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Strange Attractors of Meaning

Vladimir Dimitrov

Centre for Systemic Development, University of Western Sydney, Richmond, NSW 2753

Strange Attractors of Meaning (SAM)
Iconic and Symbolic Characteristics of SAM
Emergence of New Meanings
Instability and Fuzziness versus Stability and Precision
Symmetry Breaking and Trunsduction


We navigate through the whirling dynamics of life by making sense of social complexity, which we both create and are created by.

Dynamic Semiotics explores the process of making sense of dynamical signs, that is, signs standing for objects (phenomena, events, processes), which constantly move, change, evolve and transform in the scope of our perceptions. It is this kind of objects that contrives the fabric of social complexity.

The key hypothesis in Dynamic Semiotics says (Brandt) that in the mental space of humans - the space of our understanding-supporting thoughts and feelings, there are structures based on forms and forces linked or merged into spatio-temporal units, which make things meaningful. Complexity and Chaos reveal the dynamic topologies of these meaning-making units.

The intension of this paper is to show that the strange attractors emerging out of chaotic dynamics of the thoughts and feelings constantly swarming in the mental space of each individual encapsulate the topologies of the meaning-making units and offer a key to a unified semiotic and cognitive understanding of meaning.

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Strange Attractors of Meaning (SAM)

Mathematically, the strange attractor is defined as an attracting set with zero measure (that is, a set capable to be enclosed in intervals with arbitrarily small total length) in an embedding n-dimensional space (called phase space) and has a fractal structure (that is, a structure, which displays self-similarity on all scales of its manifestation). The trajectories, that is, the traces of the energies and forces whirling within the strange attractor, appear to skip around randomly.

The cause for a meaning to emerge can be any dynamical sign projected on the human mental space (Dimitrov and Woog). As far as the projection of each meaning-evoking sign is only an energy pattern - a kind of whirlpool in the flow of thoughts and feelings that can neither be seen nor touch but only expressed in arbitrary small spatio-temporal units of perception, its 'measure' is zero.

The phase space where meaning emerges is the 'multi-dimensional' mental space of an individual - a non-material (transcendental in Kantian term) space energized by continuously generated thoughts and feelings.

Meaning has fractal structure - once a certain dynamical sign makes sense to an individual, this individual can 'zoom' deeper and deeper into the meaning of this sign. Although each level ('scale') of meaning-exploration may differ from any other level, there is similarity between the levels, as they all relate to the dynamics of one and the same sign interpreted by one and the same individual.

The strange attractors of meanings (SAM) can exhort human actions. Although, the actions may appear randomly skipping around, they relate to the attractors of meanings, which propel them. If there is no attractor of meanings behind one's actions, the actions are simply meaningless; they are running at physical level only. The lack of intelligent support, be it mental, emotional or spiritual, is incompatible with one's growth as a holistic individuality.

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Iconic and Symbolic Characteristics of SAM

Being dynamic constructs, the Strange Attractors of Meaning (SAM) have both spatial and temporal characteristics.

The spatial characteristic of SAM relates to 'areas' of context(s) where signs reveal their meaning.

For example, the sign of cross reveals its meaning in the 'area' of the Christian texts, the term strange attractor reveals its meaning in the field of chaos theory (where this term was initiated and explained in detail); the expression class struggle becomes meaningful in the context of the Marxist ideology; quarks and gluons become filled with meaning in the scope of today's quantum research, etc.

The spatial characteristic of SAM can be described as iconic; an icon (whether pictorial representation or word or physical construction, etc.) are always attached to a certain core context. The cross is an icon in the Christian doctrine, Lorenz's butterfly attractor is an icon in the studies of Chaos, the class struggle is an iconic expression in Marxism, the Eiffel tower - an icon in the French tourism, the music of Sibelius - an icon in the Finnish culture, etc.

The temporal characteristic of SAM relates to the ability of meanings to evolve, transform and initiate new meanings.

