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Fuzziology: a study of fuzziness of human knowing and being


Vlad Dimitrov

The Authors

Vlad Dimitrov, University of Western Sydney, Australia

Abstract

Fuzziology explores the fuzziness inherent in what we know about ourselves and our experience, about our thoughts and feelings, drives for understanding and urges to create. By studying the fuzziness - its nature, sources, causes and factors affecting its dynamics, we are able to transcend the limitations, which it constantly puts on the processes of our understanding and knowing. The basic postulate and paradox of fuzziology are formulated together with its main principles, logical tools and theorems. The link between Socrates' maieutic inquiry, the ancient Vedic wisdom and fuzziology has helped us to reveal the significance of its central maxim: "Do not reject anything, but do not remain with anything either; go beyond!"


Article type: Wholly theoretical.

Keywords: Cybernetics, Algorithms.


Kybernetes
Volume 32 Number 4 2003 pp. 491-510
Copyright © MCB University Press ISSN 0368-492x


"I know that I know not" (Socrates)

Introduction: the basic postulate of fuzziology

In a broad sense, fuzziness is the opposite of precision. Everything that cannot be defined precisely (that is, according to some broadly accepted criteria or norms of precision) and everything that has no clearly described boundaries in space or time is considered a bearer of fuzziness. In a narrow sense, fuzziness relates to the definition of fuzzy sets as proposed by Zadeh (1965): sets, the belongingness to which is measured a membership function whose values are between 1 (full belongingness) and 0 (non-belongingness).

Mathematics has developed powerful tools for studying and dealing with fuzziness - uncertainty, imprecision, vagueness - that researchers encounter when accumulating facts in different fields of their inquiry. Advanced methods of probability theory and mathematical statistics, probabilistic reasoning and Bayesian networks, rough sets and fuzzy logic help researchers not only describe and explain fuzziness, but also reduce it and, if possible, eliminate from their experimental findings, theoretical statements and practical solutions. Science always strives for precise, valid and reliable results; so does any purposeful action, any reason-based activity.

Fuzziology is not another mathematical study of fuzziness. In the focus of fuzziology is fuzziness inherent in what we know about ourselves, about the sources and nature of our experience, of our thoughts and feelings, drives for understanding and urges to create and realise our potential (Dimitrov, 2002; Dimitrov and Hodge, 2002;Dimitrov and Korotkich, 2002; Dimitrov and Weinstein, 2002; Dimitrov and Wilson, 2002; Dimitrov and Woog, 2002; Dimitrov et al., 2001). This kind of fuzziness is at the core of our existence, at the essence of our humanness; therefore, it affects any field of human activity, be it mathematical study of fuzzy equations and fuzzy integrals or engineering design and implementation of fuzzy logic-based methodologies, fuzzy control systems and fuzzy robots.

Fuzziness studied by fuzziology is not "over-there", not in an outer world separated from us, but in the inner world of our own experience, in the "swarm" of our thoughts and ideas, emotions and feelings, beliefs and dreams. We see and understand as much from the outer world - the world in which we live - as we have already developed inside us while learning how to enrich our experience, hone our awareness, expand our consciousness and strengthen our capacity to sense, think, create and know.

The basic postulate of fuzziology is simple: Our understanding and knowing grow from within us and cannot be implanted or imposed from without. Human understanding and knowing are self-organising processes; and any self-organising process in nature works from inside out. The universe expands due to forces that emerge from inside of its whirling dynamics. Every single seed grows from inside when the outer conditions do not impede but stimulate this growth; so does our understanding. It expands and grows from inside following the inner urge to know when there are conditions in the external world nourishing this urge and facilitating its realization. So, there is a role for human society to play - not to impede our inner drive for wisdom, but to encourage its outward fulfilment.

The approach of fuzziology

Dynamic character of fuzziness

Fuzziness is inherent in our perception of reality and in every kind of activity based on this perception, such as experiencing and making sense of the events of life, feeling and responding emotionally (while involved in communication with one another, with nature and with ourselves), thinking and speaking, learning and understanding, knowing, acting and creating.

When developing its approach to study fuzziness, fuzziology acknowledges its dynamic character and makes an emphasis on the following four points.

Fuzziness has its sources and supporters, causes and effects, activators that increase it and make it denser and thicker, inhibitors that decrease it and make it rarer and thinner, exposers that make it easily recognisable and obscurer that make it hidden and hard to be disclosed.
Fuzziness has its own dynamics - forces and energies that make it move, change, evolve and transform, and its own carriers that are either immaterial like thoughts, ideas, feelings, emotions, longings, beliefs, dreams, aspirations, energy fields and spaces, or embodied in concrete human actions, in specific non-animated and animated forms, in discernible experiential events, in various kinds of signs and omens, phenomena and processes, human-created products and machines.
Fuzziness is able to self-organise into dynamic patterns with boundaries that can become rigid and hard-to-surpass or soft and easy-to-permeate, to form attractors or repellers in the experiential or mental space of the individuals, to structure into layers (levels) of fuzziness going deeper into one's thoughts and feelings, or into whirlpools (vortices) of mental, emotional or spiritual energy producing creative forces - powerful individual urges and drives - that enable fuzziness to transcend the boundaries of its dynamic patterns, to move from one level to another, from one attractor to another, from an individual to another.
Fuzziness can never be fully eliminated from the human perception of reality and experience of life - from our thinking and feeling, from our understanding and knowing.

