December 1986

## Introduction

Creation is elusive. It defies definition and attempts at reduction.

At the same time, creation is unquestionably important. This paper is not a courageous attempt to precisely define creation — it only attempts to clarify my understanding of a beautiful process underlying nature at all levels, a process at the heart of not just our existence, but all existence. As Rollo May wrote, “We express our being by creating. Creativity is a necessary sequel to being.”[1] I would go further to say that being is a necessary sequel to creation.

After a treatment of some of the problems related to the study of creation, we will be lead to a discussion of its form. One of the main purposes of this discussion will be to show that the process of creation has a similar form in many different realms, a form that is contained within itself, a self-similar form. The Mandelbrot set, a recently discovered mathematical form, also has this property of self-similarity. And the connections between the Mandelbrot set and creation go much deeper, leading us along a path rich with diversity. From mathematics, logic, and computers, we will move on to descriptions of complex systems of all kinds. Along the path of this discussion, we encounter cells and psyches, paradigms and particles, societies and sciences. A unity was created as I walked along this path through creation. It is my hope that I can show you a glimpse of it.

## The Fallacy of Isolation

In our efforts to understand the world, we have chosen to focus our attention, to divide, to categorize, to separate part from whole. Although this method is very effective, it has carried with it the implicit assumption that we can come to a complete understanding of an individual, isolated entity, without regard to its surroundings. (We are focusing our attention on this sentence, but is the entire meaning contained within the parentheses?) This method of isolation assumes that the world is completely ordered in time and space and conforms to our concepts of causality and localization. The idealization of isolation has plagued human thought, and the study of creation is not immune.

The concept of creation that is loosely thrown around contains an illusion. In my mind, at least, the very word ‘create’ tends to implicitly contain the idea of autonomy, the idea that while I am the cause of my creation, nothing is the cause of me. But to think of myself as an isolated, uncaused entity is an oversimplification. We use the word ‘self’ and imagine an autonomous entity. I say ‘particle’ and think of an isolated point in space, whose identity is not dependent on its surroundings. But to confuse our idealizations with reality is to forget that reality always proves to be much more complex end subtle than our conceptions of it. The natural world does not contain perfect points, but fuzzy clouds. The creation of a new organism depends on its environment, not just on its genes. The creation of a new theory In science depends on the societal conditions, not just on new data or theoretical developments. When insight hits us, surely we cannot deny that our environment usually plays an important part. The idealization of isolation ignores the encounter I have with my environment, the interaction between the particle and the space around it. It is to consider a part of nature a closed system when there are no closed systems in nature. Thus any description of a system in terms of causes which are isolated from the system will be incomplete. This incompleteness is a necessary consequence of isolation. Understanding this property of closed systems in detail will help us understand the elusive character of creativity.

## Godel’s Theorem and Incompleteness

Instead of closed natural systems, let us consider closed formal systems, isolated portions of the world of thought. Now imagine a formal system consisting of a set of axioms and rules of logical inference. Can the propositions in such an isolated system be completely understood on the basis of its axioms and rules of inference? Is there an incompleteness in our description as a result of its isolation? In 1931 Kurt Godel proved that many such systems are indeed incomplete. His proof demonstrated that “all consistent axiomatic formulations of number theory include undecidable propositions.”[2] In other words, there are true statements in mathematics which can neither be proved nor falsified using the rules contained within the system. Thus the system is incomplete in the sense that every true statement cannot be proved. There are truths which cannot be reduced to first principles. Thus, certain truths defy logical justification, some truth cannot be reduced. Godel’s theorem places limits on reduction in formal systems, it tells us that provability is a weaker notion than truth.

Now consider a formal system consisting of a set of axioms and rules of inference which correspond to the laws of nature. Godel’s theorem then suggests that this formal system may contain truths which cannot be proved, i.e. phenomena which defy reduction to natural law. While these phenomena elude, in principle, any explanation based on the laws of nature, they are still consistent with them. I am proposing that creation is such a phenomenon, that it must be studied as an irreducible phenomenon of nature, that it is a whole greater than its parts. This breaks the spell of the ‘Laplacian delusion’, as Polanyi calls it. In other words, all experience is not reducible to atomic motion, as we have been deluded into believing. For Ilya Prigogine, the second law of thermodynamics plays the creative role in the natural world: “the second law introduces a new irreducible element into our description of nature. While it is consistent with dynamics, it cannot be derived from dynamics.”[3]

