A Biologically Consistent Hierarchical Framework
for Self-Referencing Survivalist Computation

Ron Cottam, Willy Ranson & Roger Vounckx

Introduction

            Extensively scaled formally rational hardware and software are indirectly fallible, at the very least through temporal restrictions on the evaluation of their correctness. In addition, the apparent inability of formal rationality to successfully describe living systems as anything other than inanimate structures suggests that the development of self-referencing computational machines will require a different approach. We present a computational construction [1] consistent with evolutionary hierarchical emergence [2], which may serve as a framework for implementing survival-oriented processing in real environments.

A Grounding in Rationality

            Our search for anticipative computation is one of mimicking living entities. It is doomed to failure if we do not take account of critical aspects of life. Unfortunately we have learned our modeling skills in contexts exhibiting near-equilibrium characteristics, where we can easily check for a successful model by seeing if it “gives the right answers”. Temporal anticipation does not offer such a choice, as there is no easy way to disassemble a temporal context and precisely compare prediction and outcome in a way which takes into account more than local correspondence [3]. Time is irreversible, and causality requires that spatial communication is restricted in nature [4].

            It is becoming clearer that the evolution of life, both in the historical record and in the present [5], depends on the fine balance between communication and structure which is offered by operation in far-from-equilibrium environments [6]. This in no way corresponds to the near-equilibrium contexts of our modeling apprenticeship. It is instructive to note that over the past 2000 years “scientific” models have changed, paradigms have been replaced, “understanding” has expanded explosively, and yet the rationality underlying our metaphors has remained unmoved [7]. The evident difficulty of formal rationality to provide coherent descriptions of life and consciousness suggests that we should look more deeply into the grounding of the modeling upon which we rely. The historical success of formal rationality has been through simply avoiding areas in which its application was suspect. Even the logical completeness of this century’s technological marvel of quantum mechanics breaks down when it is extended to large systems [8].

            We propose a first step in correcting this deficiency, by developing a framework within which the local and the global can be related [9] in a way which mirrors the structure of the environment in which our anticipative systems and living entities must both survive. To be useful, such a framework must be capable of including in a natural manner all possible scales of the near-to-equilibrium correspondences confirmed by formally rational science, from the environmental dimensional coupling of superstrings [10] to the emission of energy from black holes [11]. But it must go a lot farther than that. It must suggest a feasible route for the development of the variety we observe in our surroundings, which is conspicuously absent from reductionist points of view. It must support the hierarchy of relationships characteristic of biology, from single cells to human societies, and the scavenging character shown by evolution in developing new properties from unrelated old ones. And it must give at the very least an indication of the nature of the phenomenon we describe as consciousness [12].

            Natural evolution proceeds by the operation of a “natural” reductionism [7]. Similarly, our scientific representations of “reality” are derived from an “artificial” reductionist stance. The key to modeling complex environments lies in the observation that to correlate our representations with “reality” we must not only match models, not even just paradigms, but also rationalities [7]. Our formal rationalities are themselves nothing but simplified models of the natural rationalities we seek to understand. Nature is always complex [13]. Complex nature must be modeled by complex rationality to achieve matching, in a similar way to that in which probability is used as a simplifying device to model otherwise unpredictable combinations of individual quantum events. Causality is not naturally complete, it describes a capacity for forming approximations [9] and maintaining their structure [14]. Formal rationality can never successfully and completely describe the enclosure of partially localised entities, such as biological cells. The maintenance of a causal domain depends not only on communication being restricted, but just as importantly on its being operative [7]: the fundamental character of causality is that of compromise.

            We propose the adoption of inter-dimensional coupling through a modified form of multiply recursive Dempster [15]-Schafer [16] probability [7], which can provide an continuous operational domain extending between formal rationality, corresponding to perfectly defined values, and nonlocality, corresponding to “ultimate vagueness” [17]. From a survivalist point of view, an evaluable degree of "normal" computational uncertainty is much more acceptable than "normally" high accuracy and occasional disaster. Small errors are more user-friendly than large ones! The resultant universal description mirrors the biological evolutionary hierarchical structure described by Lemke [18], but over a much wider range of scales and kinds of entity [9]. A correlative description of scientific and biological observations must also take account of philosophical viewpoints. Aristotle’s four causes can be identified as approximates to specific regions of the model, whose operation is consistent with Peircian semiosis [19]. The emergence of both stabilising and unstable localised entities, from quantum quasi-particles to perceptions to living entities [2], takes place in an abductive manner [20]. Within a temporal framework, this not only encompasses the properties of superstrings and black holes, but also supports the presence of a preponderance of “dark matter” on a cosmic scale.

A Survivalist Computational Framework

            If we construct an analogous operational domain based on computability [21], we find interrelational linear superposition comparable to the intermediate stage of quantum computation at one dimensional extreme, and formal binary decision-making at the other. The corresponding general dimensional limits of nonlocality and perfect localisation lie outside “reality” as we perceive it [7], and in a similar manner neither linear superposition nor formal rationality alone is sufficient to describe reality or life.

            We propose that a query-reflection architecture [1] can model the intermediate region in a manner which is consistent with the abductive emergence of animate and inanimate entities [2]. “Requests” for reaction to external stimuli are formulated as queries propagating across a varyingly dimensionally confined computational structure. Multiple sequentially accessible model planes perform as “reflective” metastatic representations of the temporal or scalar hierarchies characteristic of biological evolution and structure [9], and the systematic process closure required for functional autonomy [22] is provided by the consequent multiple communicative inter-planar reflections. Within the necessary partial (or “leaky”) enclosure of the structure in its external environment [7] we can describe operation globally as an inward propagation of data-like queries and a simultaneous outward propagation of data-like models. Data comprising the queries directly represents the stimulatory character of the “outside” environment, and it is distributed throughout the model-planes themselves, making them “real” if reduced models of the environment from easily accessible very simple representations to progressively less accessible but more complicated and exact ones. This provides for a range of temporally different reactions to external stimuli, in a manner reminiscent of the operation of the mammal brain [23].

