Back to Basics

Introduction to Systems Theory and Complexity

1994 (C) Copyright,

by Onar Åm

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Abstract

There is a very deep structure underlying the order we observe in all of life, marvellously complex order that has taken billions of years to evolve. I therefore find it intriguing and fascinating that this deep structure even dwells in ridiculously simple systems. In this essay we are going to link some of these simple systems to the deep order of complex systems. In other words, we are going back to basics.

Systems Theory

The feedback structure

In ordinary speech feedback means comments or reaction to something. However, when we speak of feedback in a systemic sense this is not what is meant. A feedback structure is a causal knot, a chain of causes that form a ring. The simplest kind of feedback structure is the reinforced feedback, popularly known as the snowball effect or vicious cycle. Characteristic for the snowball effect is that it is self-amplifying. The more complex systems in life have much more complex underlying feedback structures than the snowball effect. Nevertheless, they all have the basic circularity in common. It turns out that systems that causally bite themselves in their tails tend to develop completely new properties. This phenomenon is called EMERGENCE and the new features of the system are called emergent properties. That feedback processes are commonly known as the snowball effect is no coincidence. The metaphor visualizes feedback fantastically well. But as if that is not enough, the metaphor pictures two fundamentally different ways of perceiving the process. The snowball has two fundamentally different motions. When we follow the ball with our eyes we see that it is spinning round and round. However, when we look at how the snowball moves down the hill we see that it is moving along a straight line. These correspond to two fundamentally different ways of viewing time. In the scientific tradition of the West we are used to employing the linear view. We see time as a past, a present and a future on a line. The present is a point on this line moving towards the future leaving a trace of the past behind it. In the linear view causes are always behind the effects. This is however not the case in the circular view in which causes are connected in a circle. It doesn't make sense to speak of "in front of" or "behind" on a circle because a cause is both in front of _and_ behind another cause. This fact is what has puzzled people in the question about the chicken and the egg. The chicken and the egg relates to each other circularly:

_ chicken /| \ | | | | \ |/_ egg This view only makes sense when we regard all chickens and eggs as fundamentally the SAME. Someone who argued for the linear view would of course say that all chickens and eggs are DIFFERENT. He would draw the relation between them in a linear relationship:

egg --> chicken --> egg --> chicken --> egg --> chicken But the truth is that these views need each other. They are two different perspectives on the same phenomena. The metaphor of the snowball effect shows how these can be combined. A feedback is a circular structure rolling through linear time.

the circular view .-->--. / \ /|\ | | \|/ \ / --> --> --> --> --> `--<--' --> --> --> the linear view past present future What is so brilliant about the snowball effect is that we can see both the circular and the linear motion at the same time. Unfortunately this is rarely the case in other feedbacks. The reason is that the circle focuses on *structure* while the linear view focuses on *pattern*. A structure is abstract while a pattern is concrete. In order to see the structure we have to visualize the relations between the parameters in the system. Therefore the feedback structure is often invisible. Nevertheless, the structure is just as real as the pattern. In fact, we may see the pattern as the _unfolding_ of the feedback structure, the trace that the snowball leaves behind it.

The Domino Effect

The wave is a very common pattern that few think of as emergent. The perhaps most exciting example of a wave is the domino effect. Watching the dominos knock each other down in a wave is most fascinating. But if this pattern is emergent there must be a circle somewhere. But where? If we look carefully at the domino effect then there is almost like the dominos are knocked down by an invisible ball rolling over them. If we imagine this then we see that the domino effect actually resembles the snowball effect pretty much. The invisible ball has the same steady motion as the snowball and it leaves a trace of fallen dominos behind it, just like the snowball leaves a trace. The only problem is, how does the ball look like? It looks like this:

the domino bumps _ into a new domino /| \ | | | | \ |/_ the new domino falls How fascinating. Beneath the great differences of the domino effect and the snowball effect they turn out to be quite similar. Their similarity had gone by unnoticed had we only looked at the phenomena linearly.

What a strange way of looking at the domino effect you might say. We are treating the feedback structure as if it is an object independent of the wave. Although this approach is unusual in such a simple system it is nevertheless quite common in more complex systems. In many cultures one separates the mind from the body, designating an existence to the soul independent of the body. Systems theory suggests that there are two fundamentally different, but equally valid ways of looking at a system. Either as structure or as pattern. But at the same time it is apparent that these are only different viewpoints on the same phenomena. As such we cannot see the mind as independent of the body although we can view them separately.