Several people who have written on creativity also believe that it eludes logical explanation. Like any creation, an act of human creativity, May writes, “[cannot be] understood by reducing it to some other process.”[4] Nor can a new paradigm be understood in terms of “a reinterpretation of individual and stable data,” as Kuhn points out [5]. And Polanyi believes that “discovery is creative, in the sense that it is not to be achieved by the diligent performance of any…specifiable procedure.”[6] And Hausman comes very close to what we have concluded earlier: “the presence of novelty in a created result is to be taken as fact-as that which is at least phenomenally given. I see no way of ‘proving’ this point”[7]. In their book on fractals, Peitgen and Richter stress that “it is no longer sufficient to discover basic laws and understand how the world works ‘in principle.’ It becomes more and more important to figure out the patterns through which these principles show themselves in reality. More than just fundamental laws are operating in what actually is.”[8]

This discussion of the limits of reduction reveals the source of a fault in the claim that since creativity eludes explanation in terms of natural law, it is not a phenomenon of nature. The fault lies in the assumption that all phenomena of nature are necessarily reducible to natural law. Just as provability is a weaker notion than truth, reduction to natural law is a weaker notion than a phenomenological ‘truth.’

## Prediction and Creativity

Prediction is closely related to reduction. If we can reduce a result to specific known causes based on certain natural laws, then similar effects can be predicted. But if a phenomenon cannot be reduced to natural law, then we have no way to make certain predictions. Thus this class of phenomena obtains s quality of ‘spontaneity,’ happening without any knowable cause. In the introduction to their anthology on creativity, Rothenburg and Hausman claim that ‘it is the essence of creativity to defy prediction. . .the phenomenon of creativity affirms the presence of discontinuity and spontaneity in the world.”[9] Far from being ‘beyond’ natural law, the spontaneous nature of creation simply means that it is beyond description in terms of natural law.

An analogy is helpful in understanding this point. Consider the two classes of real numbers: the rational and the irrational Now recall a property of their decimal expansions that can he used to distinguish between these two types of numbers: rational numbers have repeating, ‘orderly’ decimal expansions, whereas irrational numbers have non-repeating, ‘chaotic’ expansions. As a consequence, we can predict the millionth digit in the expansion for a rational number: it has a certain pattern that is repeated, which allows us to deduce the digit in an arbitrary position. But we cannot predict the millionth digit of an irrational number, for there is no pattern. It is necessary for us to carry out a calculation. Now the analogy should be clear. Rational numbers correspond to the orderly phenomena which allow prediction and reduction to natural law. Irrational numbers, on the other hand, correspond to the chaotic phenomena which are unpredictable and irreducible. Moreover, just as an understanding of nature strictly in terms of predictable phenomena is incomplete, an understanding of the real numbers in terms of rational numbers is also incomplete. We cannot reject phenomena which defy reductionistic explanation any more than we can reject numbers that have non-repeating decimal expansions. If we were to demand that all real numbers have predictable decimal expansions, we would be forced–in the case of irrational numbers–to make probabilistic predictions. Similarly, when we impose a reductionistic description onto the world, we commit ourselves to a probabilistic description of irreducible phenomena. Chance is a fabrication due to our universal application of reduction. It is not God who plays dice, but ourselves.

Not only are these ‘irreducible’ phenomena present in the world, but they are vital to it and proliferate the universe at every level. As Prigogine puts it, “Wherever we look we find evolution, diversification, and instabilities. Curiously, this is true at all levels, in the field of elementary particles, in biology, and in astrophysics, with the expanding universe and the formation of black holes.”[10] Thus at all scales the world is a mixture of not just the ordered but the chaotic, not just the reducible but the irreducible. But while we know all to well how to describe and predict the ordered and reducible part of the world, we are left crippled in our attempts to describe and predict the chaotic and irreducible part. Do we have any hope of making the irreducible intelligible?

## Attempting to Understand Creation

In their attempts to make creativity intelligible, Rothenberg and Hausman adopt the paradoxical view that “Creativity is both determined and undetermined at the same time.”[11] May suggests that “it must be the totality of ourselves that understands, not simply reason.”[12] Jung explains creativity as an expression of archetypes rising from the collective unconscious, which is not in direct contact with consciousness.[13] Kuhn tries to understand creation in science by questioning the idea of development-by-accumulation and proposing the idea of a paradigm.[14] All of these approaches to understanding creativity question the use of old methods and propose a new approach based on a combination of causality and acausality, or intellect and imagination, or the conscious and unconscious, or normal science and revolutions. Opposites were brought together into conflict by these people, and in their effort to unite them some sort of understanding was formed.

In the Book of Genesis, God separated the heaven and the earth, the night from day. Space and time were each divided and ordered. To understand the chaotic, the irreducible, the unpredictable, we must go beyond just dividing space, and bring closed systems together with their surroundings; we must go beyond just dividing time, and unite cause with effect.

