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Law of Requisite Vorticity in Human Dynamics

Vlad Dimitrov

1 Introduction

This study draws on one of the most powerful idea in cybernetics - Ashby’s Law of Requisite Variety - from the perspective of the new paradigm of complexity. According to this law, “only variety can destroy variety” (Ashby, 1958), that is, control can be obtained only if the variety of the controller is at least as great as the variety of the situation to be controlled (Beer, 1973). As the variety is an expression of the richness of the field of possible states of a dynamical system, the controller must have enough information about this field in order to recognise the differences between the states and thus to manage the system. When complexity of the latter increases, this kind of information is difficult to obtain.
Dynamic interactions of the factors influencing a complex system may lead to its chaotic behaviour and emergence of patterns able to self-organise - change and move, evolve and transform in unpredictable way. It is extremely difficult to control variety generated by chaotic and self-organising dynamics. The law of requisite variety requires from the managers to seek ways how to destroy, suppress, and eliminate variety expressed in systems behaviour in order to manage it.
For example, any centralised form of managing human dynamics is a kind of application of the law of requisite variety. The living variety produced by humans’ drives towards self-realisation becomes destroyed by an imposed ‘requisite’ variety aimed at facilitating realisation of totalitarian ways of control. Today’s economic globalisation does almost the same: the variety of possible developments of the national economies is reduced to only one global economic model - a model whose realisation suits best the interests of the greatest beneficiaries and leaders of the economic globalisation in the developed capitalist world - a bunch of monstrously rich financial institutions and corporations.
At the time when the law of requisite variety was introduced, researchers were obsessed with the idea of making variety provided by nature comfortable for humans (or at least for those who can afford the comfort). The ecological degradation that we are witnessing today is partly a result of this obsession - an obsession, which still thrives (under even more sophisticated and more dangerous forms) in the reductionist reasoning of many researchers and scientists, leaders and institutions, as well as in the profit-driven actions of their financial supporters.
Can we live in harmony with the variety of nature, life, and society without destroying it, without pushing it to fit the procrustean bed of our partial models aimed at exercising power and control?
The way to live and co-evolve with the dynamic variety without killing it is through understanding:
-        the forces and energies which constantly drive the variety from within, and
-        the conditions and factors which strengthen or weaken (accelerate or decelerate, sustain or destroy) its unfolding dynamics from without.
The stunning variety, which we see and experience in nature and life, in ourselves and society, is a manifestation of the self-organising capacity of the never-ceasing complex interplay of existential dynamics - forces, energies, substances and forms. These dynamics are all-pervading and the laws which rule them are universal, although the scales where the laws operate are different.
The forces of gravitation, for example, between the heavenly bodies are displayed at a macro scale where the laws of heavenly mechanics work; the force of gravitation acting upon a falling stone acts at a mezzo scale where the laws of Newton are applicable. The gravitation between the elementary particles manifests at a micro scale of matter where the laws of quantum mechanics operate, while the ‘gravitation’ of one person to another manifests at the scale of human dynamics and needs psychological ‘laws’ of sympathy and solidarity, compassion and love.
Whatever the scale, gravitation is an expression of an universal existential interconnectedness: no thing and no being can exist in isolation - by itself, in itself or for itself - but only in dynamic relationships with other things and beings (Dimitrov, 3001).
By stating that only variety can destroy variety, the law of requisite variety focuses on the external manifestation of dynamic relationships. By stating than only vorticity can create vorticity, the law of requisite vorticity, which is introduced below, relates to the inner sources of the dynamic interrelationships. Before explaining the law of requisite variety, let us ‘zoom’ into the meaning of the term vorticity.