Meta-balance

Emergent phenomena are strange. Often very ordered behavior arises in extremely complex systems. An obvious example is the organism. Billions of interacting cells behave remarkably organized. Although various emergent phenomena are very different from each other they do have some things in common. A very important concept that connect all emergent phenomena is meta-balance. It is a very strange concept and perhaps *the* key to understanding emergence. A system that is in meta- balance may be viewed from two different perspectives. On the level of detail the system is completely *out*of*balance*. However, from a global perspective the system seems to be stable and ordered. The strange thing is that the system MUST be out of balance in order to produce global order. This is perhaps the most counterintuitive aspect of systems theory. Who would have guessed that the way to produce emergent stability in a system is to push it out of balance! Although this sounds somewhat uncomprehensible the concept is easy to demonstrate. Both the snowball effect and the domino effect are meta-stable phenomena. Let us look at the domino effect. Clearly there is a stable and ordered overall behavior of the system, the wave. But when we look at the behavior of the individual domino of the system the picture changes. The invisible ball is fueled by *falling* dominos. In other words, the ball only rolls when the dominos are knocked out of balance.

In thermodynamics "balance" is defined more accurately. A system that does not spend energy is in balance. And consequently a system is out of balance when it spends energy. Therefore, if we want emergent phenomena to arise in systems we must get it to spend energy. And not only that, we must constantly feed it with new components and energy in order to sustain the meta-balance. This makes sense. The domino effect can only be sustained as long as there is a new and erect domino in front of the falling one. In other words, we have to "feed" the invisible ball with new dominos all the time in order to keep it out of balance, just like the snowball needs to be fed with new snow in order to grow. So unlike a stable system, a meta-stable system spends energy like mad. This definitely makes sense. Just think about organisms, yourself included. If you don't continuously supply your body with food and water you'll simply die. The ball will stop rolling.

To summarize, the domino effect relies on two factors. One, *falling* dominos. And two, a continuous supply of new dominos to bump into. This pretty much summarizes the concept of meta-balance which is a universal property of all emergent phenomena. The components of a meta-stable system must be out of balance and the systems needs to be continuously supplied by new energy/components in order to keep the system out of balance.

Survival and Sameness

When we sketched the circular relation between the chicken and the egg we assumed that all chickens fundamentally the SAME. At the same time we can from a linear view argue that all chickens are DIFFERENT. How can they both be true at the same time? In order to see this we need to understand the concept of survival. When you look at the domino wave (or an ocean wave or any other wave) you get the feeling that it survives from one moment to the next. Sure, it has moved a bit, but you get the feeling that it is the SAME wave. But let us for a moment follow the invisible ball with our eyes. What do we see. As the ball is rolling it is continuously fed with new dominos. The ball leaves behind it a waste product; the fallen dominos. We realize that new components are continuously flowing *through* the invisible ball:

the domino bumps _ into a new domino /| \ | | | | \ |/_ F, F, F, F, F, F, F the new domino N, N, N, N, N, N, N, N, N falls F = fallen domino, N = new domino They enter the circle as new and fresh energy and leave behind the circle as a waste product. But here comes the point: when the wave reproduces itself into the next moment it does so by using DIFFERENT components. So if you look at the emergent wave from the component's perspective the wave is not the same. This is true for all emergent phenomena. Although you feel that you survive from one moment to the next there is taking place a continuous replacement process in your body; new energy and molecules continuously flow *through* you. In humans the replacement cycle is about 7 years. That is, it takes about 7 years for all the molecules in your body to be replaced by new ones. In the domino effect the replacement cycle is only a fraction of a second. So obviously, when we are speaking about survival and staying the same we are referring to the *structure* of the system. Although all the components of the system are replaced by new ones the structure remains basically the same. And this is exactly why it is equally legitimate to say that all chickens are the same from a structural point of view as it is to say that NO two chickens are the same from a detail point of view. In fact, from a detail point of view the chicken that we see today will not be the same tomorrow.

