# Object

An object is a representation of a relation between actions. In the simplest case it is a subset of A1x A2, where A1 and A2 are some sets of actions. Such an object is a set of ordered pairs a1, a2> with ai \in Ai. Such a pair tells that if action a1 takes place, then it is followed by a2.

An egg can be defined by pairs of actions which include:

• (look at it and perceive a white spot)
• (throw it on the floorand perceive a small pool of liquid)
• (Keep it at the temperature of the mother-hen's body for a certain number of days and a chicken hatches), etc.
A more precise definition of an object can be achieved through relations including more variables, including those which stand for other representations: we allow here metasystem transitions which, in the last analysis take us back to actions.

Suppose I am aware of a tea-pot on the table in front of me. This is a result of my having the mechanism of abstraction in the brain. I recognize the image on my retina as belonging to a certain set of images, the abstraction tea-pot'.

But there is more to it. I perceive the tea-pot as an object. The object tea-pot' is certainly not a definite image on the retina of my eyes; not even a definite part of it. For when I turn my head, or walk around the table, this image changes all the time, but I still perceive the tea-pot as the same object. The tea-pot as an object must, rather, be associated with the transformation of the image on my retina which results from the changing position of my eyes. This is, of course, a purely visual concept. We can add to it a transformation which produces my tactile sensations given the position and movements of my fingers.

The general definition of an object suggested by this example consists of three parts.

1. First we define a set R{ob of representations which are said to represent the same object; in our example this set consists of all images of the tea-pot when I look at it from different view-points, and possibly, my sensations of touching and holding it.

2. Then from the set of all possible actions we separate a subset Acogn of actions which will be referred to as cognitive; in our case Acogn includes such actions as looking at the tea-pot, turning my head, going around the table, touching the tea-pot etc. -- all those actions which are associated with the registration of the fact that a tea-pot is there.

3. Finally, we define a family of functions fa(r), where for every cognitive action a \in A{cogn, the function

fa: R{ob \to R{ob

transforms a representation r \in R{ob into fa(r) = r' which is expected as a result of action a.

The most important part here is the third; the first two can be subsumed by it. We define an object b as a family of functions fa:

b = {fa: a \in Acogn}

It also can be seen as a subset of Acogn x Robx Rob.

The set Acogn is the domain of the index a; the set Rob is the domain and co-domain of the functions of the family.

When I perceive an object b, I have a representation r which belongs to the set Rob; I then execute some cognitive actions, and for each such action a I run my mental model, i.e. perform the transformation fa on r. If this anticipated representation fa(r) matches the actual representation r' after the action a:

fa(r) = r'

then my perception of the object b is confirmed; otherwise I may not be sure about what is going on. Observing a tea-pot I check my actual experience against what I anticipate as the result of the movements of my head and eyeballs. If the two match, I perceive the tea-pot as an object. If I travel in a desert and see on the horizon castles and minarets which disappear or turn topsy-turvy as I get closer, I say that this is a mirage, an illusion, and not a real object.

The concept of an object is naturally (one is tempted to say, inevitably) arises in the process of evolution. It is simply the first stage in the construction of the world's models. Indeed, since the sense organs of cybernetic animals are constantly moving in the environment, these actions are the first to be modeled. In the huge flow of sensations a line must be drawn between what is the result of the animal's own movements, and other changes which do not depend on the movements, are objective.

Description of the world in terms of objects factors out certain cognitive actions. Function fa factors out the action a by predicting what should be observed when the only change in the world is the subject's taking of the action a. If the prediction comes true, we interpret this as the same kind of stability as when nothing changes at all. The concept of object btings in a certain invariance, or stability, in the perception of a cybernetic system that actively explores its environment.