For example, the meaning of chaos has undergone a significant evolution - from being associated only with disorder, confusion and 'states of things where chance is supreme', it is now associated with the inherent unpredictability in the behaviour of nature and with a property known as extreme sensitivity to initial conditions. The word chaos has brought into life entirely new meanings like strange attractor, fractal structure, bifurcation diagram, Feingenbaum number, self-organized criticality, etc.

The temporal characteristics of SAM can be described as symbolic in its capacity to act like a symbol, which always suggests 'something else' (by reason of relationship, association, convention, or accidental resemblance), and thus to excite entirely new meanings.

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Emergence of New Meanings at the Edge of Chaos

New meanings correspond to new strange attractors brought to life in the mental space of an individual (a group, the society). According to Chaos theory, the spontaneous creation of an attractor happens if systems parameters pass certain critical values. Then the attractor loses its dynamic stability. The region in the phase space where this happen has a specific name: Egde of Chaos.

At the edge of chaos, two (or more) strange attractors can simultaneously lose their stabilities and merge to form a new attractor (a phenomenon known as attractor-merging crisis), or one strange attractor can become suddenly destroyed (a phenomenon called boundary crisis), or can dramatically decrease/increase its size (folding/expanding interior crisis), or can split into two or more attractors (attractor-splitting crisis).

Similar crisis phenomena occur with SAM. The role of systems parameters, in other words, of systems characteristics whose dynamics can be put under control, is played by the activities consciously undertaken by individuals in order to increase the depth of their understanding of social complexity.

Example of activities aimed at deepening the levels of understanding can be any form of learning, of strengthening individual awareness, of honing the intelligence, of energizing individual ability for direct intuitive knowledge, etc. When certain critical levels of development of these kinds of understanding-oriented human activities are achieved, they play the role of critical values, that is, they make SAM enter the edge of chaos by suddenly losing their stability: shrinking or expanding or destroying or splitting or merging with other attractors of meaning that 'pulsate' in the mental space.

It is always a kind of magic when an articulated or written word spontaneously 'explodes' with meaning, if the language-state of the listeners (or readers) has entered the critical level of its understanding-oriented preparedness to make such 'explosion' happen. And there are also many examples when no meaning-explosion happens, as the individual levels of understanding are far below the critical ones - far away from the edge of chaos.

From experience we know that one and the same sign (text, formula, piece of music, dance, ritual) can be meaningless for some and full of meaning for others. And even for one and the same person, signs perceived initially as meaningless can become meaningful later. This kind of transformation requires again conditions of criticality (edge of chaos) to arise in the mental space of an individual; without people's efforts to learn and grow in knowledge, awareness, experience and wisdom, these conditions can hardly come to existence.

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Instability and Fuzziness versus Stability and Precision

The efficiency of learning crucially depends on SAM's potential to lose their stability and undergo creative crises at the edge of chaos resulting in emergence of new meanings or destruction of the old ones. Such are the attractor-merging crisis, the attractor-splitting crisis and the boundary crisis. The first two types result directly in the emergence of new SAM; the third type brings the energy liberated through the destruction of an attractor back to the mental space and thus increases the capacity of the mental space for 'production' of new SAM.

There are dynamical signs, which can trigger a 'chain reaction' of emergent meanings. Often these signs represent words and sentences able to simultaneously 'fire' several creative crises in one's mental space. In Zen Buddism, the words and expressions used by the Zen Masters can trigger "satori" (a state of spiritual climax, enlightenment) in their advanced disciples. The release of this kind of orgasmic power hidden in certain words and expressions resembles a sudden jump of all the meaning attractors existing in one's mental space directly into the 'boiling' zone at the edge of chaos - a jump accompanying with an 'explosion' of entirely new meaning attractor(s).

Meanings which tend to preserve their stability become dogmas.The dogmas impede the emergence of new SAM.

