Body as Processing Unit

Figure 3.5: A biological adaptive System as Selmodifying Input-Output System

To give a first idea about the subject we will follow the methodological approach of Card, Moran, and Newell (1983)[21]. Some of the facts can be updated by more recent publications but the general point of view is still valid.

Following the main view as depicted in the figure 3.5 we start with the overall structure

$$IO-SYSTEM(x) iff x=\langle I,O,IS,\phi \rangle$$ (3.1)

$$\phi : I \times IS \longmapsto IS \times$$ (3.2)

This is the most general schema we know to talk about systems which can self-modify their internal structures $IS$. Many variants are possible how to realize this self-modification. Card et al. propose (p.24) the following sub-functions:

$$\phi = \phi_{perc} \otimes \phi_{cog} \otimes \phi_{mot}$$ (3.3)

$$\phi_{perc} := perception$$ (3.4)

$$\phi_{cog} := cognition$$ (3.5)

$$\phi_{mot} := motor functions$$ (3.6)

In the following we assume that the input values $I$ are states of the system, which are modified from 'the outside' by stimuli thus the IS do not belong to the self-modifiable internal states $IS$. The output-states $O$ will be caused by internal states of the system, the motor states $M_{mot}$, but we count them too as not directly belonging to the internal states $IS$. Thus we have the following facts:

$$I \nsubseteq IS$$ (3.7)

$$O \nsubseteq IS$$ (3.8)

$$I \cap O = \emptyset$$ (3.9)

Furthermore do Card et al. interpret the input states as sensory buffer $SB$ with variants for every kind of sensory channel like visual $SB_{vis}$, auditory $SB_{aud}$, tactile $SB_{tac}$, etc. The internal states $IS$ are mainly interpreted as memory $M$. Card et al. distinguish between the working memory - what we will call here shot term memory - $M_{ST}$ as well as the long term memory $M_{LT}$. Another important subset will be that part $M_{mot}$ which manages the output-states. Thus we get

$$M_{ST} \cup M_{LT} \cup M_{MOT} \subseteq IS$$ (3.10)

$$M_{ST} \cap M_{LT} \cap M_{MOT} = \emptyset$$ (3.11)

$$SB \cup O \nsubseteq IS$$ (3.12)

$$SB \cap O = \emptyset$$ (3.13)

$$\phi_{perc} : SB \times M_{ST} \times M_{LT} \longmapsto M_{ST}$$ (3.14)

$$\phi_{cog} : M \longmapsto M$$ (3.15)

$$\phi_{mot} : M \longmapsto O$$ (3.16)

The main point here is that we can observe a time lag between an input stimulus $s$ to the system and a response $r$ which is depending on the stimulus. The authors Card et al. give examples of average response times $\tau$:

$$\tau_{VIS.P} = 100[50-200]msec$$ (3.17)

$$\tau_{COG} = 70[25-170]msec$$ (3.18)

$$\tau_{MOT} = 70[30-100]msec$$ (3.19)

$$Perc-act-cycle = 100+70+70=240msec$$ (3.20)

This indicates the timely dimensions in which we have to locate the durations of responses. There are other values with regard to duration times $\delta$ in the different sensory buffers or in the memories or about capacities $\mu$. These should be read in the book itself (or in other more recent publications).