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What is Boundary Mathematics

Encyclopedia of Information Science and Technology, Second Edition
Boundary Mathematics is a semiotic formalism generated by creating a distinction (a boundary) in nonexistence (of system) thus resulting in a first system. Extended to multiboundaries with a common sense reiterative reduction rule leading either to one distinction or nonexistence, this mathematical form and process is the germ of an approach to the formulation of a universal language of mathematics.
Published in Chapter:
Autognomic Intellisite
Jon Ray Hamann (University at Buffalo, State University of New York, USA)
DOI: 10.4018/978-1-60566-026-4.ch050
The 20th century saw the beginning of the evolution of learning machines from the growth of Boolean computers into Bayesian inference machines (Knuth, 2003). For some this is the crux of Artificial Intelligence (AI); however, AI research generally has yielded a plethora of specifically engineered, but formally unrelated, theories/models with varied levels of applications successes/failures, but without a commonly-explicatable conceptual foundation (i.e., it has left a theory-glut). Despite these many approaches to AI, including Automated Neural Nets, Natural Language Processing, Genetic Algorithms, Fuzzy Logic and Fractal Mathematical computational approaches, to identify only a few, AI itself has remained an elusive goal to achieve by means of a systems architecture relying on an implementation based on the systemic computer paradigm. The 21st century experience is overwhelmingly one of an ever-accelerating, dynamically changing world. Just staying in place seems nearly impossible—getting ahead is becoming increasing unfathomable in a world now characterized by an evolving dominance of Information Science and Technology Development in exponentially tighter (shorter) innovation cycles (IBM, 2008). In business, for example, there is the continuous challenge to ensure that the business’s products appear obviously differentiated from the competition, while staying current with the never-ending hot new trends that buffet the industry. A prime case in point is that of staying current with the trends in the computer solutions industry since adapting a computer dependent business (and most are) for the next big trend can be expected to be mitigated, if not made completely obsolete, by the next next big trend already on the radar screen.
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