2 What is Vorticity? 

As we discussed in the first chapter, vortices relate to the most essential property of complex dynamic interactions - their ability to self-organise. Both the maelstrom in the stormy waters and the tornado in the stormy airs are examples of natural vortices; they seem to have hidden engines which produce inwardly directed centripetal (‘sucking’) forces along the vertical axis of the whirling streams of water or air, and outwardly directed centrifugal forces. Both types of forces can be of significant magnitude, as in the case of tornado or hurricane. Of course, there are no hidden engines; it is the dynamic interaction of the ‘out-of-equilibrium’ streams of fluid entrained in a whirling motion that ‘fires’ emergent forces.
Once emerged, the inwardly directed force keeps the integrity of the vortex; there are no boundaries between the streams, as they permeate each other and the vortex appears as a holistic self-organised, self-propelled, and self-sustained structure. The vortex ‘refers’ to itself when rotating its fluid, and not to any external source of energy. Moreover, every vortex ‘speaks’ its own language through the magnitude and direction of its inner force - a force that keeps the interacting masses of fluid centred; without such a force the vortex will immediately dissolve in the flow.
When studying air dynamics, and particularly the lift achieved by an airflow over a spinning cylinder, the Russian researcher Nikolai Joukowski (1837-1931) found that this lift depends on the ‘vortex strength’ directly proportional to the angular velocity of spin of the cylinder; later, this result was absorbed by a law known as Kutta-Joukowski Law: the circulation around a contour that contains a group of vortices is equal to the sum of the enclosed vortex strengths (Anderson, 1991).
We consider vorticity as a property of the flows to form vortices. It is clear that if the fluid (air, water, plasma) is at rest, it has no vorticity, although the mere motion of the fluid does not guarantee that it has vorticity. A branch of science called fluid dynamics explores the mystery of vorticity; the research in fluid dynamics explains much about how the vortices behave and very little about why they behave in a certain way or what ‘fires’ their self-organising formation.
What seem to be crucial for realisation of vorticity are the dynamic interactions (in the form of positive and negative feedback) between streams which differ in their characteristics and yet belong to one and the same fluid. In a way, vorticity emerges out of variety of the dynamically interacting streams; when the interactions become recursive (repetitive), and their intensity increases beyond a certain level, variety transforms into vorticity which seeks embodiment into a vortex. It is obvious that the external conditions can facilitate or impede this ‘mysterious’ transformation. For example, a specific shape of the river’s bed, the presence of rocks, stones or fallen trees may help for formation of a recursive type of local interaction of the water streams, which may result in the emergence of a whirlpool.
Examples of natural vortices are whirlpools and eddies, whirlwinds and dust devils, tornadoes and waterspouts. The hurricanes and typhoons also carry powerful vortical spirals in their inner central zones called ‘eyes’. The spiral galaxy represents a gigantic disc shaped vortex, the inwardly centred force of which seems to keep together all the bodies rotating or wandering within the galaxy. The DNA molecule displays also a thread shaped vortical structure. Vortical are the structures of the eyes of mammals and their reproductive organs; vortical is the structure of the human embryo, of the unfolding spiral of the leaves and branches appearing on the stems of growing plants and trees.
Viktor Schauberger (1885-1958), a genius Austrian inventor of engineering constructions encapsulating the mechanics inherent in the “multiple movement” taking place in the vortex, has pointed out shapes that sustain this kind of movement everywhere in nature: “the beds of creeks and rivers, the gills and fins of fishes, the wings of the birds, blood vessels - all these give impulses to vortical movement.” (Schauberger, 1998).
Schauberger was convinced that life is sustained by a vortex-like, centripetal, ‘implosive’, type of movement. This type of movement is associated with coolness, suction, growth, healthiness and wholeness, while the opposite, the centrifugal, explosive, ‘radiative’ movement, generates heat, pressure, stress, illness, fragmentation and death.
The implosive movement is creative and neg-entropic, that is, it does not dissipate energy. Unfortunately, all the engines, which our civilisation uses, are based on explosion, heat and pressure. According to Schauberger, the use only of explosive movement increases the entropy and leads eventually to the destruction of nature.
Although nature knows how to balance the both types of movement (inwardly directed, centripetal movement and outwardly directed, centrifugal movement), and thus to regenerate itself and evolve, the human obsession with internal combustion engines, nuclear sources of energy (like atomic power plants, missiles and bombs), computers, lasers, microwave technologies and other type of ‘radiative’ and explosive hi-tech makes it hard for nature to restore its balance.

