp it." It seems time to accept and embrace this self-referentiality, frightening as it is in its limitlessness, going on forever like the endless Celtic knot; a fractal trajectory in eternal inconsumate courtship with strange attractors defined by its own ex nihilo "being".