# The algebra of joining and absorbing

### Y. B. Karasik, Thoughts Guiding Systems Corp., Ottawa, Canada. e-mail:karasik@sympatico.ca

Many system transformations are combinations of two basic ones:

and

Rectangle around a letter purports to show that any system has the boundary, the interior, and the exterior. The border of the rectangle symbolizes the boundary of the system.

The first transformation means that any system gets augmented by other system(s). The second transformation means that any system eventually absorbs the systems, which were added to it.

From these two basic rules a multitude of system transformations follow:

The first two transformations are ordinary replications. The latter transformation is transition from ordinary replication to replication in the form of nested dolls. A single object is first replaced by a multitude of the identical objects and then by a multitude of nested objects.

Another useful transformation is augmenting an object by an anti-object:

For example, some turbo-prop planes have engines with not one but two propellers rotating in opposite directions.

Another useful transformation is embedding of a scaled down version of anti-object inside an object:

Combination of the last two transformations gives rise to the following transformation:

Here is an example on the latter transformation: a meat grinder with 2 screw conveyors, one inside the other, rotating in the opposite directions.

The proposed algebra is simple yet limited in scope. Although it covers more transformations than the notation proposed in the editorial, it is still not enough.