In attempts to understand the creation of new states of order in complex systems, Prigogine discovered a new meaning of time beyond cause and effect. And Mandelbrot’s fractals, which turn out to be intimately connected to such complex systems, have revealed new forms in space beyond classical topology. Prigogine describes chaos in time, while fractals describe the chaos in space. Understanding how complex systems and fractals make creation more intelligible, we hope to see how they are similar to the other attempts to understand creation.

## The Mandelbrot Set and the Meeting of Opposites

Although there are many different types of fractals, we will concentrate on one particular fractal of primary significance: the Mandelbrot set. This set is defined in terms of a nonlinear iterative process in the complex plane. To better understand this we will return to our analogy involving rational and irrational numbers and show how they are solutions to certain linear and nonlinear equations, respectively.

First, we recall that polynomials can be classified by their degree, or power of x. For example, there are first degree polynomials (ax+b), second degree polynomials (ax^{2}+bx+c), and so on. The zeros of a polynomial are the values of x for which the polynomial is equal to zero. Thus, first degree (linear) polynomials have one zero: -b/a, and second degree (non-linear) polynomials have two: -b +/- [b^{2}-4ac]^{1/2})/2a. Now we notice that for the case in which our polynomials have integers as coefficients, linear equations have rational zeros while nonlinear equations have zeros which can involve irrational numbers. Thus, allowing irrational numbers (with their unpredictable decimal expansions) into our world of rational numbers (where all decimal expansions repeat) is analogous to considering nonlinear as well as linear equations.

The iterative process which is used to define the Mandelbrot set also involves a nonlinear equation, and it is this nonlinearity that makes it so interesting. To understand the iterative process, we will again return to the problem of finding zeros of polynomials. Newton developed an algorithm which determines the zeros of any nonlinear polynomial. His method involves initially choosing an arbitrary point x_{0}, which is an approximation to one of the zeros, and then finding a point x_{1}, which is a closer approximation to that zero. The value x_{1} is then used to find a closer x_{2}, which is used to find x_{3}, and so on. Thus, this process of iteration yields a series of numbers x_{0}, x_{1}, x_{2}, x_{3},… which converge to a zero of the polynomial. Since a different choice of x_{0} may result in series which converges to a different zero, we may divide the real line into regions corresponding to each zero. All x_{0} in one region will ultimately converge to one zero, while all x_{0} in another region will converge to a different zero.

The Mandelbrot set is simply those points c_{0}, in the complex plane for which the iterative process for a second degree polynomial converges. Since the iteration process converges to a point or a repeating sequence of points, the Mandelbrot set is analogous to the set of rational numbers. Points outside of the Mandelbrot set correspond to the set of irrational numbers, because their iteration process does not converge to any repeating sequence. The boundary between the two regions represents the transition from the convergent to the divergent. This is where we move from the rational to the irrational, from the predictable to the unpredictable, from reducible to irreducible, from causal to acausal, and from order to chaos. The boundary is the beautiful and intricate region where these opposites meet in conflict. It is where reason meets passion, where freedom meets limitation, where life meets death. It is at this boundary that dialectical tension is manifested in its mathematical form, and it is our love for its beauty that drives us toward it, toward creation.

## Creation and The Bridge Between Opposites

The beauty at the boundary of the Mandelbrot set can be quite exciting. It has been said that pictures of the Mandelbrot set “demonstrate that out of research an inner connection, a bridge, can be made between rational scientific insight and emotional aesthetic appeal; these two modes of cognition of the human species are beginning to concur in their estimation of what constitutes nature.”[15] Similar bridges have been seen at the boundary between opposites mentioned by many other people studying the form of creation. We will look at several now.

Rollo May writes, “we must be fully committed, but we must also be aware at the same time that we might possibly be wrong. This dialectical relationship between conviction and doubt is characteristic of the highest types of courage…”[16] And for May, it takes courage to create. It takes courage to confront the boundary of chaos, to fight the status-quo and upset order. “Creativity itself requires limits,” he says, “for the creative act arises out of the struggle of human beings with and against that which limits them.”[17] For May, our very consciousness itself is the result of a dialectical tension.[18]

Michael Polanyi explains creativity in the sciences with his concept of personal knowledge, which forms a bridge between the subjective and the objective, between the explicit and implicit. Kuhn sees the creation of scientific knowledge as a mixture of evolution and revolution. Jung sees creativity in terms of a meeting of the conscious with the unconscious. Prigogine describes the development of novelty in complex systems in terms of order and chaos. His theory of creation is the result of “Two conflicting views of the physical universe: the static view of classical dynamics, and the evolutionary view associated with entropy. A confrontation between these views has become unavoidable. Far a long time this confrontation was postponed by considering irreversibility as an illusion.”[l9] Prigogine refused to deny the irreversible, the irreducible, the irrational, and instead sought to unite them with their opposites. His view of creation in complex systems was a result of this confrontation, and it forms a more concrete bridge between fractals and the other ideas of creation we will discuss.

