Seymour Papert

Papert describes the idea which I call “the elevation of control” emphasizing two points: first, the local grouping of knowledge structures is critical to understand; second, learning may be explained by the insertion into a complex network of a simple change whose effect is profound [note 1].

…Children up until the age of six or seven believe that a quantity of liquid can increase or decrease when it is poured from one container to another. Specifically, when one container is taller and narrower than the first, the children unanimously assert that the quantity of liquid has increased. And then, as if by magic, at about tthe same age, all children change their mind: They now just as unequivocally insist that the amount of liquid remains the same…. Why does height in a liquid seem like more to the child, and how does this change?

Many theories have been advanced for how this could come to pass. One of them, which may sound most familiar because it draws on traditional psychological categories, attributes the pre-conservationist position to the child’s being dominated by “appearances”. The child’s “reason” cannot override how things “seem to be”. Perception rules.

Let us now turn to another theory, this time one inspired by computational methods. Again we ask the question: Why does height in a narrow vessel seem like more to the child, and how does this change?

Let us posit the existence of three agents in the child’s mind, each of which judges quantities in a different, simple minded way. The first, HEIGHT, judges the quantity of liquids and anything else by its vertical extent. Height is a practical agent in the life of the child. It is accustomed to comparing children by standing them back to back and of equalizing the quantites of Coco-Cola and chocolate in children’s glasses. We emphasize that Height does not do anything as complicated as “perceive” the quantity of liquid. Rather, it is fanatically dedicated to an abstract principle: anything that goes higher is more.

There is a second agent, called WIDTH, that judges by horizontal extent. It is not so practiced as Height. It gets it chance to judge that there is a lot of water in the sea, but in the mind of the child this is less influential than Height.

Finally, there is an agent called HISTORY, that says quantites are the same because once they were the same. History seems to speak like a conservationist child, but this is an illusion. History has no understanding and would say the quantity is the same even if some had indeed been added.

In the experiment with the preconservationist child, each of the three agents makes it own “decision” and clamors for it to be adopted. As we know, Height’s voice speaks the loudest. But this changes as the child moves on to the next stage.

There are three ways, given our assumption of the presence of agents, for this change to take place. Height and Width could become more “sophisticated”, so that, for example, Height would disqualify itself except when all other things are equal. This would mean that Height would only step forward to judge by height those things that have equal cross sections. Second, there could be a change in “seniority”, in prerogative: History could become the dominant voice. Neither of these two modes of change is impossible. But there is a third mode that produces the same effect in a simpler way. Its key idea is that Height and Width neutralize one another by giving contradictory opinions. The idea ia attractive (and close to Piaget’s own concept of grouplike compositions of operations) but raises some problems. Why do all three agents not neutralize one another so that the child has no opinion at all? The question is answered by a further postulate (which has much in common with Piaget’s idea that intellectual operators be organized into groupements). The principle of neutralization becomes workable if enough structure is imposed on the agents for Height and Width to be in a special relationship with one another but not with History. We have seen that the technique of creating a new entity works powerfully in programming systems. And this is the process we postulate here. A new entity, a new agent comes into being. This is agent Geometry, which acts as a supervisor for Height and Width. In cases where Height and Width agree, Geomtry passes on their message with great “authority”. But if they disagree, Geomtry is undermined and the voices of the underlings are neutralized. It must be emphasized that Geometry is not meant to “understand” the reasons for decision making by Height and Width. Geometry knows nothing except whether they agree and, if so, in which direction.

The essential and profound point in Papert’s story about computational agents is that epistemological complementarity of components permits the growth of structure [note 2].

Among the many issues left unresolved by Papert’s Piagetian reformulation, my work pursues the question of how such a change, the elevation of control, might come to pass through the child’s interactions with her everyday world of experience. It goes on to uncover a second form of such a change — but one with no immediate procedural impact — which I have named the correlation of perspectives.