It should by now have become quite apparent that some of the above concepts often appear in constellation. The concepts that belong together are these: the circular view the linear view structure pattern global perspective detail/component perspective meta-balance out-of-balance particle (ball) wave

Complexity

We now move on to a cousin of Systems theory, namely Complex Systems theory - Complexity for short. There is a third cousin in this family which is perhaps the most famous of them all: Chaos. But we are not going to pursue Chaos theory in this essay. How do these theories relate to each other? Somewhat oversimplified we may say that Systems theory studies simple systems with simple emergent behavior, Chaos studies simple systems that produces complex (read:chaotic) behavior and, finally, Complexity studies complex systems with simple overall behavior.

Why Complexity?

Systems theory and Complexity overlap and are based on the same principles. Why then two distinct disciplines? The main reason is that they belong to two different scientific traditions. But there are of course other reasons. Not all systems are as simple as the chicken and the egg. In a system consisting of millions of components it will be close to impossible to draw a simple circular structure describing the innate feedbacks. It is only possible to sketch the feedback in a very general way:

_____________________ / \ | GLOBAL | The Global Structure | STRUCTURE | serves as initial condition \_____________________/ for the components / / / \ / \ / \ \ \ | | | | | | | | | | | | | | \ \| | | | |/ / _\_| | | | |_/_ o o o o o o The local interactions of o o o components create the new o o o o Global Structure (which o o o becomes the new initial o conditions and so on) _ /| / Many locally interacting components As the diagram suggests there is a circular relationship between the "global structure" of the system and its "local interactions". The "global structure" may be defined as the web of relations in the system while the "local interaction" may be defined as each _particular_ relation. Thus, the global structure is made up of the total network of interactions at any given moment. Each and every component in the system interact with their immediate surroundings and thereby change the global structure. Since each component responds to the global structure, then in a sense the behavior of each component is determined by the whole. At the same time the independent response of all the components at one moment creates the whole of the next moment. To summarize: the global structure creates the response of the components at one point in time and the local interactions of the components creates the new global structure at the next moment. An example of a complex system is a society. A society consists of many independent, locally interacting components, namely humans. The current state of the society is the global structure. Each and every individual responds to the current state and thereby create the new state of society in the next moment. And so on.

Now let us define what we mean by a "Complex system."

A Complex system:

consists of many independent components,
these components interact locally,
the overall behavior is independent of the internal structure of the components, and
the overall behavior of the system is well-defined.

"The system consists of many independent components"

There are two important points in 1), namely that there are _independent_ components in the system and that are _many_ of them. In other words, a Complex system is NOT a whole that is built up of parts. It is a whole built up of other wholes. These components may therefore themselves be complex systems. Some examples of a complex system: an animal (consisting of cells), a cell (consisting of prokaryotic bacteria), an ant colony, a herd, an ecosystem, a car queue, a culture, a neural network and a sand pile (consisting of grains).

"The components interact locally"

2) means that a neuron only interacts with its nearby neurons, ants with its nearby ants and so on.

Also, no component interacts with all the other components in the system, at least not simultaniously. Although two components belong to the same system they may never directly interact. Why then do we say that they belong to the same system? Because they are connected through the global structure. A component is indirectly connected to all other components in the system via other components. One component interacts with a second component that interacts with a third... and so on. So although the components of the system only interact locally they have global effect on the system. An example of this is a car queue. If a car in car queue suddenly slows down from 50 m/h to 40 m/h then the car behind him would have to slow down too and the car behind that car and so on. The speed reduction of that single car will propagate like a schock wave through the car queue and affect the speed of the cars miles down the road. This illustrates how local interactions produces global effects in complex systems.

"The overall behavior is independent of the internal structure of the components"

3) means that it doesn't matter how the components of the complex system is built up *as long as they do the same things*. This means that the same emergent property will arise in completely different systems. The best example of this is the wave. Waves of course emerges in water and air, and in part I we saw that the wave emerges in the domino effect. But above we also saw that a speed reduction travels like a wave through a car queue. But that is not all. When I was little I used to watch lone ants that had lost their way into our house. If I bumped my finger into the ant it would start crawling faster in an erratic pattern, which is natural, I thought. It was probably afraid. However, it was not until years later I realized the real reason for its panic. Everyone ought to do the following experiment: poke a stick into an ant nest and see what happens. The ants that are nearby the stick will start their characteristic panicky motion. But then the strange thing happens: when the panicked ants bump into other "calm" ants these also start to panic. These in turn bump into new ants and so on. Like a wave the panic spreads in all directions until the entire ant colony is boiling. It turns out that the panicking is not panicking at all, it is an emergent alerting system of the ant colony! Waves occur in wildly different systems and it doesn't matter if the components are green cars, red cars, ants, dominos or water molecules. All that is required for the wave to emerge is that one component "bumps" into the next.

