A Model of Inter and Multi Disciplinary Domains, and their Mutual Interactions
The Melvil Dewey Decimal Classification system maps the human knowledge domains into a library classification decimal system, which means that the knowledge is discretized. The domains are countable similarly to how Cantor proved the countability of the fractions’ domain.
The debate about the “inter-” and “multi-” disciplinary domains may also be extended into “sub-domains” or from another point of view – into “super-domains”.
However, Science and Technology has rapidly developed after it was classified. If at the beginning, two decimal digits were enough to classify the world's knowledge into a knowledge domain, today we need more digits – about five. This means we are able to display about a million domains of knowledge. The decimal point indicates the sub-division in the zooming-in; the number of such decimal points is unlimited. Thus, the number of hierarchical levels in the knowledge-tree is unlimited. The maximal level is unreachable since it propagates in time.
This intriguing issue raises doubts whether the tree is the most appropriate structure in the current state of the knowledge classification. However, I believe that the knowledge tree is a convenient way of expressing various connections between the knowledge domains. There are other models such as multi-level graph-networks that approximate closer to reality. These models can be further visualized by graph diagrams.
The knowledge diagram is more complicated, considering the interaction between science and industry relative to each domain.
The model of reality might be compared to the object-oriented programming languages approximating reality in order to construct more naturally computer programs that can model the world.
The mutual correspondence of the knowledge domains is dynamic. Some examples of relatively new domains are as follows: biotechnology, bioinformatics, nanotechnology, integro-differential equations, data warehouse, data mining, requirements engineering, micro biology, and bio-chemistry. There is an overlap between the various domains.
The phrase "humans know less about more and more about less" represents the trend of future science and technology. Another interesting phrase is "an image is worth a thousand words." Figures 1 and 2 show the possible relationship between the knowledge domains represented by various geometrical objects and their properties such as color, form, perimeter type, and position.
Research and design are two complementary human activities that, from the dawn of history, have improved Western civilization. New discoveries and research were made possible by former technological innovations. Many areas of research mutually upgrade and improve themselves in a positive feedback loop. However, mathematical proofs represent a different kind of a symbiotic research-design relationship.