From Real Worlds to Virtual Worlds

Figure 3.1: GA with Genotype and Phenotype

In 'real life' the genotype is the 'code base' for the construction of a phenotype, complex bodies, which are those entities which finally will interact with the environment (earth)(cf. 5.12). In real life there is no need for an explicit fitness function because the fitness function is 'implicitly given' in the way how the environment interacts with the population of the phenotypes.

The transition from genotype to phenotype is usually called growth (or more technically ontogeny as well as ontogenesis), or as formula $ growth: ENV \times GENOTYPES \longmapsto PHENOTYPES$.

This is a rather complex process, a real masterpiece of nature. To include this in computational evolution as evolutionary programming is even in simple cases highly demanding in computation resources.

We will not discuss the subject of 'growth' here but skip to the subject of phenotypes acting as learning systems $ SYS$ in an environment $ ENV$3.1.

From the biological case we know that a phenotype is not defined by pure chance only but in a combination of a chance driven mechanism of genetic combinatorics combined with selection mechanism by the environment. Thus only those phenotypes can 'survive' which are adapted to the given environment (cf. some general books about this topic Duve (1995)[59], Davies (1998)[56]).

Every real body represents therefore a minimal combination of components which are necessary to survive in an environment like the earth. Although we do not intend to reconstruct real bodies within our learning theory it can be helpful to summarize here some key factors of real living systems to be given for a successful living (Remark: the enumeration below does not describe the most simple systems but those which are already quite able to move around in an environment).

  1. Energy: Every phenotype - here called a system - needs continuously energy $ E$ to support the processes needed to exist as a phenotype.
  2. Environment: The only source for energy is an environment $ ENV$. We will call an environment 'life friendly' if is has free energy. Otherwise 'not life friendly'.
  3. Open system: To be able to exploit the energy resources of an environment a system must be an open system which can have some input from the environment as well as some output. An open system is therefore and input-output-system or simply an $ IO-system$.
  4. Fixed/ Mobile: If the energy is moving in an environment (e.g. in water) then can the system be fixed to a certain position and 'wait' for the energy. If not, then the system itself must move around to get to the place where the energy is. We will assume here the case of mobile systems which can move.
  5. Input: The input of a system must at least enable the intake of energy or of material which contains usable energy. Additionally there should be the capability to sens the 'presence' of energy or the presence of material which contains energy.
  6. Output: The system must be able to 'move' to different 'positions' in the environment to be able to get in contact with material containing energy. Thus there should be at least one 'action' which introduces in the environment a change of the actual position of the system in the environment. Additionally there must be an action to take perceived energy or material containing energy to enable an 'intake' for consumption.

From this we can derive minimal requirements for an environment $ ENV$ with a spatial structure providing free energy $ E$ for intake by an open system $ SYS$, which can move within the environment.

Gerd Doeben-Henisch 2013-01-14