Another example of an emergent phenomena that occur in very different systems is flocking. Flocking occurs in as different systems as fish, birds, insects and sheep. A more complex example is the food-chains of ecosystems. Although there are practically indefinitely many ways of combining different species into an eco-system there only exists a handful of stable food-chains. These emerge independent of the specific species in the eco-system.

"The overall behavior of the system is well-defined"

If we disregard the components in a complex system and only look at the emergent phenomenon then it turns out that it behaves quite exact. Indeed, the simplest of all emergent phenomena, the wave, is incorporated as a part of mathematics because it has exact and well-defined overall properties. Waves are linear, i.e. they can be added, and the derivative of a sine wave is a cosine wave. Likewise more complex emergent phenomena evolves along quite distinct patterns. A thunderstorm, for instance, typically evolves along this pattern: dark clouds starts covering the sky, flares of lightning strikes followed by a rolling thunder, and it starts to hail or rain. Or look at the ant. An ant is a fantastically complex system consisting of millions of cells. Yet the overall behavior is quite simple and predictable. If you bump into an ant then it will always start moving in a panicky, erratic motion. Similarly it follows simple emergent rules for all the situations it comes into.

The Vortex

In part I we discussed the snowball effect and the domino effect. Both turned out to have a feedback structure built into them. In complexity theory we will employ some new physical metaphors to explain some important concepts. We start with the vortex.

Maelstroms in troubled waters or tornados in fierce skies are mighty examples of vortices. The strange thing about a vortex is that there seems to be some force at the center sucking great masses towards it. But this is just an illusion created by the circulating masses. If we remove the masses from the vortex to see what is at the center there is nothing. Absolutely nothing. It is like peeling the layers of an onion in the hope of finding its core. You won't find it because it doesn't exist. But when the vortex is swirling you could swear that there is a force somewhere. Where is it coming from? The answer is perhaps the most fundamental acknowledgement in all of Complexity: it comes from _within_ the system. Although there seems to be an external force organizing the vortex it is the masses in the vortex that is driving it. The reason this acknowledgement is so important is because it ends the long war between Vitalism and Materialism. Vitalists have always claimed that a "life force" is needed to run life. Materialists on the other hand have claimed that no external forces is needed to drive life. It turns out that both views are correct. The vitalists have quite correctly identified a "life force", namely the illusory sucking force at the center of the vortex. The materialist view is correct since the "life force" emerges from within the system. Nothing from the outside is organizing the vortex.

The "life forces" are real, but they do not exist in the ordinary sense. They have a socalled hyper-existence. In order to exist three conditions need to be satisfied.

the vortex must be EMBODIED,
the components of the system need to be out of balance, and
there must be feedback in the system

All these three conditions are satisfied in the vortex. 1) A vortex cannot emerge in vacuum, it needs to be embodied in a medium. This corresponds to the first part of the definition of a complex system: "a complex system consists of many independent components." 2) A vortex cannot emerge unless the water or air masses are in motion (out of balance). Vortices emerge in *running* water or in *turbulent* air. 3) A vortex is itself a circular structure and hence feedback occurs.

When all these three conditions are satisfied the illusory sucking force at the center of the vortex emerges. What we have described here is simply the concept of meta-balance in part I. For what is the force at the center if not meta-stable? The new thing that the vortex adds to the concept is that once the three conditions are satisfied the meta-stability becomes an *active* force. Once a system enters a vortex it will be trapped in its pattern.

