Through computer simulations and by studying nature there has been made a lot of observations.
- A complex system, driven to critical state, often called edge of chaos, has its own highest computational capacity. This means that the system cannot be simulated with sufficient accuracy faster than the system itself develops. Such a system can be completely deterministic, yet completely unpredictable.
- At the basis for a complex system there can be a few simple rules.
- Complex systems often have network character.
- Complex systems can show emergence, which are unexpected, often unpredictable characteristics of the system that are a result of interaction between the elements of the system.
- Complex systems can have an adaptive capability to influence, almost control, its environment and itself. Such systems are called CAS, complex adaptive systems.
- Complex systems can be unpredictable at one level, but strikingly predictable at another (weather as opposed to climate).
- Attempts at governing complex systems can yield unexpected results.
- Complex systems often follow power laws (they are scale free).
Komplicerad - många delar, svårt att greppa, krävande att förstå, men förutsägbart beteende, predikterbara egenskaper (i detalj). Systemets egenskaper kan härledas ur delarnas egenskaper.
Komplex - icke-linjärt beteende, oförutsägbart i detalj, oväntade egenskaper kan uppstå, så kallad "emergence", tex elektrokemisk aktivitet i hjärnan ger upphov till medvetande.
Komplicerad - många delar, svårt att greppa, krävande att förstå, men förutsägbart beteende, predikterbara egenskaper (i detalj). Systemets egenskaper kan härledas ur delarnas egenskaper.
Komplex - icke-linjärt beteende, oförutsägbart i detalj, oväntade egenskaper kan uppstå, så kallad "emergence", tex elektrokemisk aktivitet i hjärnan ger upphov till medvetande.
Med hjälp av simuleringar och genom studier av naturen har man gjort en mängd iakttagelser av typen (för en fylligare behandling av komplexitet se www.complexityforum.com ).
Ett
Complexity
The study of ecological and social systems, theoretical physics (non equilibrium systems) and above all computer simulations, has yielded exceptionally interesting results that have not yet reached a broader audience or crossed the border to other scientific fields.
A bit sloppy we use complexity theory as a unifying name for a set of simple patterns found in the most different areas. The prevalence of them makes some theoretical physicists call complexity something more basic than physics. Complexity theory is not metaphysics, yet more fundamental than physics.
For the sake of clarity we differentiate between complicated and complex.
Complicated - many parts, difficult to get an overview, hard to understand, but predictable behavior (in detail). The characteristics of the system can be traced/deducted from the characteristics of the parts.
Complex - non-linear behaviour, unpredictable in detail. Unexpected characteristics may emerge, "emergence", for example electrochemical activity in the brain results in consciousness.
- A kind of geometrical relation between the elements. How the elements influence each other over distance is important. Sometimes an element may influence many other elements and sometimes only a few. The elements are members of a network with links of varying strength.
- Future development is dependant on the way we came to be here. History is baked into the present and can function as trigger points for often-unthinkable chains of action.
- The system drives itself to criticality, the "edge of chaos". For example all living species use their biotope to the limit and beyond. In nature there is no holding back or economizing with resources, resulting in eternal crisis. Often only one species becomes extinct at a time, but about every 200 million years or so global ecosystems break down and we have mass extinction of species of exactly the same causes as when just one or two become extinct.
Power Law
The main characteristics of a great many processes can be described with a power law y equals x raised to some number called exponent.
Data points following a power law form a straight line if plotted in log-log diagram where the inclination of the line is the exponent, n in the formula above. We shall look at some examples.
Earthquakes. If you plot the energy of earthquakes (the Richter scale) against number of earthquakes you will get a straight line in a log-log diagram.
As tectonic plates slide and rub against each other mechanical tension fields are created in the ground (the plates) that result in numerous small fractures every second. Sometimes several fractures may occur in unison yielding a larger disturbance. Occasionally there can be created in the rock bottom a network of zones close to fracture and such that a small fracture somewhere close by can transfer load to surrounding volumes and thereby start a chain reaction of fractures that we experience as an earthquake.