The fuzziness and uncertainty are identical in their meaning, if the uncertainty is considered as embedded in human perception of reality. If the uncertainty is seen as something outside human ability to perceive, to experience, to understand and know, as something that exists "over-there", in the "objective" world that surrounds us, then uncertainty has another connotation than fuzziness. Fuzziness is a human characteristic, and not a characteristic intrinsic to an external object. Our knowledge about an external object can be fuzzy (vague, uncertain, ambiguous, obscure), but the object by itself has nothing fuzzy in its existence. The object is what the natural or human-created dynamics - forces, energies, substances and forms, which act upon it and express through its current appearance - have made it.

At the moment when we consciously direct our attention towards an external object, the object "enters" into the realm of our fuzziness - the fuzziness of our perception: experiencing, feeling, thinking, understanding, knowing, acting. We call this operation of including an external object into our fuzziness interiorisation, in analogy with Bakhtin's operation under the same name, proposed to define the process of appropriation, a story by people who together create it when involved in a common dialogue (Morson and Emerson, 1989). After the interiorisation, the subject (the perceiver, the "experiencer", the thinker, the knower, the actor) and the object (of perception, experience, understanding, knowing, acting) stop to be separated; they are linked at-one by the dynamics of the subject's fuzziness.

The bootstrapping algorithm

The approach of fuzziology is entirely centred in the self-referential nature of the process of human understanding.

For us to understand an object (a phenomenon, a process, an experiential event, ourselves, society) means to go beyond the limits of our own fuzziness related to what we understand and know about this object. But in order to move beyond the fuzziness of our understanding, the only tool we can use is again our own understanding with the same fuzziness that is embedded in it. So the process of understanding is a kind of realisation of a bootstrapping algorithm in the human mind, that is, seeding or facilitating emergence of conditions which helps one's own fuzziness to pull itself by its own bootstraps and moves to another level. The realisation of such a bootstrapping algorithm becomes possible because the fuzziness is dynamic - it moves: shrinks and expands, accelerates and slows, hardens or softens, transforms and transcends its own dynamic patterns.

By studying our own fuzziness - its dynamic nature, sources, causes and factors which effect its motion, we are able to succeed in the activation of bootstrapping algorithms and help fuzziness transcend itself and move to another level.

The levels of fuzziness correspond to the levels of our capacity for understanding, to the levels of our consciousness. To say that the fuzziness has moved to another level means that the process of our understanding has moved to another level also, and what was fuzzy and incomprehensible for the mind at the level, from where the fuzziness has pulled itself, has become clear and comprehensible. Of course, this does not mean that there is no more fuzziness in our understanding, that we have won the battle with the fuzziness and succeeded to extinguish it once and for all. Not at all!

The fuzziness is "alive" - full of vigour and potential to become denser and to expand wider, but its dynamics are "whirling" at another level. One can call the new level "higher" or "deeper", it does not matter; what matters is that one's understanding has become deeper, that one's consciousness has been expanded to a higher level, that the limitations, which fuzziness used to impose on one's thinking at the previous level, have been transcended. The inquiring mind will soon encounter the limitations that the fuzziness will bring with at the new level of its evolving dynamics, so that to challenge the mind to explore it further and make it move again.

Paradox of fuzziology

What is important in applying the approach of fuzziology is that we do not need to fight with the fuzziness of our understanding in order to eliminate it. To eliminate fuzziness, it would be equivalent to stop developing our ability to perceive, experience, think, feel, understand, know and act, as the fuzziness is inseparable from each and all of these vital processes.

The same motivation and urges, which support the self-organisation of the human consciousness, support the self-organisation of the fuzziness - its ability to expand, shrink or "pull itself by its own bootstraps". The dynamics of the fuzziness inherent in one's understanding are, at the same time, dynamics of this very process of understanding, as understanding means nothing but overcoming (going beyond, transcending) the limitations of fuzziness that is embedded in this understanding, in its motion, changes and evolution.

How easy it would be, if it were possible to separate the fuzziness from the process of understanding, to isolate it and then either to eliminate or keep it in captivity, while victoriously moving outside its boundaries. Unfortunately, this is impossible! The fuzziness permeates the whole process of one's understanding and also it permeates one's whole life, experience and consciousness.

The more we try to push fuzziness in one region in our mental space - the space of our thoughts and ideas, or in our experiential space - the space where the trajectories of our lives unfold, the wider and denser its unexpected emergence in other regions.

When we create (seed, facilitate) conditions to energise and strengthen - broaden and deepen - the process of one's understanding, we simultaneously create conditions to energise the fuzziness dissolved in this process. Here lays the greatest paradox of fuzziology, no matter whether it is focused on studying the fuzziness of a single individual or the fuzziness of the society as a whole.

The higher the impetus to grow and evolve in consciousness, the more vigorous the expression of the fuzziness inherent in this growth and evolvement.

This paradox propels the development and application of the approach of fuzziology - an approach of:

The above-formulated paradox puts emphasis on the significance of the practical realisation of the approach of fuzziology; each step in expanding its field of realisation has a greater value, as it deals with fuzziness of more potent nature.

