A complex system is thereby characterised by its inter-dependencies, whereas a complicated system is characterised by its layers. However, “a characterization of what is complex is possible”. Ultimately Johnson adopts the definition of “complexity science” as “the study of the phenomena which emerge the elements of statistical learning second edition pdf a collection of interacting objects”.

Many definitions tend to postulate or assume that complexity expresses a condition of numerous elements in a system and numerous forms of relationships among the elements. However, what one sees as complex and what one sees as simple is relative and changes with time. 1948 two forms of complexity: disorganized complexity, and organized complexity. Phenomena of ‘disorganized complexity’ are treated using probability theory and statistical mechanics, while ‘organized complexity’ deals with phenomena that escape such approaches and confront “dealing simultaneously with a sizable number of factors which are interrelated into an organic whole”. Weaver’s 1948 paper has influenced subsequent thinking about complexity. Some definitions relate to the algorithmic basis for the expression of a complex phenomenon or model or mathematical expression, as later set out herein.

Weaver perceived and addressed this problem, in at least a preliminary way, in drawing a distinction between “disorganized complexity” and “organized complexity”. In Weaver’s view, disorganized complexity results from the particular system having a very large number of parts, say millions of parts, or many more. Though the interactions of the parts in a “disorganized complexity” situation can be seen as largely random, the properties of the system as a whole can be understood by using probability and statistical methods. A prime example of disorganized complexity is a gas in a container, with the gas molecules as the parts.

Organized complexity, in Weaver’s view, resides in nothing else than the non-random, or correlated, interaction between the parts. These correlated relationships create a differentiated structure that can, as a system, interact with other systems. The coordinated system manifests properties not carried or dictated by individual parts. The organized aspect of this form of complexity vis-a-vis to other systems than the subject system can be said to “emerge,” without any “guiding hand”. The number of parts does not have to be very large for a particular system to have emergent properties.