            We can represent the queries and reflections either as the interactions of propagating waves with the model-layers, or as the transfer of packets of information between active centres which “sum” information before re-emitting it. In the limit of the difference between successive model planes tending to zero the two formulations are equivalent, and may be described by a single pseudo-one-dimensional equation [1]. Simplistically, we can imagine the complete structure as two cross-coupled counter-propagating feed-forward neural networks, where each provides the weighting required for operation of the other through local model-planes which are equivalent to feed-back neural nets. This corresponds extremely closely to a proposed “physical” representation of Peircian semiosis [20].

Self or External Referencing?

            The entire framework we propose is fractal in both the complicated scalar sense and the complex diffuse [9] sense. The globally derived dimensional extremes of nonlocality and formal rationality associated with finally-causal conservatism are fractally mirrored as local dimensional extremes tending towards formal causality. Present progressively styled self-referencing at a higher more global level is related to present perfect self-referencing at a lower more local level, and the overall effect is that of Matsuno’s [24] living memory. Internalist and externalist viewpoints control the reflectivities of opposite sides of each model layer, and the model layers themselves are internally fractal in a similar manner. This is the nature of real complexity in a hierarchical evolutionary system, which appears in two competing forms, related to complication and diffuseness.

            In our search for anticipative computation we find that every aspect of the computational model we propose appears in complementary mirrored forms. Diffuse and complicated. Rationality, causality, order, communication, localisation, simplicity, fractality, complexity, information… The duel between these two facets constitutes the process we refer to as life, and is the basis for anticipatory computation.

References

[1] Langloh N, Cottam R, Vounckx R and Cornelis J. Towards Distributed Statistical Processing - AQuARIUM: a Query and Reflection Interaction Using MAGIC: Mathematical Algorithms Generating Interdependent Confidences. In Smith S D and Neale R F, eds, ESPRIT Basic Research Series, Optical Information Technology, 303-319, Springer-Verlag, Berlin, 1993.

[2] Cottam R, Ranson W and Vounckx R. Emergence: Half a Quantum Jump? Acta Polytechnica Scandinavica: Emergence, Complexity, Hierarchy, Order, 12-19, Finnish Academy of Technology (Espoo), 1998.

[3] Matsuno K. Dynamics of Time and Information in Dynamic Time. BioSystems 46, 57-71, 1998.

[4] Prigogine I and Stengers I. Order out of Chaos: Man’s New Dialog with Nature, Flamingo-Harper Collins, London, 1984.

[5] Deacon T. The Symbolic Species, 458, Penguin, London, 1998.

[6] Langton C G. Computation at the Edge of Chaos: Phase Transitions and Emergent Computation. Physica D 42, 12-37, 1990.

[7] Cottam R, Ranson W and Vounckx R. Life as its own Tool for Survival. To be presented at The Forty Third Meeting of the International Society for the System Sciences, Pacific Grove, CA, 1999.

[8] Antoniou I. Extension of the Conventional Quantum Theory and Logic for Large Systems. In Einstein Meets Magritte, Vrije Universiteit Brussel, Brussels, 1995.

[9] Cottam R, Ranson W and Vounckx R. Diffuse Rationality in Complex Systems. InterJournal of Complex Systems Article, 235, 1998.

[10] Green M B, Schwarz J H & Witten E. Superstring Theory, Volume I, 184 Cambridge U P, Cambridge, 1987.

[11 Hawking S W. Black Holes are White Hot. Annals of the New York Academy of Sciences 262, 289, 1975.

[12] Cottam R, Ranson W and Vounckx R. Consciousness: the Precursor to Life? In The Third German Workshop on Artificial Life: Abstracting and Synthesizing the Principles of Living Systems, Verlag Harri Deutsch, Thun, 1998.

[13] Mikulecky D. Robert Rosen: The Well Posed Question and Its Answer – Why Are Organisms Different From Machines? To be presented at The Forty Third Meeting of the International Society for the System Sciences, Pacific Grove, CA, 1999.

[14] John Collier: private communication.

[15] Dempster A P. Upper and Lower Probabilities Induced by a Multivalued Mapping. Annals of Mathematical Statistics 38, 325-339, 1967.

[16] Schafer G A. Mathematical Theory of Evidence. Princeton University Press, 1976.

[17] An expression due to Stan Salthe.

[18] Lemke J L. Opening Up Closure: Semiotics Across Scales. In Closure: Emergent Organizations and their Dynamics, Gent, 1999. To be published by the New York Academy of Sciences.

[19] Taborsky E. Architectonics of Semiosis (Semaphores and Signs). St Martins Press, 1998.

[20] Edwina Taborsky: private communication.

[21] Cottam R, Ranson W and Vounckx R. Computability as an Evolutionary Context. In The Second German Workshop on Artificial Life, Dortmund, 1997.

[22] Collier J D. Autonomy in Anticipatory Systems: Significance for Functionality, Intentionality and Meaning. In Dubois D M, ed, Proceedings of CASYS’99, The Second International Conference on Computing Anticipatory Systems, Springer-Verlag, New York, 1999.

[23] LeDoux J E. Brain Mechanisms of Emotion and Emotional Learning. Curr. Opin. Neurobiol. 2, 191-197, 1992.

[24] Matsuno K. Living Memory and the Internalist Stance. In Closure: Emergent Organizations and their Dynamics, Gent, 1999. To be published by the New York Academy of Sciences.
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