MIND AS REFLECTION OF PROCESS PHYSICS AND THE SEMANTIC OF REALITY
by Horacio Velasco

In my article , "THE OBJECTS OF MEANING FROM THE LIMITS OF LOGIC", the process physics model of reality recently originated (dating only since 1997) and under on-going development by Dr. Reginald Cahill and his PhD students, Christopher M. Klinger, and Kirsty Kitto, at Flinders University in Adelaide, Australia was taken up (with the kind help of Dr. Cahill). Building upon the works of Goedel, Turing, and especially Chaitin at the foundations of mathematics disclosing the epistemological limitations of self-referential syntactic systems (i.e. symbol manipulating systems rich enough to contain ordinary arithmetic), the model adverted to is unique and radical because it rests upon the most secure imaginable foundation: the acknowledged limitations of our very capacity to reason and compute as rigorously shown by the works of Goedel, Turing, and Chaitin.

Process physics shows that the objects of our experience ultimately derive from the proto-physical, generalized limitations of self-referential syntactical systems (i.e. the random, structureless truths corresponding to the vast preponderance of truths disclosed by the work of Chaitin in extending the works of Goedel and Turing[1]) in what is called Self-Referential Noise and the Self-Organized Criticality dynamic operating upon it and which it reciprocally permits to operate in a subtle bootstrap, axiom-less model posited to reflect reality. Combined with the fact that symbolic dynamics (i.e. the marriage of information theory with nonlinear dynamics) instructs us (as disclosed in my article, THE DISADVANTAGES OF OMNISCIENCE) that for reality to be meaningful, then an element of unpredictability or predictive fallibility is required, it could therefore be concluded, as the article did, that the literal objects of meaning apparently derive (astonishingly so!) from the limits of logic.

Now, Dr. Cahill, in a further elaboration of their process physics model[2], only underscores its robust correspondence with reality, Life, and Meaning by stressing its semantic aspect through the model’s expression as a sub-symbolic, stochastic neural network (SNN) model reflective of the workings of Mind by way of emergent effects in structures suggestive of biology. At the same time, what apparently amounts to a quantum theory of gravity that generates the objects of Meaning for Mind while resolving the outstanding problems of physics is also, satisfyingly enough, generated by the model.

Resort to a SNN model has been made, according to Dr. Cahill, for the simple reason that the information processors known as neural networks, deriving their inspiration as they do from the conviction that the brain’s cognitive abilities are not to be attained by exhaustive logical representations supposed to reflect the workings of mind but rather by approximating or duplicating the brain’s architecture[3], are powerful examples of subsymbolic information processing—which, after all, the process physics model of reality is intended to be by transcending the limitations of logical syntax to achieve experiential contact instead with the fundamental, irreducible semantic of reality. (Incidentally, the fundamental conviction inspiring neural networks adverted to above apparently finds support from one of the fathers of the modern computer, mathematician John von Neumann, when he declared in a posthumous monograph[4], as worded by Coveney and Highfield[5], "that mathematics is a secondary language, derived from the primary language employed by the body’s central nervous system").

The SNN is implemented through a seeding syntax or mathematical model involving link and node variables and rules of change for these variables. Because this seeding syntax and indeed any syntax capable of emergence must be suppressed or dispensed with to generate a semantic account of reality beyond the grasp of any particular syntax, the rules of change for the link and node variables must generate a nonlinear, iterative process corresponding to the fractal or scale-invariant linking of nodes in the dynamic known as Self-Organized Criticality (SOC).

SOC achieves the suppression of syntax because the emergent self-organizing behavior it represents possesses the property of universal criticality, rendering any start-up syntax bereft of ontological significance by inclusion in the embrace of SOC. In this way, even the node and link variables themselves dissolve into an unending regress of evolving sub-networks of relationships (they may be conveniently considered as mere names for the sub-networks) and semantic information finally emerges from these relationships in what are called the attractors or self-organising patterns of the iterative network.

