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About the Theory of Triune Continuum

The name of Triune Continuum Paradigm originates from one of the three theories that were employed for the paradigm definition, from the theory of Triune Continuum. This theory was defined in the following PhD thesis:

A. Naumenko. "Triune Continuum Paradigm: a paradigm for General System Modeling and its applications for UML and RM-ODP", Ph.D thesis number 2581, Swiss Federal Institute of Technology - Lausanne. EPFL, June 2002.

This theory allows for introduction of abstract ontologies that are formally necessary and sufficient to cover the modeling scope of different modeling contexts on the most abstract level. Triune Continuum Theory introduces three continuums that represent in models the scope of general system modeling.

The first two continuums are:

- spatiotemporal continuum (where subjective space-time metrics are defined to be used in subjective representations);
- constitution continuum (where subjective constitutional metrics are defined to be used in subjective representations, e.g. objects that are defined in relation with their environments).

These two continuums are introduced in relation with each other as complements within the universal general system modeling scope. In other words: everything in the scope, which is not space-time, is constitution; and everything in the scope, which is not constitution, is space-time.

The third continuum is:

- information continuum (which emerges from mutual relations of the first two continuums and contains corresponding information about these relations, e.g. information about objects and their environments being related to spatiotemporal intervals or to points in space-time).

Thus the three continuums are triune : none of them exist without the others; either the three exist altogether, or they do not exist at all. Indeed, as soon as the first (spatiotemporal) continuum is introduced, everything in universal scope that does not belong to the first continuum immediately shapes the second (constitution) continuum; and the third (information) continuum immediately emerges as information about the mutual relations of the first two continuums (e.g. as spatiotemporal information about the constitution).

The notion of Triune Continuum is important for various system modeling frameworks, which are used in diversified domains of human activity (e.g. to analyze, to design and to develop coherent structures providing useful functionalities in domains spread from jurisprudence and health care to software engineering and machine-building industries). Using the notion of Triune Continuum it is possible to introduce and justify minimal sets of modeling concepts that are necessary and sufficient for those diversified frameworks to cover their respective representation scopes. To understand these useful implications of the theory of Triune Continuum you can continue exploring the Triune Continuum Paradigm.

To learn more about the theory of Triune Continuum (in particular, about the notion of continuum, about different applications of the theory and their usefulness) you can read the following publication:

A. Naumenko. "A report on the Triune Continuum Paradigm and on its foundational theory of Triune Continuum"; in PHISE'05, the 1-st International Workshop on Philosophical Foundations of Information Systems Engineering. Proceedings of the CAiSE'05 Workshops, Vol. 2, pp. 439-450; J. Castro, E. Teniente (Eds.); Porto, Portugal, June 2005. FEUP edições. ISBN 972-752-077-4.

About the Triune Continuum logotype

Triune Continuum logotype

Triune Continuum logotype represents the idea of Triune Continuum that was described above on this page.

In the Triune Continuum logotype the three smaller circles, positioned within the bigger circle, represent the three continuums introduced by the theory. The black and the white circles represent the first two continuums (spatiotemporal and constitution) that are introduced as complements to each other. That is to say, “everything in the scope, which is not space-time, is constitution; and everything in the scope, which is not constitution, is space-time” – is represented by the black and the white circles that make sense only on the white and the black backgrounds respectively. The third circle, showing Taoist symbol of yin-yang, stands for the third (information) continuum, the continuum that represents information about mutual relations of the first two continuums. The color strips of spectral decomposition of white light in the background with an unlimited number of their nuances symbolize the unlimited richness of information that can be represented by means of the three continuums.

Taoist symbol of yin-yang in the Triune Continuum logotype is a tribute to the Taoist philosophy that generalizes the idea of Triune Continuum in its principal book “Tao Te Ching” by Lao Tsu (604-531 BC) as following:

    The Tao begot one.
    One begot two.
    Two begot three.
    And three begot the ten thousand things.

                       Lao Tsu (604-531 BC)
                       "Tao Te Ching", Chapter 42.

Indeed, in our case:

“The Tao begot one.” – stands for: Universal scope allows for modeling.

“One begot two.” – stands for: Modeling intrinsically assumes two essences: space-time and model constitution (hence the first two continuums).

“Two begot three.” – stands for: From space-time and model constitution necessarily emerges information about their mutual relation (hence the third continuum).

“And three begot the ten thousand things.” – stands for: Information about mutually related space-time and model constitution is unlimitedly rich.

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