## Complex Systems and the Form of Creation

In Prigogine’s attempts to understand the process of creation, he begins with a criticism of older treatments:

“Classical physics, even extended by quantum mechanics

and relativity, gave us relatively poor models of time

evolution…this theoretical framework seems to indicate

that in some sense the present already contains the past

and the future. We shall see that this is not so. The future

is not included in the past.” [20]

Prigogine’s discussion of the Laplacian delusion makes explicit the connection between the nonlinear iterative processes of the Mandelbrot set and the evolution of complex dynamical systems. His thesis outlines three important properties of irreversible phenomena: “First, irreversible processes are as real as reversible ones…Second, irreversible processes play a fundamental constructive role in the physics or the world. . .Third, irreversibility is deeply rooted in dynamics.”[21] For Prigogine, irreversible processes correspond to the irreducible phenomena which we have discussed earlier. Thus by affirming the reality of irreversible processes, he does not limit nature to the reversible, the predictable, or the ordered. In fact, these irreversible processes give rise to novelties at the transition between order and chaos. And while irreversibility, like creation, is unpredictable and irreducible, it is still a natural phenomena, for he shows us its roots in the natural laws of dynamics.

The physical laws of dynamics are described in the language of mathematics by differential equations. These equations define an iterative process similar to the ones mentioned earlier that are used to generate the Mandelbrot set and to find zeros to polynomials. Given the initial coordinates (p_{0}, q_{0}) of a particle, this process generates the future coordinates (p_{1}, q_{1}), (p_{2}, q_{2}), (p_{3}, q_{3}),… When the differential equation is linear, as is usually the case, this iterative process yields a predictable sequence. In other words, we can deduce the position of the particle at an arbitrarily time in the distant future (or past), just as we can deduce any digit of the decimal expansion of a rational number. But if the differential equation is nonlinear, the sequence cannot always be predicted for arbitrary times in the distant future, just as with the irrational solutions to nonlinear polynomials. The sequence can converge for certain initial values, but for other initial values arbitrarily close, the sequence could diverge into chaos. In the case of non-linear laws, then, we can have chaos, and unpredictability.

One might argue that since the initial coordinates are known, we could compute the future position step-by-step, just as we generate the digits in the expansion of an irrational number, and ‘predict’ the outcome at any arbitrary time in the future. Although digits cannot be predicted from a pattern, they can nonetheless be generated by iteration. The problem with this objection is that for sufficiently complex systems, it is impossible in principle for all of the initial coordinates to be determined with sufficient accuracy to predict the behavior after long periods of time. Since we are not omniscient, we must be content with an approximate knowledge of the initial conditions. Thus, to trace the development of our system, we carry out the iteration for every initial condition within our margin of error. But, as was stated earlier, arbitrarily close initial conditions can lead to sequences with qualitatively different behavior. Thus we have no way of predicting even approximately where the particle will be, for it may diverge into chaos, or it may not. (And to complicate matters, fluctuations outside of the system influence the system’s evolution as well, and these influences are unknown, and thus enter into the description as ‘random’ fluctuations.)

The essential ingredient for this chaotic behavior is the nonlinear differential law, for only in the case of a nonlinear law does the iterative ‘feedback’ process amplify small variations in initial conditions thereby producing such extreme differences in the resulting behavior. What makes some laws linear and others nonlinear is the distance from equilibrium. A system near equilibrium has a linear restoring force, and small displacements from equilibrium will result in predictable behavior, acting to restore the equilibrium. But when the system is pushed far from equilibrium, the equations governing its behavior are no longer linear. Strange things happen. Unpredictable, chaotic states are formed, which are followed by new states of order, new states of equilibrium. Order is created out of chaos.

With this process in mind, we will now outline a general form of creation in complex systems. There are roughly four stages in the cycle. First, there is orderly development near equilibrium. Here, the system is characterized by predictability. Second, the system is pushed away from equilibrium by internal or external forces. Third, in the far-from-equilibrium state, the system becomes unstable and very sensitive to small fluctuations. The transition from order to chaos occurs, and the system becomes unpredictable. Four, the system undergoes self-reorganization, adapts to the applied pressure, returns to equilibrium, and continues orderly development. We will now show how this general form is present in particular cases of creation.

