Models of Self-Replicators

Introduction

Structural models and patterns are vitally important for human beings. From birth, we base our emotional and cognitive representations of the external world on species-specific signals (the human face) and exploit these signals to structure our instinctive behavior. The creation of cognitive patterns to represent the world lies at the very heart of human cognition. It is this process that underlies our efficient use of signs, our ability to communicate with natural languages and to build cognitive artifacts, the way we organize the external world, and the way we organize external events in our memories and our flow of consciousness. Patterns are sometimes calls schemas, or models, and discussed in terms of a gestalt (Piaget, 1960; 1970; Koelher, 1974). In the middle ages a pattern meant “the original proposed to imitation; the archetype; that which is to be copied; an exemplar” (from the On Line Etymology Dictionary). Modern use dates back to the XVIII century. In 1977 Christopher Alexander introduced a new way of using the term in architecture. For Alexander, a pattern was a model used to encode and organize existing knowledge, avoiding the need to reinvent the knowledge every time it was needed. For Alexander a pattern was “a three part rule, which expresses a relation between a certain context, a problem, and a solution” (Alexander et al., 1977).

Patterns can be enormously diverse and some may be very complex. Others, however, can be very simple. Some can be described in terms of processes determining the replication of their internal components. They can be recognized by their structural characteristics, defined in terms of color, shape, and the relationships between their components. Sometimes they are organized symmetrically. Symmetry is a formal, structural characteristic of a pattern. As Pliny pointed out in his Natural History, (Book 34, Ch. 65; Loeb edition, Vol. 9, 174/76) the word “symmetry” is of Greek origin and has no equivalent in Latin. In the golden age of ancient Greece, “symmetry” was one of a group of terms denoting harmony, rhythm, balance, stability, fine proportions and well-organized structures. However, the sense of the word has changed over the centuries. Today, the term belongs to geometry where it is tied to the concept of bilateral or mirror symmetry. The existence of symmetry is proved - or can be proved - by applying well defined rules, defined in a formal mathematical or physical system. Yet the original uses of the word - tied to the emergent esthetic qualities of symmetry - remain as valid as ever.

There are many way of measuring symmetry and of defining it in operational terms (Stewart, 2007). We can study symmetry:

• 1.

  With respect to the passage of time;

• 2.

  As a spatial relationship;

• 3.

  As a geometric transformation such as reflection, rotation and changes in scale;

• 4.

  Through other kinds of functional transformation;

• 5.

  Through abstract elements in theoretical models of language, music and thinking strategies.