3 Existential Vorticity

In the wholeness of the existential dynamics, where everything constantly moves (emerges, sustains, disappears and re-emerges again), must be a centre, an essence that holds all the whirling dynamics in an unbreakable unity (Bohm, 1980).
Unity is sine qua non for the existential dynamics; they change, adapt, evolve and transform from one material embodiment to another only in integrity - interconnection, interrelationship and interdependence. As the existential dynamics have always been and will always be, their uniting centre seems timeless (permanent, eternal).
The spiralling wholeness of the galaxy looks like a gigantic vortex with a centre that holds together all its swirling dynamics. The infinity of the existential continuum seems to consist of countless number of galactic vortices; the centre of each of them mirrors and relates to the centre of a larger one, in a similar way as the centre of our solar system mirrors and relates to the centre of our galaxy, and the centre of our galaxy relates to the centre of a larger 'mega-galaxy', and so on ad infinitum.
The study of the nonlinear vortical dynamics of the whirlpools and tornadoes have shown that at the central axis of any highly energised whirlpool a kind of 'hollowness' forms and sustains a cavity, an emptiness, with no material filling in it. Such hollowness can be theoretically expected along the central axis of the all-embracing existential vortex. Being free of material substratum, the centre is free from the effect of time: the emptiness persists along the axis without changes, without birth and death, growth and decay. While empty from material substrata, the centre is impregnated with an immense creative potential, similarly to the potential of the hollowness located along the axis of a whirling black hole - a hollowness full of gigantic sucking power.  
Being simultaneously voidness (void of substance) and plenitude (full of inner energy) and something else, which transcends the duality of being full or empty (something which is neither voidness nor plenitude), the hollowness of the centre of the existential vortex can stand for a kind of abstraction that is not transient but eternal in the whole existence.
All embodied-in-matter motions, dynamics and interactions, all animated and non-animated emanations of existence gravitate to the voidness in order to release their energy when undergoing decay, and to the plenitude in order to be filled with energy and emerge as manifestations of different (transformed) forms of matter, in accordance with the law of conservation of energy. This makes the vortex pulsate in a unique existential rhythm, a rhythm reflected in the pulsations and cycles of all the forms of nature.
While keeping the integrity of the existential dynamics, the impregnated-with-energy hollowness at the centre of the universal vortex endows these dynamics with ability to self-organise into various levels or scales; one can distinguish between the levels of non-animated and animated dynamics, between the levels of plants, animals and human dynamics. Each level reveals sub-levels of self-organisation that share similar features with one another; an analogy can be found with the fractal structures of Mandelbrot, which reveal geometrical similarity between their scale levels, when zooming into them. Each level has its own rhythm - a rhythm that reflects the universal rhythm of the whole existential vortex.
One can hardly imagine how incredibly great must be the magnitude of the overall self-organizing drive in the universe that serves to support all the levels of the existential dynamics. This drive must act as an immense self-propelling engine (similar to the 'engine' of a gigantic tornado) that feeds with energy the whole universe with its astonishing variety of ever-moving, evolving and transforming phenomena and processes at innumerable levels of manifestation. One can recognise the work fulfilled by this universal engine in the blossom of a flower as well as in the waves of the ocean, in the pulsation of a simple cell as well as in the beats of our hearts, in the rhythm of our breathing as well as in the rhythm of the cycles of the solar activity.

