7.0 SUMMARY AND CONCLUSIONS
Within the specific domain of plastic injection molding, it was seen how a given design can be broken down into features. These features are a categorization of elements of a part, suitable for use as elements within rules. The rules in turn form a theory of what makes a part un-manufacturable.
The computational reasoning process depends on abstractions that have been gleaned from what can be called an uncharacterized continuum of reality. It is difficult to imagine the reality as a continuum because as one looks out upon the world one automatically starts recognizing salient features. A new-born baby may at first be unable to differentiate between the face of a parent and the family dog, but the development of differentiation capabilities is markedly rapid. Differentiation becomes key to understanding and making sense of the continuum.
As adults, the world is seen in terms of features, or as elements of data, distinct from an undifferentiated background of the continuum. The abstraction of this data itself is a classification, which imposes more than a taxonomy. The format of this data imposes a way of thinking. Humans are taught early to make firm distinctions such as between plants and animals, as opposed to all-things-blue and all-things-green.
It has been seen how abstractions from the continuum of reality can in turn be abstracted. This has been shown in the abstraction of complex features from the abstractions of simple features, which were in turn developed from topological abstractions. Given that one starts with data, however biased it may already be, there is an imposition of order in the form of classification, typing, or rules (as it has been argued here, classes and types are essentially rules). These rules often are specific to certain types of data. As the data increases or becomes clearer, the rules generalize to accommodate. Eventually, given a rich set of data with which to formally confirm or refute a hypothesis, a theory is generalized from the rules. A law is the ossification and application of a theory, continually confirmed by a data involved.