## Examples of Complex Systems

In Prigogine’s studies, he describes how his model of creation applies to complex systems in many areas of science: chemical kinetics, hydrodynamics, ecology, economics, molecular biology, and evolutionary biology. Thomas Kuhn concentrates on the creation of new paradigms in a scientific community. In his theory, science grows through the stages of normal science, growing uneasiness with the paradigm, paradigm rejection, and acceptance of a new paradigm which structures the orderly progression of normal science. Rollo May focuses on creativity in the individual. He sees “two general characteristics that…seem evident in creative processes: novelty or the unprecedented, and order, or control and design.”[22] Rothenberg and Hausman note four widely accepted stages of creativity not unlike those of Kuhn and Prigogine: preparation, incubation, illumination, and verification. [23] And both Lonergan and Prigogine discuss the interaction between the individual and the complex system of society, a conflict which we will find plays a key role in creation. We might even go so far as to say that the universe itself is a complex system, reorganizing itself after each big-bang.

## The Origin of Pressure

It is the unstable, non-equilibrium state resulting from a pressure on the system that makes creation possible. These pressures can be divided into internal pressures caused from creation processes on a smaller scale, and external pressures caused by extreme conditions on the boundary of the system. In both cases, the system is pushed far from equilibrium.

Internal pressures in Prigogine’s study can result from presence of an ‘innovator’ in the system. As he describes it,

“the new constituents, introduced in small quantities, lead to

a new set of reactions among the system’s components. This

new set of reactions then enters into competition with the

system’s previous mode of functioning. If the system is

‘structurally stable’ as far as this intrusion is concerned, the

new mode of functioning will be unable to establish itself and

the ‘Innovators’ will not survive.”[24]

An example of such a situation might be a viral infection. The virus invades and disrupts the previous mode of functioning of individual cells, pushing the organism away from its order. The restoring force would be the resulting production of antibodies, killing off the intruder and bringing the system back to equilibrium. An external pressure might be adverse environmental conditions, such as exposure to extreme heat or cold, food deprivation, or an attack by a predator. The aim of both internal an external pressures is the same–only their approach is different. External pressures are direct assaults, while internal pressures result from infiltration. Both attacks are forces that express the organism’s vulnerability, the limitations of its freedom.

In the case of Kuhn’s paradigms, the pressure takes the form of an anomaly. As Kuhn puts it, “when an anomaly comes to seem more than just another puzzle of normal science, the transition to crisis and to extraordinary science has begun.”[25] Science is most often thought of as being pushed away from normal science by anomalous infiltrators in either theory or experiment. For example, a theoretical inconsistency lead Einstein to develop his special theory of relativity, while experimental evidence forced Kepler to propose the elliptical shape of planetary orbits. But science can also have external pressures, placed on it from outside. For example, religion and science have a long history of conflict. And the society’s needs and desires can impose tremendous pressure on the process of scientific inquiry.

We can usually trace internal and external pressures back to a conflict between freedom and limitation. In both theory and experiment, the continued expression of the present paradigm becomes limited by some negative statement of a theoretical impossibility or an experimental failure. In Prigogine’s words, “the newly discovered impossibility becomes a starting point for the emergence of new concepts.”[26] Conflict leads to creation.

On the individual level, conflict also is the source of pressure, both internally and externally. It is the individual’s freedom conflicting with physical and societal limitations. May stresses that “each of us must develop the courage to confront death… we also must rebel and struggle against it. Creativity comes from this struggle–out of the rebellion the creative act is born.”[27] We rebel against the limits of society, the limits of death, and the limits of our own world views. But a rebellion from these limits can come only after a recognition of them. And to recognize the limits of our thought, we must step outside them and question the premises of our views. Humans can, and often do, ignore their limitations.

It is not a trivial matter to transcend a system from within it. As Kuhn paints out, “political revolutions aim to change political institutions in ways that those institutions themselves prohibit.”[28] This paradox is at the heart of creativity. Rothenberg and Hausman describe it as “a human capacity. . .that seems to transcend human capacities.”[29] Through intellectual iterative processes, our awareness is fed back upon itself, allowing us to go beyond the predictable, the causal, the ordered. In this way we can break out of the trap of casual thought within a system. We can break the order, throw ourselves into chaos, and experience life to its limits. We become our own infiltrators, pushing ourselves away from equilibrium, away from predictability, and toward creation.

## The Hierarchy of Creation

Creation on the individual level feeds into, as well as on, creation at other levels. Innovative individuals, who impose pressure on themselves and rebel against the external pressures of physical and societal limitations, are society’s means of imposing pressure upon itself and confronting its own limitations. Because pressure originates from both inside and outside a system, creation in the part and creation in the whole are intimately connected, and take a similar form. Thus creation has a self-similar structure: at different levels the same theme is repeated. The parts contain an image of the whole. This self-similarity is also a characteristic of fractals. The shape of the Mandelbrot set can be found repeated within itself at every scale. Moreover, it can be shown that this self-similarity is a direct result of the nonlinear feedback processes which are at the heart of both the Mandelbrot set and creation.