The vortex concept is important because it enables us to say something fundamental about the world. Complex Systems scientists are becomming more and more convinced that there exists natural vortices in nature. Imprinted in nature so to speak. They lie latent and non-existent waiting to be embodied in a real system. Then, when turbulence is created in a system the vortices wake to life and start sucking. The system will be sucked into the strongest nearby vortex and stay there until it for some reason is perturbated out of it and enters a new vortex. And more important, different systems are sucked into the same vortices. It is no coincidence that the eye or the wing has evolved many times in evolutionary history. It is no coincidence that the same food-chain structures emerges in wildly different eco-systems. And it is no coincidence that the wave appears over and over again in completely different systems. These are vortices that scientists have identified and know well. They are not just empiric discoveries, they are equally much imprinted in nature as 2+2=4.

The vortex concept teaches us something fundamental about the world, namely that there is not just one fundamental level of laws in nature, but many. The Western scientific tradition has always strived towards a set of fundamental laws of nature. Complexity has crushed this dream. In a world with a single set of physical laws there will always arise complex systems (as long as there are many components in the world). And when this happens fundamentally new forces wake up from their non-existence. These new forces may interact and form still new forces. And so on. The evolution of life is also the evolution of reality. The biological world continuously fosters new worlds with new emergent laws built upon the old ones.

The Resonance

We have discussed three different but fundamentally circular phenomena; the snowball effect, the domino effect and the vortex. But there is also a fourth physical phenomenon that we shall have a look at, the resonance. As you soon will see the resonance has exactly the same properties as the three other structures. And just like the other metaphors the resonance emphasizes yet another important property of complex systems.

What is a resonance? In ordinary speech it is a sound prolonged by a repeated process. It may be a howling wind, whistling, a guitar feedback or the sound of a pipe organ. The technical definition is pretty much the same although it is not restricted to sound waves. A "repeated process" is exactly a feedback of some sort. Let us look at the structure of a simple resonance which is a common problem for musicians:

sound \ \ | | \ / <----loudspeaker microphone __ / |\ | | | | \ / `-->amplifier--' Musicians have microphones on their stage. Unfortunately these do not only pick up the voice of the singer, they also pick up the sound pouring from the loudspeakers. Suppose now that this signal is amplified so much that it comes out louder than originally in the loudspeaker. What would happen? The signal would enter the microphone, be amplified and come out louder still. And so the snowball starts rolling. The result is a howling sound which destroys the musician's gear if it is not stopped.

But the interesting thing now is not the feedback structure, we have discussed that already, but the howling sound. If we had spectrum analyzed the above feedback we would have seen something very interesting. At first there would be no distinct spectral pattern, but as the feedback is triggered we see the emergence of a peak in the spectrum. This peak grows and becomes thinner and thinner. If the peak is allowed to grow indefinitely it will end up as just one frequency. In other words, a sine wave.

(1) (2) (3) a^ a^ a^ | m| m| m| | p| p| p| | l| l| | l| | i| i| | | i| | t|_ _-__ __-- t| - - t| | u| -- -- u| _-- -_ u| | | d| d|- -- d| __- -__ e|--------------> e|--------------> e|--------------> frequency frequency frequency This a characteristic development pattern of a resonance. So what does the resonance tell us that we haven't already seen in the snowball effect or in the vortex? The answer is: information reduction. The feedback above started out with a signal that contained _many_ frequencies. But it ended up with just one frequency. And more: no matter what the starting signal is the feedback always ends up with the same lonely sine wave. Of course, we already knew this last thing. The system is always sucked into the same vortex no matter what the starting point is. The new thing is the information reduction. Think about whistling. The starting point of whistling is always turbulent, noisy air. But after going through a refining feedback process in your mouth and lips a distinct whistling sound emerges. In other words, the resonance acts as an *emergent filter*. The feedback filters away all the other frequencies and leaves just a single one. But in addition to filtering the other frequencies it *amplifies* the remaining frequency. The resonance is therefore called an active filter in Filter Theory. Note the similarity between the vortex and the resonance. In the vortex there is an active force at the center which the matter is sucked towards. In the resonance a system is sucked towards and trapped in a pattern (the sine wive).

How is this relevant to Complex systems? Complex systems often contain billions of independent components. That they are independent means that each and every one of them is a free variable in the systems. Therefore it is natural to assume that we also need billions of variables to describe the system, right? But this is not the case with complex systems. From the sea of variables there emerges an overall behavior which can be described with surprisingly few variables. Instead of producing wildly complex behavior the system is often trapped in very simple patterns. As such we can say that the emergent phenomena acts as an active filter process - a resonance if you want. In the definition of a complex system we stated that an emergent phenomenon is well-defined. The resonance illustrates what that means. A complex system is a high-dimensional system which produces a low-dimensional behavior.

