Self-Organization of Complex Systems

Self-Organization of Complex Systems

DOI: 10.4018/978-1-7998-1706-2.ch002

Abstract

The previous chapter suggested it is possible and productive to apply a systematic approach to the study of the evolution of human and his mind. It is time to move on to research methods. A human is a complex open system, and thus, application of a systematic approach is correct. It is necessary to check how well-known methods are suitable for modeling complex systems as part of a systematic approach. For this, the axiomatic basis of the methods was compared with the known properties of complex systems. Such verification leads to the conclusion that it is necessary to create such a modeling apparatus that will most closely correspond to these properties. The chapter describes the components of such an apparatus (axiomatic basis and self-organization scenarios).
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Background

Let's look at previous studies, grouping them by the questions in this chapter.

Researches have shown that the human body and its subsystems are complex systems date back to the post-medieval period and associated with the names M. Servetus and W. Harvey.

The achievements of their followers made it possible to rely on reliable anatomical and physiological foundations when discussing a human as a complex system (Georgieva et al., 1981; Luria, 1985; Gegenfurtner, & Sharpe (Eds.), 1999; Ivanitskiy, 2008; Carter, 1998; 2014).

One of the founders of neurophysiology was Pavlov (1949) and Anokhin (1978). Modern brain research (including using MRI) has allowed us to go much further. In particular, a detailed map of the brain was compiled (Carter, 1998), correspondences between certain abilities and areas of the brain were found (Miller & Cohen, 2001; Fuster, 2003), the state of neural networks for various types of brain activity was recorded Human Brain Project (Human Brain Project, n/d,), brain rhythms were determined for various states of wakefulness and sleep (Zidermane, 1988; Libet, 2004), and data on brain physiology were substantially replenished.

Numerous works have been devoted to the search for the relationship of consciousness, mind, emotions with various areas of the brain and states of its activity (Edelman, 1989; Pribram, 1991; Abbott, Sejnowski, (Eds.), 1999; Damasio, 1999; Beauregard, (Ed.), 2003; Chalupa, & Werner, (Eds.), 2004; Hameroff, 2006; Harris, & Jenkin, M. (Eds.) 2007; Monserrat, 2001; 2007).

These results provide enough material to substantiate the idea of a human in general and his brain, in particular, as complex open systems.

The idea of the unity of man and the Universe has philosophical and mathematical components.

The origins of this doctrine are in ancient times. Let’s remember the myths of Purusha or Pan-gu, from whose bodies the Universe was created; very developed representations of Taoism and, especially, Sankhya (Radhakrishnan, 1956-1957), describing a complex picture of the structures of consciousness and the Universe, their mutual connections and synchronizations. Ancient natural philosophy shows that such ideas were truly global. Antiquity includes the concept of the unity of microcosm and macrocosm; ideas about the origin of all things from the primary elements of water (Thales) and fire (Heraclitus), Protagoras thesis about man, as the measure of all things.

Modern researchers sometimes return to these ideas, of course, already at the level of modern knowledge. For example, M. Todeschini’s (Todeschini, 1949) theory of the role of the fluid in explaining the motion of celestial bodies, gravity, manifestations of life and nervous activity is consistent with Thales’s ideas, the Big Bang theory is consistent with Heraclitus’s point of view, and the anthropic principle of cosmology (Kuzhekina, Voronina & Lukoyanova, 2016) correlates with Protagoras thesis. Some scientists find a similarity between quantum physics and Taoism (Capra, 1999) or Confucian philosophy (Chung, 2014)1.

The founder of the theory of complex systems – a kind of reincarnation of ancient natural philosophy of philosophy – was a biologist L. von Bertalanfi (Bertalanffy, 1950).

The development of mathematical methods for modeling complex systems is associated with the names of M. Mesarovich, and Y. Takahara (Mesarovic, Mano & Takahara, 1973; Mesarovic, Takahara, 1978). Note, that the classical mathematical paradigm, largely based on the logic of Aristotle, was used.

Key Terms in this Chapter

CO: Convolution.

??: Object Model: Graph or layering-convolution LC-diagram, which show some invariants of S- space structure and evolution.

?: S-set.

ME: “Man-environment” model.

s: Subject.

D: Diffraction operation.

?: S-elements perpendicularity.

Mr: Measurement result.

IIDS: The intuitive information display system.

HME: Human-machine-environment system.

?,•: S-elements: wave, soliton.

?: Object.

I: Interference operation.

L: Layering.

C: Coincidence operation.

RDM: Recognition and decision model.

||: S-elements parallelism.

s: Superposition operation.

IDS: Information display system.

A, P Modalities of Existence: Actual and potential of S-space, S-sets, and S-elements, rules of their mutual transition, depending on the effects of the external factors.

?, ?, ? Modalities of Condition: Expansion, weakening, disappearance.

{DICS}: All Sp operations.

TF: Target function.

Sp, °S-space: Axiomatic wave model of a complex system. Includes 17 axioms that define the structure of space, state, and interaction of elements, the procedure for measuring.

p: Potential - “captured” part of the universe; intuitive characteristic of the ability to interactions; is expressed in conventional units.

? Observation: The influence of external factors (for perception and recognition tasks mostly).

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