The smaller Mandelbrot replicas of the whole are linked to the whole by a region of chaos. One must confront the boundary to bridge the part and the whole. Creation is found in the conflict between part and whole as well as at the boundary of either set itself. There is a tension between part and whole that is an essential element in creation.

In Prigogine’s model, we have seen that a small internal fluctuation, or ‘innovator,’ can disrupt the order of the system. But often the system suppresses this fluctuation, the innovator is killed. It is only near instabilities, when the system is very sensitive, that the innovator can change the course of the whole system. In Prigogine’s words, “internal fluctuations. . .which are generated spontaneously by the system itself, tend to be small except when the system is near a bifurcation.”[30] There is a similar difficulty associated with scientific change, according to Kuhn: “novelty emerges only with difficulty, manifested by resistance, against background expectation.”[31] And scientists do not easily let go of a paradigm when it fails. When awareness of anomaly rises, however, the paradigm begins to feel stress under the pressure, its insecurity rises.[32] On the other hand, the innovative scientist feels pressure also. The system resists him, and tries to maintain equilibrium. It has defenses, similar to antibodies in our biological example earlier. Individuals are isolated from the community, attacked by their colleagues. It is only the courageous who can create despite these attacks.

May recognizes both the conflict between the individual innovator and societal order and the conflict between unconscious ideas and our conscious order: “The creativity of the spirit does and must threaten the structure of presuppositions of our rational, orderly society and way of life.”[33] “I define…[the] unconscious as the potentialities for awareness or action which the individual cannot or will not actualize.”[34] Like the society that does not want to acknowledge the individual innovator struggling to break the societal order, the conscious mind represses awareness and action that is in conflict with its order More importantly, May sees the importance of the meeting of part and whole in creation: “The creative act is…an encounter…there must be a specific quality of engagement.”[35] He continues to say, “A continual dialectical process goes on between world and self and self and world; one implies the other, and neither can be understood if we omit the other. This is why one can never localize creativity as a subjective phenomenon; one can never study it simply in terms of what goes on within the person.”[36] It is the conflict of the part and whole that leads to creation, and it is in their union that creation occurs.

## From Order to Chaos

When internal and external pressures succeed in pushing a system into the region of nonlinearity, order is lost. The transition from order to chaos is the fractal boundary, the region of magical beauty, the region of creation. At this boundary, we lose the distinction between part and whole.

Amazing phenomena are found at the transition from order to chaos. Prigogine tell us that “in the case of a nonlinear type of chemical reaction long-range correlations appear. Local events have repercussions throughout the whole system…such long-range correlations appear at the precise time of transition from equilibrium to nonequilibrium.”[37] The part unites with the whole, and the system acts as a unit. In addition, the system becomes extremely sensitive to small perturbations, as if its ‘awareness’ had been heightened.

In the case of scientific creation, we recall Kuhn’s description of scientific response to crisis. He notes that when an anomaly is persistent, more and more of the field’s eminent men “come to view it as the subject matter of their discipline.”[38] The anomaly consumes the entire scientific community, forcing itself upon the whole.

The union of part and whole was expressed by May’s idea of an encounter. Creation for him is rooted in the union of the individual and the world: “Creativity,” he writes, “is the encounter of the intensely conscious human being with his or her world.”[39] A similar unity can be found in Robert Frost’s poem “Mowing.” A worker becomes lost in his work and enlightenment results from his union with nature. Individual identity is lost, awareness rises, and perception widens. Jung has a similar view in which he sees creativity as the emergence of universal symbols from the collective unconscious. When this emergence occurs, we become one with our race.[40]

This union of part and whole is the climax of creation. From chaos, however, we must return again to order.

## From Chaos to Order

In Prigogine’s book *Order Out of Chaos*, he describes how matter regains order from chaos, how it reorganizes itself, how it can–like humans–evolve through a process of conflict, climax, and resolution.

“these far-from-equilibrium phenomena illustrate an

essential and unexpected property of matter: physics may

henceforth describe structures as adapted to outside

conditions…a kind of prebiological adaptation mechanism.

To use somewhat anthropomorphic language: in equilibrium,

matter is ‘blind,’ but in far-from-equilibrium conditions it

begins to be able to perceive…”[41]

Adaptation is mentioned by Jung and May as well. May writes, “creativity…concerns an issue related to man’s survival- his understanding and improvement of himself and the world at a time when conventional means of understanding and betterment seem outmoded and ineffective “[42] The adaptive role in scientific change is clear: science must adapt to new experimental observation, or else it fails. The key element in such an adaptation is the redefinition of the system’s rules, an altering of its basis of functioning, a change in its identity.

