Many people sum up this aspect of complex systems by saying that the whole is more than the sum of the parts.
Relations between parts and between the effects of interactions must be considered as additional 'relational' parts, in some sense.
Rosen's abstract relational biology approach focuses on a definition of living organisms, and all complex systems, in terms of their internal organization as open systems that cannot be reduced to their interacting components because of the multiple relations between metabolic, replication and repair components that govern the organism's complex biodynamics.
He deliberately chose the `simplest' graphs and categories for his representations of Metabolism-Repair Systems in small categories of sets endowed only with the discrete "efficient" topology of sets, envisaging this choice as the most general and less restrictive.
Rosen said that organization must be independent from the material particles which seemingly constitute a living system.
As he put it: The human body completely changes the matter it is made of roughly every 8 weeks, through metabolism, replication and repair.In mathematical biology he is known as the originator of a class of relational models of living organisms, called systems that he devised to capture the minimal capabilities that a material system would need in order to be one of the simplest functional organisms that are commonly said to be "alive".In this kind of system, stands for the 'repair' subsystems of a simple organism, for example active 'repair' RNA molecules.Approaching organisms with reductionistic scientific methods and practices sacrifices the functional organization of living systems in order to study the parts.The whole, according to Rosen, could not be recaptured once the biological organization had been destroyed.Rosen's posthumous work Essays on Life Itself (2000) as well as recent monographs by Rosen's student Aloisius Louie have clarified and explained the mathematical content of Rosen's work.Rosen's work proposed a methodology which needs to be developed in addition to the current reductionistic approaches to science by molecular biologists. Relational is a term he correctly attributes to his mentor Nicolas Rashevsky, who published several papers on the importance of set-theoretical relations in biology prior to Rosen's first reports on this subject.The mechanistic view prevails even today in most of general biology, and most of science, although some claim no longer in sociology and psychology where reductionist approaches have failed and fallen out of favour since the early 1970s.However those fields have yet to reach consensus on what the new view should be, as is also the case in most other disciplines, which struggle to retain various aspects of "the machine metaphor" for living and complex systems.By proposing a sound theoretical foundation for studying biological organisation, Rosen held that, rather than biology being a mere subset of the already known physics, it might turn out to provide profound lessons for physics, and also for science in general.Drawing on set theory, his work has also been considered controversial, raising concerns that some of the mathematical methods he used could lack adequate proof.