At the same time, the paradox acts in favour of increasing the applicative power of the approach of fuzziology: the more "virile" the fuzziness, the greater its capacity to transcend itself. This is of primal importance for the evolution of the human thinking - for deepening of our understanding and expanding of our consciousness.

The paradox of fuzziology requires a high level of alertness at every stage of development of our consciousness to avoid absolutizing of what is considered known. According to the paradox of fuzziology, one can expect that the higher the level of consciousness (that is, the wiser the individual), the easier the fuzziness can pull itself from that level, and yet it is clear that efforts need to be applied and conscious actions to be undertaken for this to happen. Otherwise, the fuzziness cannot be made to move, no matter how high is its self-organising potential.

Socrates' wisdom at the origin of fuzziology

Meno's paradox

In Plato's Meno Socrates explores what has been called Meno's paradox of learning:

If we do not know what X is, how can we recognize it?

If we can not recognize X, how can we learn what X is?

Socrates' discussion developed Meno's paradox into a more general paradox of human inquiry:

We know what X is. (Then we are not motivated to inquire into what X is.)

We don't know what X is. (Then we are motivated to inquire, but are frustrated by the paradox, since we cannot recognize instances of X, or what X is in general, to find out what X is.)

Socrates' approach to Meno's paradox of learning included four steps:

generating hypotheses;
testing the hypotheses against examples;
philosophic examination of the hypotheses; and
drawing out implications for learning and inquiring further.

The approach used by Socrates made him aware of the following famous paradox: The less we know, the more certain and precise we are in our explanations; the more we know, the more we realise the limitations of being certain and precise.

Although Socrates' wisdom was incomparably deeper and broader than the transitory knowledge of his contemporaries, he used to say with a proverbial humility: "I know that I know not". The awareness that "I know not" made Socrates capable of revealing the gaps in the "precise" and "certain" knowledge of his opponents. When the Athenians went to the famous Delphic Oracle to ask who was the wisest man in Athens, the answer of the Oracle was "Socrates". "But how can he be the wisest if he permanently tells us that he knows not", responded the crowd. "That is why he is the wisest among you", was the answer of the Oracle.

The acknowledgment of the fuzziness in human knowledge serves a stimulus for a lifelong inquiry and search for truth and wisdom; and it is this search that makes human life meaningful.

Meno's paradox and the paradox of Socrates are at the conceptual basis of fuzziology.

Maieutic inquiry

Maieutic inquiry (from the Greek word maieutikos, which means "midwifery") is a method developed by Socrates; Socrates used to call himself a midwife who would bring about the birth of new ideas in people. The method implies asking people questions so that to draw knowledge out of them - a knowledge that, according to Socrates, they already have (Taylor et al., 2001).

Maieutic inquiry is based on the famous Socratic axioms that:

The practical realisation of maieutic inquiry is through a dialogue between two sides - one asking questions (the inquirer), and the other (the respondent) trying to answer them based on available pieces of knowledge. Both sides are interested in the process of inquiry: the respondent - to confirm the significance of the available knowledge, the inquirer - to reveal its limits and thus to facilitate emergence of new insights. If such an emergence occurs, the inquirer and the respondent move together beyond the limits of what was considered known by them before initiating the process of inquiry.

Socrates was convinced that one can always generate questions which push the boundaries of what is assumed to be known; so these boundaries are never fixed. Every time when the known is locked into patterns with rigid (non-fuzzy, crisp) boundaries, it tends to become a dogma, and the dogma is not knowledge any more. The fuzziness of the boundaries of any domain of human knowing is a vital condition for its evolution and transformation. This was revealed by the wisdom of Socrates more than 2,400 years ago. And not only this.

It was clear for Socrates, as it was for Pythagoras, 150 years before him, that human beings must strive, at any cost, to understand the enigma of spiritual continuity of existence. What does this mean?

First of all, the great thinkers of the ancient Greece believed that human life does not finish with death. People can be fully aware of real-life events, the experience of which proves that there are qualities in human nature that survive body's disintegration. If one cannot succeed in reaching such a degree of awareness, life appears entirely meaningless - we come to life in order to die after a while, or create offspring destined to die also.

"Life which moves towards death, how can it be called life?" asked the ancient thinkers and answered: "Life that implies death is a hidden death, not life." It must have been hard for Socrates's wisdom to accept that nature could approve such a meaningless life for humans endowed with a gigantic capacity to explore and understand both themselves and the universe. He must have been convinced that humans are exponents of a much greater Life extended beyond its physical manifestation only. But it must have been clear for him also that human awareness of spiritual continuity of life does not come automatically. Its awakening needs efforts - genuine and persistent efforts on behalf of the whole triad of one's body, mind and soul supported by devotion and determination to reveal the immortal essence of Life before the moment of death of the physical body.

Fuzzy as it might appear from the standpoint of our science today, the exploration of spiritual continuity of life was at the core of Socrates' self-inquiry into this greatest enigma of human existence, and his famous: "I know that I know not" reflects the soundless mystery of this enigma. Maybe it was Socrates' understanding of spiritual continuity of life that made him categorically reject the suggestion to ask for mercy when unjustly accused by the society in Athens - a society full of envy, hatred, stupidity and ignorance. How far was (and continues to be) any society from understanding individuals whose thinking is miles ahead the average "they-say" fuzziness of thinking of the colourless majority in society and its senseless rulers or leaders!