4 Vorticity of Human Dynamics

Human dynamics form a specific level in the holistic dynamic structure of the universal existential dynamics. The challenge is to be aware of the integrity of this structure and to act so that to preserve its wholeness. Unfortunately, often the human society acts in the opposite direction.
The impediment of the self-organising urge of nature through the ever-increasing production of infinite variety of artificial (human-made) forms, using explosive and ‘radiative’ types of energies and technologies, inevitably backfires on us, as we are realisations of the same urge. It is much wiser to explore what propels and sustains natural dynamics, and to learn how to ‘collaborate’ with them without destroying their self-organising impetus and therefore their vorticity.
The basis for this kind of understanding and learning can be the following transparent and self-evident presumption: ‘they’, the self-organising forces of nature, and ‘we’, the humans, are inseparably connected. Moreover, our ‘internal vorticity’ – vorticity that supports the individual impetus for self-finding, self-fulfilment, and self-realisation - is nothing but a manifestation of vorticity of nature, of its self-restoring, self-supporting and self-unfolding capacity. In the largest part of us, this type of vorticity is still in its potential (‘seed’-like, dormant) state. What we learn in schools, universities and work places is how to dissipate our energy outwards: to produce an external variety and not an internal vorticity. When the energy is exhausted, we become sick, old and helpless. And that is what we call life - life with variety but without vorticity, ‘life’ which moves towards death (life which implies death, how it can be called “life”?)
Vorticity implies creating energy, charging our life ‘batteries’, going deeper into ourselves in search for the inner centre, for the umbilical cord which connects us with the never-exhausted treasure of energy in the universe, with its timeless essence.
Vorticity of human dynamics is a journey inward and not so much outward, although the splendour of nature can facilitate the inner journey. Still we know very little about this journey. All our studies have been directed towards the world around us: to explore and use it, to conquer and exploit it, to classify and separate it, to possess and hence to destroy it. Most of us either do not know what does an ‘inner journey’ mean or know about it only as a theoretical abstraction or a religious dogma, and not as a living experience.
Without ability to create vortices out of the ‘swarming’ dynamics of our thoughts, and beliefs, feelings and emotions, aspirations and dreams, all the energies they carry irreversibly dissipate in the space around, while bringing more pain than joy, more illness than health, more suffering than happiness, more thoughts of sadness than waves of inspiration.
A wheel can move only because in its centre there is something, which never moves, which remains unmoved. The ‘wheel’ of the world that we perceive through our senses constantly moves, but there is a centre inside which remains unmoved, as it mirrors the timeless essence of the all-embracing existential vortex. It is a challenge to discover this centre; no vorticity can manifest without a centre. With zero vorticity we are in a standstill, we do not evolve. Outwardly we move, we produce variety and entropy, ‘order’ and chaos, but this has absolutely nothing to do with our inner growth.
There is a tremendous difference between growing as a whole and growing only in our mental ability or in our ability to feel or sense or experience. When only one part grows, it leads to disharmony, to development of a kind of cancer, be it physical, emotional, mental or spiritual. When the growth is holistic, it is harmonious and healthy, and leads to wisdom. How to create vorticity?

5 Law of Requisite Vorticity 

The law of requisite vorticity states that only vorticity can create vorticity. Vorticity is like energy and energy, according to the law of conservation, can only be transformed from one type of energy to another. In other words, only energy can create energy: from a state of potentiality, energy becomes motion, explosion, growth, transformation, and then again ‘implodes’ into potentiality. Vorticity behaves in the same way; once ‘imploded’ in the fluid dynamics, it may turn into whirlpools and tornadoes (when appropriate conditions arise), and then again to calm down into a dormant state. Vorticity is energy, and the proof of the law of the energy conservation is proof of the law of requisite vorticity.
Vorticity at the macro scale of the existential dynamics projects onto the scale of the human dynamics. The way we ‘fire’ (educe, create) vorticity in our inner dynamics is by ‘connecting’ ourselves consciously to the existential vortex, to the powerhouse of the universe. There is no other way. One alone is responsible to make this connection as a result of his (her) own efforts.
Theoretical knowledge, philosophy and mere logical speculations are not enough to make vorticity embody into a living vortex of one’s dynamics. It is impossible to borrow vorticity from somebody else, from a book, from a teacher, from a guru. Those who have succeed to connect themselves with the timeless essence of the existential vortex can be of help to others not so much through preaching and instructing, but through their own ways of being and behaving. The inspiration power of one’s words lasts only for a while, the inspiration power of one’s own life lasts forever.
When centred, we are able to find who we are at present, to accept ourselves as being here and now, and not as we were before or as we imagine ourselves in future. When centred, we are real and our dynamics are authentic and not identified with false masks and pretended behaviour. When centred, our inner energy is focused, our attention keeps concentrated and we stay alert, vigilant and aware of what we experience, feel and think.
There is another formulation of the law of requisite vorticity, which is analogical to the Kutta-Joukovsly law: Vorticity of a group of individuals is not less than the sum of the individual vorticities. “Not less” implies that vorticity, once ‘fired’ in the participants of the group, can increase as a result of the interactions within the group. It is important to underline that, although the group interactions can increase vorticity of the individual dynamics, they cannot replace the earnest and persistent efforts required for an individual to keep connected with the centre of the existential vortex.   