In the light of chaos theory, the formation of a dogmatic meaning can be explained through the expanded form of the interior crisis - when some meaning attractor expands up to a such degree in the mental space (of an individual or group) that there is simply no place for emergence of new SAM. The prejudices of people, their rigid stereotypes and standards in thinking, their doctrines and ideologies, plus all kinds of mental, emotional and spiritual patterns deliberately implanted through an intensive propaganda, social brainwash and other (direct or subtle, rough or gentle, simple or sophisticated) methods of mind control act as powerful catalyzers for an expanding interior crisis to burst out. Once this happens, it is hard (if not impossible) to stimulate emergence of new SAM.

The folded form of the interior crisis is also non-productive; this type of crisis results in a gradual lost of meaning - the attractor shrinks in time and disappears without being able to stimulate emergence of a new SAM.

As we have seen the instability of SAM is of a vital condition for emergence (discovery, creation) of new meanings. This instability directly reflects in the fuzziness of any meaningful statement related to the social complexity (Dimitrov).

The famous principle of incompatibility of Zadeh - the founder of fuzzy logic, says: "As the complexity of systems increases, our ability to make precise and significant statements about their behaviour diminishes until a threshold is reached beyond which precision and significance (or relevance) become almost mutually exclusive characteristics." (Zadeh, 1973)

In other words, as complexity increases, precision and meaningfulness become incompatible. While precision thrives on stable (fixed) meanings, the fuzzy meanings are unstable - they can simultaneously relate to several attractors and express specific types of meaning-generating crises. Instability of the fuzzy meanings make them flexible for interpretation and open for evolution and transformation. And these are precious qualities necessary for understanding social complexity.

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Symmetry Breaking and Trunsduction

Although SAM are able to provide energy and information for actions, the transition from the human mental space, where SAM abide to the physical world where human actions take place is not easy - often it requires a great amount of efforts.

We can understand the importance of a certain kind of knowledge for our, say physical health, and yet we can be unable to act according to this knowledge. In the mental space, SAM can function in a perfect harmony, that is, at the edge of chaos where the potential for creating new meanings reaches its maximum. We can happily perceive the meanings of our brilliant plans and dreams and scenarios, but the moment we start to move towards their realization, the symmetry in the pulsation of SAM suddenly breaks.

Spontaneous symmetry breaking in physics is often illustrated by a simple example from elementary classical mechanic - the example of a ball on the top of the 'Mexican Hat'. The initial state of the system is clearly symmetric under rotations about the vertical axis, and there is no predetermined direction for the ball to move, because gravity acts only in the vertical direction. Yet, the initial state is 'perfectly unstable', and the ball will eventually move (fall) in one direction or another. And as it loses energy through friction, it will eventually come to rest somewhere in the rim of the Mexican hat. Its final situation there is 'perfectly stable', but no longer has rotational symmetry. The physicists say that the rotational symmetry in the underlying forces is 'broken' by what actually happens. The actual position in the rim is purely random, and cannot be predicted by the theory. The actual outcome has no deep significance, yet it influences what happens from then on, for all times.

Symmetry breaking occurs every time when virtual becomes real. The energy, which propels the attractors of meaning in the virtual reality of our thoughts and feelings need to be 'transduced' into energy which propels the attractor of actions.

How does the process of transduction work? What are the conditions, which stimulates it and what are the conditions which impedes its realization? How the fuzzy meanings are transform into concrete actions? The answers of these questions will be at the focus of our next paper devoted to social complexity.


1. Brandt, P. 1995 Morphologies of Meaning, Aarhus: Aarhus University Press

2. Dimitrov, V. and R. Woog 1997 Studying Social Complexity, Complex Systems, 11, 6, pp. 501-509

3. Dimitrov, V. 2000 Introduction to Fuzziology, Internet Publication:

4. Zadeh, L. 1973 A  New Approach to the Analysis of Complex Systems, IEEE Trans. Syst., Man,
Cybern., SMC-3, 1

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©Vladimir Dimitrov, 2000

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