Being a method for exploring fuzziness of human knowledge and thus facilitating, through the skill of maieuticos, the "birth" of new insights, the maieutic inquiry of Socrates is used in the research practice of fuzziology.

Conditions enhancing maieutic inquiry

Maieutic inquiry depends essentially on the active interaction of the inquirer and respondent. This kind of inquiry does not represent a problem-solving process; the both sides do not search how to eliminate fuzziness from what they label as "known" and "unknown" about the issue(s) of their concern. Fuzziness is an intrinsic characteristic of human knowing and cannot be eliminated from any stage of its evolving. It is rather a kind of dialogue which helps the sides dissolve the impediments on the way to their understanding of the discussed issue(s) and thus loosening the knots into which they might have entangled themselves consciously or unconsciously by their prejudices, fixed ideas, borrowed solutions and delusions.

The interactions of sides involved in maieutic inquiry aim at liberating their creative potential from the pull of forces born out of human egocentricity and egotism, blind attachments and addictions, social brainwash or power-based manipulations - forces able to convert fuzziness of knowing into hard-to-surpass ignorance.

The dialogue of maieutic inquiry unites rather than separates the dialoguing sides, and makes them act at-one when dealing with the limits of known.

Among the conditions that facilitate emergence of creative insights in an open maieutic dialogue are:

The first condition - thirst for understanding and knowing - relates to the proverbial ability of Socrates to inflame his students, to fire them with such a great passion to know that nothing seemed more important for them than the search for truth, a lifelong search undertaken together with their Master.

The second condition - authenticity - relates to Socrates' humble expression that "the only thing he knows is that he knows not", and points again to the organic connection of maieutic inquiry with fuzziology. Socrates' expression is not only an indicator of his humility and modesty. In the ability to prevent mind from formation of rigid patterns of knowledge, and thus to keep the process of knowing in a receptive and open state of changing its fuzziness, lies the secret of a wise person. Wisdom is authentic and the words of wisdom are never precise. But what they express does not appear fuzzy for those who can understand it. On the contrary, its message is illuminating; it can "move" minds, hearts and souls of different people, evoke meaning in different situations and stimulate people's urge to know more about themselves and reality.

The third condition - holistic questioning helps not only reveal the fuzziness in what is accepted as "known for sure", but also make the process of knowing deeper and further, and not let it crystallise in frozen patterns in our mind. "Never stop questioning!" is the message of Socrates. Answers live only for a short time, the questioning goes forever.

Maieutic way: from knowledge to wisdom

The holistic questions asked by Socrates and fuzziology are open, dynamic and inextricably linked ultimately to the fuzziness of the whole fabric of human experience and knowledge. They are questions endowed with power to transform the fuzziness of knowledge into the illuminating - enlightening, inspiring and soul-elevating - "preciseness" of wisdom.

Maieutic inquiry of fuzziology can be seen as an inquiry into conditions under which knowledge can be transformed into wisdom. There are crucial differences between knowledge and wisdom.

While wisdom needs the vibrant fuzziness of human thoughts, words and actions in order to inspire and evoke their creative understanding, knowledge constantly tries to reduce the fuzziness, substitute it with precise definitions or simply get rid of it.

Knowledge can be transferred, borrowed from books and experts, imparted and taught; wisdom is non-transferable, it is a unique individual treasure accumulated while riding on the tides and ebbs of life.

Knowledge is inevitably partial, it sets boundaries, hangs labels, separates and tries to generate precision - precision that always turns out to be meaningless when dealing with spontaneity of one's life unfolding. Wisdom is holistic; it accepts the unlimited - the timeless and the infinite - and sees clearly that the precise formulas and definitions never work in life.

Below are examples of some holistic maieutic questions:

Why do we exist on this planet?

What is the purpose to be born and then die?

Is it possible to escape the death sentence that each of us was born with? How?

What is the meaning of one's life?

Where do our thoughts and feelings come from, our emotions and longings, aspirations and dreams?

What propels the life-sustaining rhythm of each person's heart?

What makes the cells and organs in the body not stray away but function in accordance?

From where come the waves of inspiration?

How do we intuit?

What does enlightenment mean?

The above questions directly zoom into the fathomless depth of our essence as creatures endowed with potential to comprehend reality.

Attempts to answer a maieutic question may lead to other questions, and their answers may fire another inquiry. The maieutic way of exploring fuzziness of human knowledge - its nature, sources and dynamics - never ends. Nor is there an end to the emergence of new insights about the truth of existence to those who, like Socrates, see the mission of their lives in revealing it.

While using the technique of maieutic inquiry, fuzziology continues to explore the same process to which Socrates devoted his life - the process of transforming fuzziness imbedded in human knowledge into insights that springs out of human wisdom.

Principles and theorems of fuzziology

Principles

Principle of incompatibility

As the complexity of a system increases, human ability to make precise and relevant (meaningful) statements about its behaviour diminishes until a threshold is reached beyond which the precision and the relevance become mutually exclusive characteristics (Zadeh, 1973). It is then that fuzzy statements are the only bearers of meaning and relevance.

This principle was used by Zadeh for extending the applicability of his fuzzy set theory and fuzzy logic to the analysis of complex systems.

Principle of connectivity-in-dynamics

No thing and no being can exist in itself or for itself but only in a dynamic relationship with other things and beings.