Such a restructuring is brought about by the nonlinear iterative processes which are characteristic of systems that can change their own basis of operation. Not only does the identity of the part unite with the whole in creation, but a new identity emerges. “In complex systems,” Prigogine writes, “both the definition of entities and the interactions among them can be modified by evolution. Not only each state of the system but also the very definition of the system as modelized is generally unstable…”[43] And for Kuhn, science is defined by the paradigm under which it operates, thus when the paradigm changes, science itself changes: “The transition from a paradigm in crisis to a new one…is a reconstruction of the field from new fundamentals…that changes some of the field’s most elementary theoretical generalizations…”[44] And because individuals identify so strongly with their own world views, when they are forced to reorganize the way they think at a fundamental level, their identity necessarily changes as well.

When systems change, the need for adaptation does not totally determine the order which emerges. Many different solutions to the problem are possible. Experimental data alone are not sufficient to totally determine a theoretical framework; Paradigms are accepted for all sorts of reasons. Kuhn grants that the biggest claim of a new paradigm is its ability to resolve the crisis, but aesthetics can also be an important deciding factor.[45] This is reminiscent of Polanyi’s role of passion in science. May also sees the role of beauty as a type of selection principle: “The harmony of an internal form, the inner consistency of a theory, the character of beauty that touches one’s sensibilities–these are significant factors determining why a given idea emerges.”[46] Thus, a natural selection based on survival and adaptation is complemented by a selection based on beauty.

## Balance and the Threshold of Pain

We have seen that creation requires a displacement from equilibrium. Thus, systems which are locked into equilibrium states will not be able to adapt and evolve. In the other extreme, however, a system can be pushed too far away from equilibrium, beyond its ability to recover at all. It is this pair of extremes which I wish to discuss now.

The pressure that pushes a system away from equilibrium can be likened to a source of stress. If a person is pushed too far, this stress becomes distress. Likewise, if a paradigm encounters too many anomalies, science may have severe problems recovering. And if too much tension is built up within the global community, we could conceivably destroy ourselves. As May puts it, “Passion can destroy the self. But this is not passion for form; it is passion gone berserk.”[47] Normal science is necessary. Peace is necessary. Order is necessary. Creation is not to be equated with chaos. Creation arises out of order and chaos both, not just one or the other. As Polanyi reminds us, passions can misguide us if we do not subject them to reason. Or, as Rank puts it, the productive type has a will that “exercises a far-reaching control over but not a check upon the instincts.”[48] We cannot be so scared of chaos that we continually impose control and order, never letting go of our comfortable world views. On the other hand, we cannot be so eager for change that we continually throw ourselves into chaos, never hanging on to any one view long enough to learn anything from it. In this sense, healthy creation is like climbing a ladder: We must be able to cling and let go at the same time.

While a society composed entirely of innovators would collapse in chaos, most people are hanging onto the ladder, scared that they may fall if they try to climb up. Most of us fear disorder, chaos, lack of control, conflict with society, and conflict within ourselves. In reaction to the pains and frustrations of facing these fears, we often chose to ignore them, or develop a scotosis, in Lonergan’s terms. We repress our pain, turn down our sensitivity, and isolate ourselves. But as a result, we undermine creation, and thus our ability to adapt. It is a form of self-destruction. The creative person must have the strength and courage to face these fears, to “move ahead in spite of despair,”[49] as May puts it. Science, under the Laplacian spell, has formed a scotosis which has blinded it to the chaotic and unpredictable. Only recently, with the study of complex systems and fractals, has science developed the courage to break this spell. Perhaps other disciplines will follow by rejecting the mechanistic world view in favor of a more courageous one. While a healthy system seeks equilibrium, it does not resist challenges that push it away from equilibrium. As MacKinnon describes it, the healthy person “achieves a constructive integration of these conflicting trends.”[50] Such an integration takes courage, whether the conflict exists in science, ourselves, or humanity.

## A New Order

After a healthy confrontation at the boundary of chaos, after challenging the limits of freedom, we pass into another region of order. We have broken through the chaotic barrier separating two regions of order in the Mandelbrot set, and in our world. The magic at the boundary feeds our new state of order, from which causal expression resumes. Ideas are executed, theories are elaborated. And if the sophistication of order matches that of chaos, if our skills meet up to our insight, then this expression will lead to productive evolution.

In closing, one suggestion presents itself. Can we say that a system necessarily progresses to higher states of order? If so, to what end are systems naturally evolving? Is there a goal? If there is a goal, I would like to propose that it is beauty.