The rules of change for the link and node variables of the SNN are only able to generate SOC because of the self-referential noise (SRN) or proto-physical randomness "reverberating", as it were, in the network. Dr. Cahill explains: "With the noise absent the iterator would converge in a deterministic and reversible manner to a constant matrix. However in the presence of the noise the iterator process is non-reversible and non-deterministic. It is also manifestly non-geometric and non-quantum, and so does not assume any of the standard features of syntax based physics models." Furthermore, the SRN also answers any objections about violations of the Second Law of Thermodynamics which require that available resources (or, in this case, proto-resources) be dissipated if organized structures are to emerge and to be maintained: the SRN effectively serves as an endless source of negentropy or available proto-resources for the generation and maintenance of self-organising structures in the iterative network as the SRN effectively opens systems in which self-organisation may occur by affording those systems more encompassing, environments that generate information through their selective effects upon the open systems. In this connection, it should be noted that process physics predicts a positive cosmological constant (indicating a universe that expands forever into infinity), a prediction in agreement with the latest observations gathered by astrophysicists.

The nonlinear, iterative process used to generate SOC amounts to the introduction of a time-like process. Hence, according to Dr. Cahill, in process physics "the absence of intrinsic undefined objects" always associated with syntactic, logical, formal systems is linked with the [phenomenon] of time. "Conversely, in [non-]process physics the presence of a priori [i.e. undefined] objects is related to the use of the non-process geometrical model of time [i.e. the identification of time with "the one-dimensional continuum or geometrical line"] and its geometrical time metarule [i.e. the stipulation "that one must actively imagine a point moving along a line at a uniform rate"] being an approximate emergent description from process time."

From the SRN-driven, iterative process described above (which may be identified with what has been called quantum foam in other contexts also essentially admitting the failure of syntactic physics to afford adequate phenomenological description) emerges a fractal, 3-dimensional, process space. This process space self-assembles from constituents arising from node connections that form a "random graph unit which we call a gebit as it acts as a small piece of geometry formed from random information links." Over ongoing iterations, the gebits compete for new links and undergo mutations. Eventually, however, they lose their ability to engage in further linkagesand begin to decay.

We therefore see why the space the gebits generate is called a process space: "[I]n sharp distinction to the non-process continuum geometrical spaces that have played a dominant role in modelling physical space," the informational process space of process physics is under perpetual construction as its component gebits give way to new ones assembled from SRN. If the SRN is "turned off", then the process space (which is essentially a "Prigogine far-from-equilibrium dissipative structure driven by the SRN" ) decays and ceases to exist. Clearly, such a space is in closer attunement to biology than the space of non-process physics. Clearly, also such a space is also deeply related "to the logic of the limitations of logic," [which, as generalized into proto-physical SRN, probably explains the universal observance in biology of boundaries at all levels of organized complexity].

The process space described exhibits what are called topological defects arising from the fractal connection of some of the gebits. These topological defects correspond to the emergence of quantum phenomena and eventually, of classical phenomena. Thus space and matter clearly derive from the same network processes, "the full generic description" of which is afforded us, according to Dr. Cahill, by quantum homotopic field theory (QHFT). ("Homotopic" refers to homotopy; which is simply the embedding of one space into another.) The elaboration of QHFT (which amounts to a quantum theory of gravity[6]) as preliminarily[7] accomplished by Dr. Cahill and his students will not be attempted here. Suffice it to say, QHFT "has the form of an iterative functional Schrodinger equation for the discrete time-evolution of a wave-functional where the configuration space is …the set of all possible gebits… " At the appropriate scale, QHFT should yield the more conventional quantum field theory (QFT); furthermore, through what are called Quantum State Diffusion (QSD) terms which act as residual SRN effects that afford decoherence of sufficiently large quantum systems[8] (i.e. when gravitational effects become noticeable), it should also yield classical or Newtonian systems eventually.

The decoherence process described essentially vindicates, according to Dr. Cahill, the argument by Penrose that quantum gravity is, at bottom, involved in the process. However, Dr. Cahill also stresses that this vindication has come about because of deeper considerations afforded by process physics [i.e. nothing less than the epistemological limitations of syntactic systems], not because of some "ad hoc argument such as the quantisation of Einstein’s classical spacetime model."

In this connection, learning how process physics explains the possible genesis of gravity should be most appropriate. Recalling that matter is, in process physics, topological defects in the emergent process space, it would be expected for such defects to have extra-normal gebit connectivity. Indeed, matter is actually a violation of the 3-D connectivity of the process space, according to Dr Cahill. A consequence of this is that in the region of the matter fields, gebits decay faster: they have a higher turnover because they are less effective at attracting new gebits (i.e. because they are compacted into matter fields) and therefore suffer from non-replenishment. This, in turn, results in the matter fields acting as net sinks for gebits as the neighbouring process space undergoes a diffusion/relaxation process in which the space effectively moves towards the matter.