This principle relates to the integrity of existence vitally supported by universal dynamics, whose creative, sustaining or destructive powers are constantly demonstrated at different scales of the manifested world. It is through these dynamics that everything that exists, from an elementary particle to a gigantic galaxy, becomes connected in an all-embracing web of relationships.

Principle of fractality

The geometry of nature is fractal and reveals itself as self-similar structures at different scales of manifestation. This principle is at the basis of Mandelbrot's theory (Mandelbrot, 1982) of fractals and demonstrates the way self-organisation works while unfolding the complex dynamics of nature. Self-similarity is a kind of fuzzy repetition; each scale has common features with every other, and yet there are noticeable differences.

Fractals are inherent in the holistic unfolding of individual, social and existential dynamics: the macrocosm is a projection of the microcosm, onto which it projects itself; the external world of individuals is a projection of the inner world of their experience, which fractally repeats that outer world; each level of development of consciousness has similarity both with the previous (less developed) and the next (more advanced) levels and yet has its own distinguishable characteristics, its own strength and weakness.

Theorems

First impossibility theorem

It is impossible to eliminate fuzziness from any explanation that tends to make sense of

The validity of this statement follows from the first two principles of fuzziology. According to the principle of connectivity, the wholeness of existence, its manifested activities and its creative potential are results of an all-embracing connectivity of everything that exists, that moves, changes and transforms in a gigantic self-organised Web of Interdependent Dynamics. According to the principle of incompatibility, it is impossible to offer precise and yet meaningful explanations related to the overwhelming complexity of this web. Hence, any possible explanation that makes sense of the integrity of existential dynamics, their unlimited actual or virtual appearance (as "manifested activities" or "potentiality to create") inevitably contains fuzziness.

The first impossibility theorem prevents fuzziology from looking for and from designing techniques to eliminate the fuzziness of our knowledge of social complexity; such techniques are hardly to be found. The fuzziness of social complexity has its deep roots in the very essence of existence - an essence whose self-propelled unfolding makes the universe "incomprehensible" to our "frail and feeble minds" - expressions used by Einstein when describing his religion. "My religion consists of a humble admiration of the illimitable superior spirit who reveals himself in the slight details we are able to perceive with our frail and feeble minds. That deeply emotional conviction of the presence of a superior reasoning power, which is revealed in the incomprehensible Universe, forms my idea of God" (quoted in his New York Times obituary of 19 April 1955).

Human "frail and feeble minds" are products of the unfolding of the mysterious essence of existence. Therefore, its fuzziness is not something "over-there" that can be objectified, rationally defined and then studied and modelled; it is deeply inside each of us and, therefore, escapes the grasp of our reasoning. It can be felt, experienced and eventually realised in life. Being out of the realm of logical formulations (no matter what kind of logic we decide to use, be it inductive, deductive, abductive, binary, multi-valued or fuzzy), the journey into the existential mystery needs "preparation", in which the reasoning power of the human mind plays an important role, to co-ordinate sense impressions, perceptions, sensations, feelings and emotions into a meaningful whole.

Fuzziology acknowledges the irreducible fuzziness of human knowledge about the essence of the existential dynamics. The awareness of this fuzziness activates the potential of fuzziology in construing reality where the conscious revelation of our deep, inner experience plays the paramount role in making sense of existence, not the intellectual speculations about the outward, "objective" world as perceived through our senses. The information from our senses inevitably passes through mental and emotional filters, consciously or unconsciously established in the process of socially informed interactions. Some of these filters can irreversibly distort the sensory information to such a degree (as the result of bias and prejudice, brainwashing or propaganda, attachments and delusions) that it entirely ceases to help people navigate the social complexity of their lives.

Second impossibility theorem

It is impossible to understand and deal with fuzziness related to a higher (more developed, expanded) level of consciousness from the point of view of a less developed level. The validity of this statement follows from the principle of fractality when applied to the unfolding of existential dynamics. From their manifestation at the scale of non-animated nature, described by the ancient thinkers as being built by fire, light, air, water and earth, dynamics unfold to express themselves at various scales (levels) of animated nature, at the scales of plants, animals and humans. The unfolding of these dynamics runs parallel with a self-propelled expansion and growth of complexity at each scale of manifestation. There is a stunning diversity at the level of minerals, and also at the levels of plants and animals.

The complexity at each level of existential dynamics' unfolding cannot be reduced to the complexity of the previous level: animals' lives are of a higher order of complexity than the life of the plants, which are themselves much richer and diverse than the "life" of minerals. When dynamics enter the human scale, it is human consciousness (as a holistic experience and awareness and knowing of our own nature and the nature of reality in which we exist and evolve) that expands and grows.

The fuzziness of knowing at each level of development of human consciousness can hardly be grasped from a lower level of consciousness. What may appear as a "fuzzy mess" for individuals with a certain level of development of their consciousness can be seen as saturated with meaning, if they exert effort and succeed in developing a higher level of awareness and intelligence, or/and in sharpening their capacity to think, feel and experience holistically, rather than solely from a more narrowly established point of view ("worldview").