Wild Nature

Evolution

In part II we saw that feedbacks act like emergent filters, information reducing processes. We may view this filtering as SELECTION. A 150 years ago the great biologist Charles Darwin discovered that the mechanism of biological evolution was exactly such a selection process. He called it Natural Selection, which was nothing more than the survival of the fittest. Those organisms that were not fit to reproduce were filtered away by going extinct. Those that survived, survived. Those that didn't survive, didn't survive. It was as simple as that. Darwin viewed organisms as would-be perpetual machines that went through a natural filter process. Only the perpetual ones come through. A perpetual machine is fun. Originally it meant a machine that didn't need energy from the outside to run. But that is not what we mean here, rather a machine or system that is able to perpetually run and reproduce itself. Organisms are exactly such perpetual machines.

An organism has one "mission" in life: keep itself running long enough to make a copy of itself. In order to run it needs to maintain the continuous flow of energy and matter through it. In other words, it has to eat. Let's play with this idea for a while. A car keeps running by "eating" gas. Does that mean that a car is alive? The problem is that it makes no effort for getting new gas. It relies on us humans to fill it up. So an organism would at least have to use its food to go look for more food, thereafter reproduce. With this in mind it is not hard to understand how natural selection works. Those that are not capable of finding food and reproduce (i.e. those that are unfit) will be weeded away. A car wouldn't live for long. The moment it ran out of gas it would be out of the race.

So far so good. But when looking back on the history of life we see an enormous diversity of organisms. We get a feeling that Natural Selection is somehow creative. Thus, it is not only a filter, it is also a resonance. It amplifies the fit organisms while the unfit are weeded away. But something is missing here. It is still hard to see why Natural selection should be creative. What are we overlooking? In order to make Natural Selection creative we need to drive it OUT OF BALANCE. How do we drive a biological system out of balance? The answer is so simple: competition for limited resources. When organisms compete they make their own fitness unstable. What is fit today may not be so tomorrow. A dynamic fitness landscape is the source of new emergent phenomena, which makes natural selection into something more than a passive filter process. Dynamic fitness renders *creativity* and *intelligence*. This is the most prosperous emergent phenomena that evolution has produced because it opens up for the evolution of evolution. We've seen it in the biological evolution. We've seen it in the mind and we've seen it in cultural evolution. I will give an example from economics.

200 years ago market economy was conceived. The law that governed business for a long time was this: invent a fantastic new product, organize a corporation and produce that product successfully for decades. For a very long time this magic formula was superior because corporations often were in a monopolistic economic state. The market seemed inexhaustible, bewildered as it was by all this new technology. Companies could almost uninhibitly flood the market with their products. The lifetime of a product spanned over years, maybe decades, so the need for a rigid organization to plan the long term productions was urgent. But in the post-war climate this has drastically changed. The immense gap between supply and demand has readily been filled. There no longer exists a starving market (at least not in western countries). The market has become rather picky as the customers never before have had so many products and services to choose from. This is because there are now more competing businesses and countries than ever before. Much of Asia, for instance, is experiencing a period of astronomical growth and has created a much tougher economic environment resulting in greater competition. At the same time the traditional mass industries seem to be a dying race. They are at large being replaced by information-, communication- and service industries. The changes in the world situation are substantial. And, more importantly, there seems to be no end to it. While vast periods of stability have dominated most of the technological evolution, change is becoming the normal state rather than the exception. The dissipation of a starving market has lead to complex ramifications of ever changing demands, and along with the hunger of the market disappeared its uniformity. The loyalty of customers is diminished resulting in shorter lifetimes of products. In many businesses they no longer speak of years and decades but of months and -gasp- weeks. Even though some businesses will never reach cycles of just a few weeks the trend is clear: shorter product lifecycles and shorter market demand response. What before was one of the major advantages of linear systems, the rigidity, has now become their major drawback. In a dynamic world the ability to adapt to the non-stop stream of change is an absolute necessity to retain competitivity. Our own recent economical history is therefore a perfect example of complex system that has been thoroughly driven out of balance by competition. The result is an evolution of intelligence itself. Today a company cannot rely on making one fantastic product and believe that they can sleep on it for years. Other companies will quickly copy your idea and come up with a counterproduct at half the price. And the trend is amplified. Therefore, in the future the only competitive advantage of companies will be their creativity, their intelligence and their ability to adapt. We are entering a new era of economic evolution: the evolution of evolution, an evolution of creativity itself.