The process described clearly corresponds to gravity, Dr. Cahill points out. Furthermore, because the diffusion/relaxation of space operates without discrimination upon all surrounding matter, the in-fall mechanism is independent of the nature of the surrounding matter and may therefore be identified with Einstein’s Equivalence Principle. Beyond this, process physics is also in agreement with extant knowledge as regards the event horizon and Hawking radiation: an event horizon indicating the presence of a black hole is generated "if the in-fall rate exceeds the rate at which 'motion' through the process space is possible" and "[s]uch an event horizon is sufficient condition for the occurrence of Hawking radiation."

QHFT and QFT represent induced syntactical systems from process physics’ semantic account of reality. The relative poverty of such induced syntactical systems compared to process physics’ semantic account of reality may be gleaned in reference to ensemble truths and contingent truths. The process system generated by SOC and driven by SRN exhibits both ensemble and contingent truths. The ensemble truths are generically true and are also accessible from the induced formal systems (i.e. they can be computed). The contingent truths, by contrast, cannot be accessed from the induced syntactical systems (i.e. they are qualitative aspects of reality that defy all computation and formulae[9]). Such contingent truths lead to induced metarules that attempt to mitigate the deficiencies of the induced syntactical systems without being able to completely remedy them (far from it actually).

For process physics to be a successful contender for the Theory of Everything (TOE), it must, according to Dr. Cahill, "prove the uniqueness conjecture": that the ensemble but not the contingent truths of the process system are unique. "This would involve demonstrating both the effectiveness of the SOC filter and the robustness of the emergent phenomenology, and the complete agreement of the later with observation."

More than the agreement of the emergent phenomenology with observation, process or semantic physics, being richer than syntactic physics, should also be expected to provide explanations for some aspects of that phenomenology left unexplained by syntactic physics. A good example in this regard is that process physics is able to provide an explanation for "one long standing unsolved problem in physics, namely an understanding of inertia." Dr. Cahill explains that the inertia corresponding to objects continuing in uniform motion unless acted upon by external forces was built into the syntactic description of Newtonian physics rather than being predicted by the model. This failure to explain motion is, of course, just what one would expect, according to Dr. Cahill, from an "essentially…static modelling of reality, with motion indirectly accessed via the geometrical time metarule…"

Process physics, however, provides a simple explanation for inertia: "[M]otion is self-replication of the gebit connectivity patterns in a set direction. Since the newest gebits, and hence the stickiest gebits, in each topological defect, are on the side corresponding to the direction of motion, the gebits on that side are preferentially replaced. Hence the motion is self-consistent and self-perpetuating."

That process physics could be implemented by a model of Mind in the SNN to reveal the fundamental semantic, temporal, experiential nature of reality is deeply satisfying for a number of reasons: 1.) the essential semantic nature of reality has been thrust upon us by the rigorously proven limitations of self-referential syntactic systems, and so rests upon the most secure imaginable and uncompromisingly honest intellectual foundation; 2.) it is, of course, Mind in which semantic and the Meaning to which it corresponds is ultimately registered[10]; 3.) Mind, as the theoretical statistician turned economic theorist and pioneering biophysical economist, Nicholas Georgescu-Roegen argues, appears to be required for the experience of what Dr. Cahill calls the "present moment" or the "now" required if we are to make meaningful observations at all.

To elaborate upon this third point: Georgescu-Roegen tells us of an illustration by Nobel Prize-winning physicist, Percy Bridgman, showing that with the advent of relativity in physics, it is perfectly possible for two separated observers travelling in different directions through space to register a signal from a third position in space as two different facts. One observer may, for instance, detect a " ‘a flash of yellow light’ " while the second registers the same signal as " ‘a glow of heat on his finger.’ " Bridgman’s point, according to Georgescu-Roegen, is that for relativity to be able to assert that about the same event implies that even relativity physics really presupposes simultaneity in some absolute sense despite its attempt to show simultaneity’s problematic nature with the registration of a single event as two distinct facts. Furthermore, relativity physics does not show how this absolute simultaneity could be established.