Far from social elitism, being an illustration of this theorem, it serves to reinforce the distinction between knowledge as an accumulation of facts, theoretical explanations and practical skill and wisdom as holistic insights into existence born while living and experiencing existential dynamics in their all-embracing integrity and infinity. What the wisdom of Socrates could grasp was far beyond the understanding of his contemporaries. And the enigmas of life which appeared fuzzy to Socrates and kept the passion of his inquiry alive till the day he was unjustly accused and killed, quite possibly never bothered most of the Athenians at that time.

The fuzziness inherent in the deepest spiritual wisdom of the ancient Vedas, considered the oldest written text on our planet (coming to us in written form between 4,000 and 6,000 years ago) is almost impossible to grasp with the level of consciousness of our generations - consciousness deeply immersed in a constant pursuit of materialistic acquisitions, selfish accomplishments and anti-human manifestations of ego-centred power.

One practical message of the second impossibility theorem is that the life-threatening fuzziness of all the serious ecological, economical and social problems, which today's humanity creates, and by which more and more people are tormented, can hardly be solved using the present level of consciousness typical for the rulers of the developed capitalist "democracies", driven by an insatiable thirst for money and pleasures, competitive advantages and power.

Possibility theorem

We CAN understand as much of the world as we have developed and realised within ourselves. The validity of this proposition follows from the principle of fractality and from the second impossibility theorem. The principle of fractality makes us understand why the macrocosm mirrors the microcosm and the world outside reflects the world inside us, through a self-similarity that is never identity. The inner world is made not only of our senses, feelings and thoughts shaped into images, ideas, aspirations, expectations, hopes, dreams, but also of our deep spiritual attitudes and beliefs. We perceive the world around us through all of them. The power of our will is also in the inner world, together with our infinite potential to create and realise ourselves in innumerable activities. We never cease to modify the external world through actions emerging from our inner worlds.

The external world also affects the world inside us. The lower the level of consciousness, the stronger the influence of the external world, the more silent the voice of the inner world and the weaker our spiritual drives for self-realisation.

From the second impossibility theorem it follows that when we grow in consciousness, we are able to see more of its projections onto the world around us, to develop and realise outwardly more of our inner potential to create. It is then that another type of fuzziness, inaccessible from the previous levels of consciousness, starts to irritate and challenge our minds and souls.

Transcending duality and non-duality

Transcendent logic

When studying fuzziness of human understanding, fuzziology looks for ways of transcending both duality and non-duality inherent in thinking.

With duality the mind constantly asserts

Fuzzy logic based non-dualism accepts that

Spiritually enhanced non-dualism rejects the existence of dualism itself, maintaining that reality is an illusion (samsara in Buddhist terminology):

Both duality and non-duality keeps the mind entrapped in logical speculations, and may lead to confrontation, one-sidedness and error (in the case of dualistic thinking) or to compliance, confusion and passivity (in the case of non-dualistic thinking).

Any insightful act of understanding vitally needs the energy of polarities expressed in dualistic thinking, as well as serenity accompanying their reconciliation in the framework of non-dualistic thinking. The way to take advantage of dualistic and non-dualistic thinking simultaneously is through expanding our consciousness so that we can flexibly switch from one to another mode of thinking, without being attached to either.

We call the logic of fuzziology transcendent - a logic where even the duality between fuzziness (both A and not-A are true up to some degree) AND its negation - the lack of fuzziness (either A or not-A is true) ceases to exist, and researchers find themselves in a state of creative nescience or creative emptiness, characterised by extreme openness and responsiveness. In such a state we are ready to experience new dimensions of reality or discover new possibilities and meanings.

The Vedic maxim "Do not reject anything! But do not remain with anything either! Go beyond!" encapsulates virtuality of the transcendent logic and points to its possible use in fuzziology as a mind-energiser, as a stimulator of human creativity and catalyst for seeking mutual understanding and social harmony.

In the endeavour of fuzziology to transcend duality between fuzziness and non-fuzziness lies an essential difference between fuzziology and pyrrhonism - a radical skepticism initiated by the ancient philosopher Pyrrho of Elos, 4th century BC. Pyrrhonism postulates that certainty of knowledge is unattainable, so there are no ways to go beyond its inherent fuzziness. For fuzziology such ways exist and fuzziology aims at exploring them in the context of individual and social realisations of human dynamics.

Activating consciousness resonance

While exploring fuzziness, fuzziology reveals also ways of transcending it and thus expanding the field of the human inquiry. The fuzziness of understanding problems, emerging out of complexity of life as it unfolds cannot be resolved at the same level of knowledge that we have when these problems appear. (One can see here an analogy with the Gödelian problems in mathematics and other fields of knowing - they cannot be resolved using the same assumptions under which they have appeared.) Only when our consciousness is expanded or "raised to a higher level" of reasoning and understanding, then the tension fades and the problems, being seen in a new light, are no longer problems. When problems dissolve, we say that the fuzziness related to them has been transcended.

The qualitative jump in consciousness to a higher level results in transcending fuzziness accumulated in one's experience and knowing related to lower levels of consciousness. As far as consciousness is a holistic characteristic of human dynamics and not only a product of mind, the growth of consciousness is possible when the factors responsible for the integrity of all three inseparable constituents of human individuality - body, mind and soul, become simultaneously activated. We shall refer to this simultaneous activation as a consciousness resonance.