Small fracture cracks, too small for us to perceive them, and earthquakes that crush cities and kill hundreds of thousands of people have exactly the same cause.
We are not used to this. We have learnt that most things follow the normal distribution, that the bell shaped Gauss curve describes the world, and for sure, it is often a useful model. If we, for instance measure peoples length or the weight of potatoes and plot the result vs. number we get the well-known Gauss curve. These variables are normally distributed and there is a typical size (the middle, top, of the bell curve). A few are small or very large, but most are somewhere in between close to the typical size.
Crushing potatoes. If we now deep freeze the potatoes we just weighted in the former example and then throw them into a wall so that they are crushed and then pick up the pieces, weigh them taking note of how many there are of the different sizes of the pieces, we will find a power law, a straight line in a log-log diagram as we plot weight against number.
You find power laws for
Number of wars - number of people killed in war
Size of movements at the stock exchange - number movements of each size
Number of individuals of each species in a biotope - mass of an individual of each species
Size of cities - number of cities of each size
Size of forest fires - number of forest fires
Number of heartbeats - pulse rate (measured on myself for 13 h 43 min, see figure above!)
Number of links pointing to a website - number of websites of each size
Behind many phenomena in the most apart situations there lurks power laws. They have the following especially fantasy stimulating characteristics.
- There is no typical size; the process is scale free.
- Similar occurrences of all sizes are just as natural and are basically of the same origin if they belong to the same power law (the same exponent).
- It is impossible to predict if an occurrence that is governed by a power law will be large, small or medium.
- The processes are rooted in
Big events must have important causes, that we like to think, but as we have seen even the largest occurrences may have the smallest origins.
A new strategy
A consequence of the scientific results is that we cannot be as sure, as we previously thought, that the future can be predicted. For example the theoretical limit to weather forecasts is 14 days and will never be exceeded.
Very large and very small occurrences can have the same origin and it is impossible to predict when they occur if they will be of significance or not. The possibility to foretell the future is small and unexpected things can suddenly happen. Of course this is of the greatest importance for our choice of strategy.
Plans will not hold together, but planning, especially for contingencies, will become ever more important. Our flexibility, agility and preparedness for action must increase, as must our ability to observe what is about to happen. We show this by aid of Boyd´s theory, the OODA-loop.
- Observe - without filter or blinkers. Observe with a free and floating mind. Do not tarry at any object.
- Orient - destruction & creation, throw away old junk; create new mental models.
- Decide - sometimes a decision must come immediately without hesitation. (Large decisions are taken within seven heartbeats. Smaller decisions may take longer - Hagakure by Yamamoto Tsunetomo).
- Act - flexible, agile execution of decisions.
Munenori & Takuan talks about principles and attitudes that support and harmonize with OODA-loop. In classical budo there are components that are useful, enlightening and clarifying.
The ability to change is fundamental, as is the ability to organize. It is a question of organizing from nothing or from an unsuitable organization into one that is well adjusted to the new circumstances. There must be a potential for this to happen not as a regular exercise but suddenly and unexpectedly.
It is all about rising preparedness and ability to cope with what you have never met before and to act and organize in a world you do not yet know, to orient without a map in a strange land.
One therefore must drive the organization to the edge of chaos since systems at the edge of chaos have the highest intrinsic computational capability and adjusts to new circumstances faster than any other organization.
For a fuller treatment of complexity see links
http://necsi.org/
http://serendip.brynmawr.edu/home.html
http://www.santafe.edu The center for computer based complexity research
http://jasss.soc.surrey.ac.uk/JASSS.html
http://www.cser.ualberta.ca/journal.htm
http://www.comdig.org
Complexity Organizations
http://www.santafe.edu/ Computer based and mathematically oriented complexity research
http://www.plexusinstitute.com/ Soft non-mathematical approach
http://necsi.org/
http://www.emergentpublications.com non-mathematical, human systems & management
http://isce.edu/ The Insititute for the Study of Coherence and Emergence (I.S.C.E.)