0. Maximization of Transfer. Any agent is regarded as displaying intelligence and insight when it is able to transfer actions used in previous situations to new situations. For example, a robot might need to transfer a task developed for one region of a work-space onto another region of a work-space. The ability to transfer past solutions to new problems is at the very core of what it means to have knowledge.

   Also transfer can be regarded as equivalent to re-usability, which is a major issue driving software-development, e.g., it was the major stimulus in the development of object-oriented technology.

   The book argues that transfer is basic to aesthetics. For example, a symphonic movement by Beethoven has remarkably few basic elements. The entire movement is generated by the transfer of these elements into different pitches, major and minor forms, overlapping positions in counterpoint, and so on. We argue:

   Aesthetics is the maximization of transfer.

   That is, transfer is the basis of all intelligent behavior, and we argue that intelligence is equivalent to aesthetic structuration. Furthermore, those objects in which transfer is maximized are actually those objects that people call art-works.

0. Maximization of Recoverability. A basic factor of intelligence is the ability to give explanations. An agent must be able to infer the causes of its own current state, in order to identify why it failed or succeeded - and edit its behavior. This is basic, for example, to design, where one might need to go back to a previous stage, and proceed in a different direction.

   But note also that, with respect to an apparently very different set of issues, recoverability is basic to computer vision which requires recovering, from the retinal image, the environmental processes that produced that image - an inference often referred to as inverse optics. With respect to a related set of issues, all science is about the recoverability of those causal processes that lead to the results on the measuring instruments. We shall see that a basic aspect of a musical work is that it is organized to ensure recoverability.

This section presented our two fundamental criteria of intelligence: maximization of transfer and maximization of recoverability. It will be seen that, if generativity satisfies these two criteria, then it has a powerful mathematical structure. Essentially, this involves giving a new approach to geometry that incorporates intelligence (aesthetic structuration) into the very definition of shape.

3 Complex Shape Generation

The primary goal of the book is to handle complex shape. Such a shape might be a highly complex design, such as a Beethoven symphony, or an assembly in