110

measurements. Other “multiple testing” corrections are not quite so hard, because the dis­

tribution of the results usually satisfies a normal distribution.

Nevertheless, it can be generally stated that it is much easier to carry out such evalua­

tions with clear hypotheses and less likely to fall prey to random deviations or come to

false conclusions from the large data sets.

9.3

Typical Behaviour of Systems

9.1

Ordered systems can be described by simple mathematical equations, for example the

flight behaviour of a rocket or an airplane (function in time as independent variable, with

the x, y and z coordinates for the position) or of a train (route plan). As we can see, this

behaviour is predictable and can be described exactly for the entire period of the flight or

train journey.

In addition, the system can also be easily controlled, for example by the aircraft pilot

using the joystick or the acceleration/deceleration of the train by the train driver. The so-­

called state space of the system (where the train or the plane is at which point in time) can

be described exactly, for every hour, for every minute.

A random system cannot be predicted at all for the next moment. The ideal example is

a dice roll. No one can predict whether the next roll will be a one, a two, or a three, or even

a six. And it stays that way. Also, the next roll is just as random as the previous one. This

Table 9.1  System behaviour (ordered, random, chaotic) with typical properties

System

Order

Mayhem

Random

Example

Clocks, planets

Clouds, weather

Noise (sound), dice

Single event

predictable

Very accurate

Only briefly (weather

forecast)

Not at all

→ simple laws

Effect of small

disturbances

Very small

Escalating over time,

explosive

No effect, random

disturbances are averaged

out

Possible states

Few pure states

Many: Circling around

attractor

Noise of all possibilities

(1 to 6 on the dice)

Dimension

Finally

Low, e.g. circular

orbital plane, healthy

pulse

Infinite (any sequence is

possible)

Control

Simply

Difficult, but effective

Barely (dice)

Attractor

Clear point, exact

circular path (strange,

fractal)

Scattered around the

attractor

No attractor: Any state

possible

9  Complex Systems Behave Fundamentally in a Similar Way