6 Vorticity Activators

Vortex is a metaphor of oneness which is centred and which creates and preserves energy. There is no rigidness in the vortical structure, no pre-designed boundaries, no extremes and polar points, no division! The streams are whirling and yet relaxed, ‘surrendered’ to the vortical dynamics and yet responsible for their integrity, ‘receptive’ and yet preserving their creative energy. There are no conflicting and resisting points in the liquid masses, but open-for-interaction streams involved in a genuine play.
Because of this, the metaphor of vortex (and vorticity) is extremely powerful in the context of human dynamics.  When our inner dynamics become centred in a self-sustained vortex, we are awakened and alert, ‘undivided’ and focused, sensitive and receptive. Vorticity cannot emerge in us, if we are disconnected from the supply of energy created by the existential vortex. In order to become a vehicle for this energy and thus to incite the spin of our vorticity, we need to be relax and at ease with ourselves, humble and surrendered, authentic and genuine. We need to throw our artificiality, our false attitudes, routines, pretence and prejudices – they always act as inhibitors of human creativity. The will to power and the ego are the most serious obstacles for firing vorticity, because they demand a great amount of dissipative energy. Pride and anger, greed and fear, arrogance and ignorance, competitiveness and violence also impede the vortical implosion.
Our research in social fuzziology – the study of fuzziness (uncertainty, vagueness) inherent in human knowing and understanding (Dimitrov and Hodge, 2002) reveals ten qualities of human dynamics, which stimulate vorticity:
* thirst for understanding the natural forces acting both in us and the world around;
* not fighting with the energy hidden in the ‘seeds’ of our own potential, but on the contrary, helping and protecting these seeds, giving them ‘soil, water and light’ to grow;
* not to control but understand;
* to persist in mastering the power of our minds and wills and not obeying blindly their dictate;
* not to waste energy for suppressing the urge for self-fulfilment;
* not to reject the known but not to accept it either, to move beyond;
* not to be afraid of the unknown;
* not to force the flow of existence to follow one’s desires, but to put efforts in understanding and riding on its dynamics;
* not to discriminate only between the polar points in the life dynamics, but to see the running current which make these points one;
* to be ourselves and not imitate or repeat what other think and say;
* not to yield to customs and traditions, instructions, rules, prescriptions and directions.

The three ancient methods of relaxation, concentration, and meditation can help one’s search for  peace and centre. In a state of deep relaxation, when not only the physical body of the practitioner is free of stress and tension but also the minds and heart are calm and peaceful, one can experience the energising effect of the centre of the inner dynamics. After such an experience, one feels like being born anew, charged with natural energy, the effect of which is similar to the effect of inspiration. Because of this re-vitalising effect, relaxation positively influences the health of people, brings peace and calmness to mind and fills the hearts with warm feelings of kindness and good will. It is in the state of relaxation, when the mind becomes silent and the obstacles, which the ego unconsciously or consciously creates on the flow of the life-supporting energy, gradually dissolve.   When there are no obstacles, the flow of energy is ready to activate vorticity of the inner dynamics.
Concentration seems to be opposite to the relaxation. The energy, which freely moves through every single cell of the human body, becomes focused on visual images, mental constructs, spiritual beliefs, certain points (organs) of the body, the rhythm of breathing, etc. Concentration stops mind jumping from one idea to another and thus strengthens its capacity to understand – analyse, synthesise and intuit.
Mediation helps practitioners 'listen' to the rhythm of the existential vortex, and makes them experience those blissful oceanic feelings of union with the timeless essence. Meditation combines the effect of relaxation (peace, calmness and tranquillity) with the effect of concentration (sharpening the flow of mental or emotional energy). In the oldest scriptures of humanity – the Hindu Vedas - the stage of mediation is considered deeply spiritual, while the life-supporting rhythm of the universe is characterised as divine.

7 References

1.     Anderson, J. (1991) Fundamentals of Aerodynamics , McGraw-Hill, New York.
2.     Ashby, W.R. (1958) “Requisite Variety and its Implications for the Control of Complex Systems”, Cybernetica , 1(3):83-99.
3.     Beer, S. (1973) Brain of the Firm , John Wiley, Chichester.
4.     Bohm, D. (1980) Wholeness and the Implicate Order, Routledge, London.
5.     Dimitrov, V. (1998) “Communication as Interaction in Synergy with Uncertainty”, Internet publication ,  
6.     Dimitrov, V. and Hodge, B. (2002) Social Fuzziology , Physica-Verlag, Heidelberg
7.     Schauberger, V. (1998) Nature as Teacher , Gateway Books, Bath.

Copyright, 2002, V.Dimitrov