"A wound that never heals"

Complex systems are wholes that are built up from other wholes. It is tempting to believe that a clockwork is a complex system. But it is not. A clockwork is built up of parts, not wholes. Removing a cogwheel has fatal consequences for the clockwork. It simply breaks down. A complex system on the other hand is not as crucially dependent on its components because they are wholes themselves. If a cell dies or an ant is lost then this has little effect on the system they belong to. If an animal is wounded then the wound is healed. If a neuron dies we do not loose a significant part of our memory.

In order to be in an overall meta-balance complex systems need to be out of balance on the level of the components. How are complex systems driven out of balance? The answer is simple: through the independence and freedom of the components. Complex systems are meta-stable because they are built up of interacting wholes. The freer the components behave the more out of balance the complex system is driven which in turn is the source of meta-balance.

But there is a price to pay for meta-stability. While on one side the unbalance is the source to meta-stability it is also the source to a fundamental schizophrenia of all complex systems. The freedom of the components brings an element of noise into the system. Complex systems will therefore never be complete unities. There will always be an upwelling of anomalies and "slipping" from within the system. So although an organism seems like a complete unity it is not. There is always an inner conflict between the wholes that the organism is built up from. Organisms are wounded in a fundamental way that can never be healed. They are essentially fragmented, broken into wholes. Organisms are fragmented both in time and space. We humans, for instance, can never hold on to a moment. There are instances - a state of mind, an era, a relationship - that we will experience only once. It will happen only once and no matter how hard we try to hold on to it, it will crumble away like falling sand through your clutching hand. This is because one moment is fundamentally disconnected from the next. Just like the dominos organisms are doomed to "fall" from one moment to the next. Likewise, no matter how well you know a person or how strong the bondage is between you there will always be moments of friction, of tenderness, of conflict. The fundamental schizophrenia of complex systems is what makes organisms "irritable." Organisms are irritated by their environment and relations, but they are also irritated from within. We may say that organisms are wounded wholes. This woundedness is captured in the concept of wilderness.

Wilderness

Human order is the opposite of mess. We tend to look at order as control and rigidity. But the order that emerges in complex systems is soaked with an element of wilderness. When we look at clouds we never see stright lines or nicely "ordered" patterns. And a wild jungle stands in stark contrast to the well-trimmed gardens of the human world. Neither the jungle nor clouds nor organisms are ordered in a traditional sense, yet they are not completely disordered either. Somehow we get the feeling that nature balances somewhere between chaos and order. It is a "messy" kind of order. In all complex systems there is an element of noise. That it is wild means that we can never fully control it. We are never safe from the spontanious emergence of anomalies in the system because they are an innate part of the system. Life is intrinsically wild and slippery. It refuses to be controlled. Therefore Life is by definition impossible to rigidly define. We are unable to completely capture organisms with our concepts. We can never be sure that Life will be the same tomorrow as it is today. Life has the extraordinary ability of making its own definition obsolete.

For those who want to play with wilderness and see how it works here is an experiment you can perform:

If you see a bunch of paper clips that are neatly chained together then you will know that someone put them together, someone _designed_ the chain. Complex systems have the ability of designing themselves. To watch a system self-organize is always fun and fascinating. And paper clips are so simple and handy that anyone can play with them. In order to make a simple Complex system you need to do the following. Obtain _many_ paper clips. (condition 1 in the definition). Open the paper clips half way up so that they are easily able to hook up to each other. Put all the disconnected paper clips in a jar. Now we need to drive the system out of balance. How do we do that? Simple: start shaking the jar. This will drive the system out of balance and make the paper clips interact with each other. After shaking the jar, open it and look at the result. Bingo, the paper clips have self-organized into chains. But it will not be a perfect chain like the one produced by human design. No, the chain will be WILD. There are anomalies in the chains, chains connected to other chains, many paper clips in one joint and so on. Wilderness is the wonderful pattern of life. Not order, not disorder. Complexity.

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