214 Abir U. Igamberdiev
The operation defined by β, designates the system as a whole within itself. It acts as a
generator of the complete enclosed structure of an (M,R) systems (Letelier et al., 2006). In
other words, β has a semiotic value signifying the system as a whole. In the true (M,R)
system, the β parameter is unique according to Rosen (1991) and is beyond the genotype and
the phenotype. From the point of view of optimality, the uniqueness can be restricted by the
organizational invariance of the system in the biological realm or by the observability in the
physical realm. There is no rigid algorithm to take β, this operation has its own ambiguity, but
when the β is taken (an arbitrary choice which determines the Saussurean arbitrariness of a
sign), this ambiguity becomes frozen and the internal computation becomes possible. The
original Rosen‘s approach deals with a transformation which is in fact an inversion in time:
the inverse of the evaluation map resulting in the organizational invariance is a formation of a
finite spatiotemporal structure of the body of a given biological organism. Later, Gunji et al.
(2008) came to the idea of describing the organizational invariance of the biological system
from the point of view of ―heterarchy‖ that naturally involves self-reference through inherited
logical inconsistencies between levels. A description of heterarchy is presented as a pair of
the property of self-reference and the property of a frame problem interacting with each other.
The semiotic coupling of them embodies an inheritance of logical inconsistency.
THE BIOLOGICAL EXPANSION OF THE UMWELT
The idea of Rosen about the organizational invariance of biological systems has a certain
similarity with the concept of nomothetic organization of living systems developed by Sergei
Meyen. The organizational invariance assumes that the system possessing it develops
according to certain rules, i.e. nomothetically. The term ―nomothetic‖ is based on what Kant
described as a tendency to generalize or to derive laws that explain objective phenomena. The
term is suggested by the Kantian philosopher Wilhelm Windelband and extensively used by
Meyen (1977,1978). Nomothetics in biology describes the laws appearing in diversity sets
generated by biological variability.
The biosystem develops and transforms in a way that it maintains its ̳organizational
invariance‖. The organizational invariance is a spatiotemporal characteristic which is
expressed in a certain ideal pattern called archetype. The archetype determines the attribution
of a biosystem to a certain taxonomic group. The idea of a taxonomic class can be expressed
through the same organizational invariance. Archetype has a certain structure, being consisted
of merons, the generalized structural components of the homology parts of a certain
archetype. Merons are not rigidly fixed and can be divided into a set of alternative states that
can appear sequentially in time. The complete set of alternative states of a meron and of
transitions between them within the archetype is called refrain. Meyen associated an
application of the same transformation to different initial forms with theme development in a
musical composition; that is why he named this phenomenon "refrain", an archetype-like
character usually more complex than an ordinary morphological trait. The law of
polymorphism associated with meron is really the law of the organizational invariance of a
given biological system formulated in Rosen‘s concept. Meron, according to Meyen, also
possesses its own individual time. This time appears as a variability pattern referred to an
individual biological system and includes a component which is uniform in all objects being