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:
"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:
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
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:
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
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 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
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
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.
return to the Triune Continuum
Paradigm page >>