Complexity increases in three dimensions

To understand the evolution ladder of the operator theory, one must learn to distinguish between three types of structural complexity.

The first type (also 'direction' or 'dimension') describes the different ways by which existing operators (physical particles or organisms) interact and create systems ('interaction systems') which are not operators. Examples include stars, planets, the global ecosystem, bee colonies, populations, etc.

The second type describes the arrangement of elements inside existing operators ('internal differentiation'). Examples include organelles in cells and tissues and organs in multicellulars.

The third type, the 'operator dimension', describes an evolution ladder. This ladder starts with the quarks and continues with the steps towards the hadrons, atoms, molecules, prokaryotic cells (the bacteria sl), endosymbiontic cells (also considered as eukaryotes), multicellular organisms and multicellulars with brains. Every step on the ladder must involve the shortest route nature allows (it must be the 'first-next possibility'). A step can either be based on interactions, or on internal differentiation. Every step causes a new closure type and a new operator.

Explanation of three dimensions (Power Point)
Animated explanation of the formation of the operators (Power Point)