## Notes

[1] May, The Courage to Create, p. viii.

[2] Hofstadter, Godel, Escher, Bach, p. 17.

[3] Prigogine, Order Out of Chaos, p 16.

[4] May, The Courage to Create, p. 36.

[5] Kuhn, The Structure of Scientific Revolutions, p. 121.

[6] Polanyi, Personal Knowledge, p. 143.

[7] Hausman, in The Creativity Question on, p. 344.

[8] Peitgen and Richter, The Beauty of Fractals, p. 1.

[9] Rothenberg and Hausman, The Creativity Question, p. 22.

[10] Prigogine, Order Out of Chaos, p 2.

[11] Rothenberg and Hausman, The Creativity Question, p. 23.

[12] May, The Courage to Create, p. 161.

[13] Jung, in The Creativity Question, p. 124.

[14] Kuhn, The Structure of Scientific Revolutions, p. 2.

[15] Eilenberger, in The Beauty of Fractals, p. 179.

[16] May, The Courage to Create, p. 12.

[17] May, The Courage to Create, p. 134.

[18] May, The Courage to Create, p. 136.

[19] Prigogine, Order Out of Chaos, p 14.

[20] Prigogine, From Being to Becoming, p. xvii.

[21] Prigogine, From Being to Becoming, p. xviii.

[22] Hothenberg and Hausman, The Creativity Question, p. xi.

[23] Rothenberg and Hausman, The Creativity Question, p. 69.

[24] Prigogine, Order Out of Chaos, p 189.

[25] Kuhn, The Structure of Scientific Revolutions, p. 82.

[26] Prigogine, Order Out of Chaos, p 217.

[27] May, The Courage to Create, p. 27.

[28] Kuhn, The Structure of Scientific Revolutions, p. 93.

[29] Rothenberg and Hausman, The Creativity Question, p. 3.

[30] Prigogine, From Being to Becoming, p. 147.

[31] Kuhn, The Structure of Scientific Revolutions, p. 64.

[32] Kuhn, The Structure of Scientific Revolutions, p. 67.

[33] May, The Courage to Create, p. 78.

[34] May, The Courage to Create, p. 57.

[35] May, The Courage to Create, p. 39.

[36] May, The Courage to Create, p. 51.

[37] Prigogine, Order Out of Chaos, p 180.

[38] Kuhn, The Structure of Scientific Revolutions, p. 83.

[39] May, The Courage to Create, p. 56.

[40] Jung, in The Creativity Question, p. 125.

[41] Prigogine, Order Out of Chaos, p 14.

[42] Rothenburg and Hausman, The Creativity Question, p. 5.

[43] Prigogine, Order Out of Chaos, p 204.

[44] Kuhn, The Structure of Scientific Revolutions, p. 84.

[45] Kuhn, The Structure of Scientific: Revolutions, pp. 154-6.

[46] May, The Courage to Create, p. 73.

[47] May, The Courage to Create, p. 163.

[48] Rank, in The Creativity Question, p. 117.

[49] May, The Courage to Create, p. 3.

[50] MacKinnon, in The Creativity Question, p. 179.

## References

- Arragotti, Stan,
- “The Mandelbrot Set”, Unpublished, University of Oregon Honors College Thesis, 1986.
- Grudin, R.,
- Vision, Forthcoming.
- Hofstadter, D. R.,
- Godel, Escher, Bach, Vintage Books, New York, 1979.
- Kuhn, Thomas S.,
- The Structure of Scientific Revolutions, University of Chicago Press, Chicago, 1970.
- Mandelbrot, Benoit B,
- The Fractal Geometry of Nature, W. H. Freeman and Co., New York, 1983.
- May, Rollo,
- The Courage to Create, Bantam Books, New York, 1975.
- Peitgen, H. O. and Hichter, P. H.,
- The Beauty of Fractals, Springer-Verlag, Berlin, 1986.
- Polanyi, Michael,
- Personal Knowledge.
- Prigogine, Ilya,
- From Being to Becoming, W. H. Freeman and Co., New York, 1980.
- Prigogine, Ilya, and Stengers, Isabelle,
- Order out of Chaos, Bantam Books, New York, 1984.
- Rothenberg, A. and Hausman, C. R., ed.,
- The Creativity Question, Duke University Press, Durham, N. C., 1976.

## Acknowledgements

In addition to the above listed authors, I would like to thank Robert

Grudin, professor of English at the University of Oregon, and students of the Honors College seminar on creativity in Fall 1986 for their implicit contributions to the material in this paper.

*Uncategorized*

Posted on 2 December 19860