Consciousness resonance involves all factors responsible for human integrity. What are these factors? First of all, factors which contributes in keeping human body healthy and human mind capable to think and decide, no matter what kind of logic it prefers - fuzzy, binary, inductive, deductive, abductive, etc. But these factors are not enough!

Consciousness resonance cannot occur when neglecting the soul factors: among them sensitivity and responsiveness, awareness and ability to stay awake, passionate desire to get out of the "attractor" of egocentric thoughts and desires, compassion and love, willingness to explore more subtle dimensions of reality and to share with other's skill, knowledge and wisdom.

Consciousness resonance does not eliminate fuzziness. Fuzziness is an eternal companion to any process of knowing. At the same time, when conscious resonance helps us to go beyond the limitations of the fuzziness or succeed in making some problem dissolves, it opens space for new problems to emerge bringing with them new types of fuzziness to puzzle our thoughts and feelings. At any level of consciousness there are many phenomena and processes challenging the "swarm" of our perceptions, our beliefs and hopes, views and attitudes, aspirations and dreams.

What the consciousness resonance does is firing the bootstrapping algorithm of the fuzziness present at a certain level of the individual consciousness.

The consciousness resonance is a creative instant of an illumination, a flash of intuition, a sudden understanding of the truth of the phenomenon (process, event, actor) on which one's thinking and feeling has been focused. The initial impression is that the fuzziness has disappeared entirely, that one has succeeded in experiencing the truth of the studied phenomenon as it is, without using any mental or emotional filter, any borrowed-from-outside knowledge. Yes, the fuzziness has withdrawn itself - has "pulled itself with its own bootstraps" - from a certain level of one's thinking, experiencing, understanding and knowing - from a certain level of development of one's consciousness; but it has not disappeared forever. It is "ready to explode" and spread again at the new level of understanding and hence at the new level of development of one's consciousness.

The "bootstrapping" theorem

Consciousness resonance provides both the necessary and sufficient conditions for the fulfilment of the bootstrapping algorithm. The proof of this proposition lies in the holistic character of the human consciousness - it determines our humanness, it is both the cause and the effect of our human nature; without consciousness we are just animals. The three constituents of the human individuality - body, mind and soul - are three pillars, three powers supporting the individual consciousness and its ability to evolve and grow without limits. The body epitomises the human power to act in the physical world, the mind expresses the power of our thoughts and feelings (and includes the power of the human heart as a source of our deepest emotions, longings and love), and the soul connects us with the infinity of the human spirit. The resonance between the three human powers represents an apotheosis - the highest peak in the realisation of the creative potential of the human consciousness (at the level of development reached by the individual). Moreover, the resonance triggers also a further growth of the individual consciousness, as there are no other powers in the human nature to support this growth, beside those of the human body, of the human mind and heart, soul and the spirit.

The growth of our consciousness is at the same time a growth of our capacity to understand (experience, learn and know), and therefore it inevitably affects the fuzziness inherent in this capacity. When our capacity to understand increases, the fuzziness becomes "thinner" and "weaker" and folds its dynamics; when there are obstacles on the way of our understanding, the fuzziness becomes "denser", "stronger" and expands its dynamics. When the fuzziness "jumps" from one level of understanding to another, it "pulls itself by its own bootstraps". By bringing the mind power to the top of its realisation, the consciousness resonance makes it possible for the individual to "jump" from one level of understanding to another; in this sense, the consciousness resonance "provides" fuzziness with the necessary conditions to initiate its bootstrapping. And vice versa, when the fuzziness completes the "bootstrapping algorithm", it disappears from one level of understanding and appears at another, possible deeper, level (the fuzziness can never be eliminated in an absolute way). The disappearance and re-appearance of the fuzziness represent jumps in the human understanding and hence demonstrate spontaneous occurrences of consciousness resonance. So, the consciousness resonance provides also sufficient conditions for the fulfilment of the bootstrapping algorithm of the fuzziness in the individual understanding.

Consciousness resonance is like a spontaneous coherence occurring with a swarm of "agents" (insects, birds, ants, neurones, thoughts, feelings, and even people when acting under critical conditions) - all the apparent fuzziness of the swarming behaviour suddenly disappears in a magic way. "Agents" become able to act in sync and harmony, as if they are at-one - one multi-agent entity, one multi-facetted unity, one inseparable whole - a flash of understanding whose light is able to penetrate through any layer of fuzziness.

Resonance at social level

The term resonance has a clear meaning in physics - it is a process of initiating a vibratory response in a receiver that is attuned to an emitter. The emitter is considered as a source of vibrations - they can be periodic, aperiodic or chaotic. In the process of resonance these vibrations "fire" sympathetic vibrations in the receiver, the magnitude of which is often greater than the magnitude of the vibrations generated by the emitter.

We know about the existence of mechanical, acoustical, electromagnetic, quantum and superstring resonance. The Adaptive Resonance Theory developed by Grossberg (1988) and widely applied for modelling human cognitive processes by artificial neural networks, uses resonance between two major neuron fields to explain how these networks can learn to recognize, classify and predict patterns and events of the environment both in supervised and unsupervised (without teacher) modes of learning.