The upshot of the foregoing considerations, according to Georgescu-Roegen, is that we must recognize once and for all that Mind, whether that of an individual or those of several individuals bound by the same observation (i.e. which implies the present moment or absolute simultaneity), "is as indispensable an instrument of observation as any physical contrivance." Accordingly it is appropriate that a model of reality stressing its fundamentally semantic nature through the experience of the present moment as distinguishable from a recordable past and an unknowable future (recall that it is the introduction of such irrevocable time that results in the removal or suppression of syntax in process or semantic physics) is implemented by a model of Mind.

To be sure, the SNN model is in the same boat as relativity physics in establishing absolute simultaneity. As Dr. Cahill freely confesses: "In process physics it has not yet been determined whether or not the non-local processes, say those associated with EPR connections, enable the determination or not of an absolute frame of reference and so absolute simultaneity." It is to be hoped, however, that such a determination of absolute simultaneity (as well as further developmental refinements towards definitive coherence and viability of the theory) is eventually to be forthcoming: the SNN model is so comprehensive and robustly organic in its charms (with its potential binding of epistemology, ontology, physics, biology, mind, and meaningful experience), it ought to be true.

Acknowledgement:

The author acknowledges the help extended by Dr. Cahill by way of clarifications, both technical and non-technical, in the composition of the foregoing article. Dr. Cahill is not to held responsible for any remaining errors, whether of commission or omission, in the text.

Notes and References:

1. Gregory Chaitin. (May /June 2000). "A Century of Controversy Over the Foundations of Mathematics."COMPLEXITY 5, No. 5, pp. 12-21; Gregory Chaitin. (May 1975).
   "Randomness and Mathematical Proof." SCIENTIFIC AMERICAN, vol. 232, no. 5, pp. 47- 52 (I am unable to cite precise pages from the articles above because my copies of them are downloads from the web which I subsequently edited as Word documents, thus inducing probable non-correspondence of pages with the original articles); John L. Casti. (1994).
   COMPLEXIFICATION: EXPLAINING A PARADOXICAL WORLD THROUGH THE SCIENCE OF SURPRISE. (New York: HarperPerrenial ed., 1995), pp. 143-144.
2. Reginald Cahill. (2001). PROCESS PHYSICS: INERTIA, GRAVITY, AND THE QUANTUM. (Contribution to the 3rd AUSTRALASIAN CONFERENCE ON GENERAL RELATIVITY AND GRAVITATION, Perth, Australia, July 2001.); Reginald Cahill. (2001). SMART NANOSTRUCTURES AND SYNTHETIC QUANTUM SYSTEMS. (To be published in BIOMEMS AND SMART NANOSTRUCTURES, PROCEEDINGS OF SPIE CONFERENCE #4590, ed. L.B.Kish.) (Same constraint as elaborated in note 1 in regard of citing of pages).
3. John Casti, COMPLEXIFICATION, pp. 157-161.
4. Nicholas Georgescu-Roegen. (1971). THE ENTROPY LAW AND THE ECONOMIC PROCESS. (Cambridge, Massachusetts: Harvard University Press), p. 91.
5. Peter Coveney and Roger Highfield. (1995). FRONTIERS OF COMPLEXITY: THE SEARCH FOR ORDER IN A CHAOTIC WORLD. (New York: Fawcett Columbine), p. 4.
6. E-mail communication to me from Dr. Reg Cahill dated 4 December 2001.
7. E-mail communication to me from Dr. Reg Cahill dated 21 December 2001. Dr. Cahill, among other things, informed me that the "details" of the transition in theoretical modelling from the iterator behavior to QHFT "are very difficult to prove."
8. Ian Stewart. (1995). NATURE’S NUMBERS: DISCOVERING ORDER AND PATTERN IN THE UNIVERSE. (London: Weidenfeld and Nicolson), p. 110.
9. Ibid., p. 59.
10. Daniel Dennett. (1995). DARWIN’S DANGEROUS IDEA: EVOLUTION AND THE MEANINGS OF LIFE. (New York: Touchstone, 1996), pp. 204-205.
11. Nicholas Georgescu-Roegen, THE ENTROPY LAW AND THE ECONOMIC PROCESS, pp. 74-75.