Human life crucially depends on the process of resonance. Lehar (1999) argues that the muscle of the heart demonstrates a kind of chaotic resonance, for "the individual cells of the cardiac muscle are each independent oscillators that pulse at their own rhythm when separated from the rest of the tissue in vitro. However, when connected to other cells they synchronise with each other to define a single coupled oscillator." In the quoted paper Lehar sees the whole brain as a kind of resonator "whose natural frequency of oscillation as a whole is observed in the global oscillations detected in the electro-encephalogram. This fundamental oscillation sweeping across the whole brain establishes a reference frame or coordinate system in the form of a spatial standing wave, and the higher harmonics on this standing wave represent the spatial percepts of objects perceived in the world, with the phase of those harmonics relative to the fundamental determining the location of the percept in the perceived world."

Resonance is widely used in descriptions of dynamic interactions at a personal or interpersonal level that are unusually effective, spontaneous, and complete.

"We say that we `resonate' with an idea of another person when we share an unusually rich set of perceptions that implies to us that we are `on the same wavelength' - another form of the metaphoric link to physical models. It is a common experience that often is striking in the strength and complexity of shared understanding, and it is associated with successful interactions in pairs and groups of people, and with universally recognized shared experiences. Productivity and creativity are evidently enhanced, and cooperative responses to emergencies and catastrophes seem to be facilitated" (Nelson, 1999).

The world wide web and Internet communication, by making possible instantaneous sharing of people's thoughts, skills and feelings serve as powerful catalyzers for the resonance to occur at the level of society.

The idea of resonance occurring at the level of society closely relates to the concept of noosphere - a term coined in 1944 by the Russian academic Vladimir Vernadsky (1863-1945) to describe a new emerging "sphere of intelligence, wherein humanity could employ its evolutionary gifts as a creative collaborative agent of evolution - and where the widening conflict between technosphere and biosphere could be transformed into synergy" (Allen and Nelson, 1986).

The same term noosphere was used in the book "The Future of Man" of Pierre Teilhard de Chardin (published after his death in 1955). He suggested that the Earth in its evolutionary unfolding is growing a new organ of consciousness, called the noosphere. The noosphere is analogous on a planetary level to the evolution of the cerebral cortex in humans. The noosphere is a "planetary thinking network" - an interlinked system of consciousness and information, a global net of self-awareness, instantaneous feedback, and planetary communication.

In order to plug in the noosphere, the individual needs to discover the "password"; the role of the password is the level of development of one's own consciousness. Without this password, the noosphere is only a gigantic pile of facts and ideas, pictures and graphics, hypotheses and theories, descriptions and explanations of findings in different branches of human knowing. It is the individual who needs to transform the pile into an integrated whole - a whole which has meaning for this individual, if and only if s/he has succeeded in discovering the "password". How to discover the password? By concentrating one's physical, mental and spiritual efforts and igniting the consciousness resonance. So, it is the consciousness resonance - the bootstrapping of the fuzziness of one's individual understanding - that can give the individual access and key for understanding the exciting secrets of the noosphere.


References

Allen, J., Nelson, M., 1986, Space Biopheres, Synergestic Press, London.

Dimitrov, V., 2002, "Introduction to fuzziology", Dimitrov, V. , Korotkich, V. , Fuzzy Logic: A Framework for the New Millennium, Physica-Verlag, Heidelberg and New York.

Dimitrov, V., Hodge, B., 2002, Social Fuzziology, Physica-Verlag, Heidelberg and New York.

Dimitrov, V. , Korotkich, V. , 2002, Fuzzy Logic: A Framework for the New Millennium, Physica-Verlag, Heidelberg and New York.

Dimitrov, V., Weinstein, A., 2002, "Use of fuzziology when dealing with hard negotiation", Dimitrov, V. , Korotkich, V. , Fuzzy Logic: A Framework for the New Millennium, Physica-Verlag, Heidelberg and New York.

Dimitrov, V., Wilson, S., 2002, "Fuzziology and lifelong learning", Dimitrov, V. , Korotkich, V. , Fuzzy Logic: A Framework for the New Millennium, Physica-Verlag, Heidelberg and New York.

Dimitrov, V., Woog, R., 2002, "Fuzziology in search of insights for understanding global economy", Dimitrov, V. , Korotkich, V. , Fuzzy Logic: A Framework for the New Millennium, Physica-Verlag, Heidelberg and New York.

Dimitrov, V., 2001, "Fuzziology and social complexity", Mastorakis, N. , Advances in Fuzzy Systems and Evolutionary Computation, World Scientific Engineering Society Press, NY, Athens.

Grossberg, S. , 1988, Neural Networks and Natural Intelligence, MIT Press, Cambridge, Mass.

Lehar, S., 1999, "Neuron Doctrine"Internet publication.

Mandelbrot, B., 1982, The Fractal Geometry of Nature, Freeman Co, San Francisco.

Morson, G.S. , Emerson, C. , 1989, Rethinking Bakhtin: Extensions and Challenges, Northwestern Univ. Press, Evanston, Ill.

Nelson, R., 1999Internet publication.

Taylor, C. et al, 2001, Greek Philosophers: Socrates, Plato, Aristotle, Oxford Univ. Press.

Zadeh, L., 1965, "Fuzzy sets", Information and Control, 8, 338-59.

Zadeh, L., 1973, "A new approach to the analysis of complex systems"IEEE Trans. Syst., Man, Cybern..

Further Reading

Greene, B., 2000The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory.

Judith, A., Pierre Teilhard de Chardin, web site http://www.