eesti teaduste
akadeemia kirjastus
Estonian Journal of Engineering

A 6D space framework for the description of distributed systems; pp. 140–171

Full article in PDF format | doi: 10.3176/eng.2012.2.04

Elmo Pettai


This paper proposes a six-dimensional (6D) space framework and an appropriate reference entity for the description of organizations and realization of identifiable matter. The aim was to compose and present a new differentiable and well-structured syntactic reference entity on the basis of a general 4D space-time system. The entity should be visual, capable of providing people who develop, integrate or analyse distributed motional applications with basic means for navigation and adequate comprehension of motion. The common length, width and height dimensions determine the 3D subspace for definition of the geographic points of the motional concept. Time and the newly-founded content and merit dimensions together form a 3D realization space that inherently describes existence of motion outside the geographic points. The content dimension is used to declare the quantitative values of the quantities and properties of motion. The merit dimension is used to declare the qualities of quantities and properties. The transformation in the dynamic realization space is defined by the named quantities and properties. The time dimension is used to define the dynamic channels for the valuable content of a named quantity or a property of motion. The temporal content values of the named quantities and properties of matter are defined at the geographic points. Symbolic names of the axes of the new 6D axis system are: length, width, height, time, and the newly introduced content and merit. An ontology is proposed by the author to define the hierarchy of the merital names. The content axis uses the basic hierarchy with Arabic numerals to define the quantitative values of the quantities (properties). The 6D axis system that is semantically interpreted as a syntactic reference item is universally usable to describe the motion of a distributed concept, a model or a real entity, including transformation between different qualities of motion. Potential usage of the new 6D axis system together with the ontology is described. An example in the field of electrical engineering and industrial automation technology is presented. A visual user interface is discussed.


  1. Boule, M. Mob Rule Learning: Cump, Unconferences, and Trashing the Talking Head. Informa­tion Today Inc., New Jersey, 2011.

  2. Kumpulainen, L., Laaksonen, H., Komulainen, R., Martikainen, A., Lehtonen, M., Heine, P., Silvast, A., Imrin, P., Partanen, J. and Lassila, J. Distribution Network 2030: Vision of the Future Power System. VTT Tiedoteita-Research Notes 2361, Espoo, 2006.


  4. Erning, P., Langer, K., Rüdele, H. and Schultz, D. Not lost in translation. ABB Rev., 2009, 3, 63–65. Asea Brown Bowery Ltd, Zürich.

  5. Haykin, S. and Kosko, B. Intelligent Signal Processing. IEEE, New York. 2001.

  6. Wesson, P. The Meaning of Dimensions. University of Waterloo, Ontario, 2007.

  7. Wilkins, D. R. William Rowan Hamilton: mathematical genius. URL: cws/article/print/22749

  8. Stelea, C. I. Higher Dimensional Taub-NUT Spaces and Applications. Thesis, University of Waterloo, Ontario, 2006. URL: cistelea2006.pdf

  9. Wesson, P. S., Ponce de Leon, J. Kaluza–Klein equations, Einstein equations, and effective energy-momentum tensor.  J. Math. Phys., 1992, 33, 3883.

10. Wesson, P. S. The geometrical unification of gravity with its source. Gen. Relativity Gravit., 2008, 40, 1353–1365.

11. Fabbri, L. Taking Kaluza seriously leads to a non-gauge-invariant electromagnetic theory in a curved space-time. Ann. Fondation Louis de Broglie, 2004, 29, 641–649.

12. Liko, T. Induced current and redefinition of electric and magnetic fields from non-compact Kaluza-Klein theory: an experimental signature of the fifth dimension. Phys. Lett. B, 2005, 617, 193–197.

13. Vedula, S., Baker, S., Seitz, S. and Kanade, T. Shape and Motion Carving in 6D. The Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, 15213.

14. Miller, D. Abstract Syntax and Logic Programming. Lecture Notes in Computer Science, Springer, 1992, 592, 322–337.

15. Magee, B. The Story of Philosophy. Dorling Kindersley, London, 1998.

16. Rehg, J. and Satori, G. Programmable Logic Controllers. Pearson Education, New Jersey, 2007.

17. Action (physics). Http://

18. Namespaces in XML 1.1, 2006.

19. Haykin, S. Communication Systems. Wiley, 4th ed., 2001.

20. Elert, G. Equations of Motions. The physics hypertextbook, 2008, physics/mechanics/motion-equations/

21. Altova MapForce 2008. User and Reference Manual. Altova GmbH., USA, 2008.

22. Kim, L. XMLSPY Handbook. Wiley, Indianapolis, 2003.

23. URL:, 21.11.2008.

24. Standard EN 61850-7-1:2003. Communication networks and systems in substations. Part 7-1: Basic communication structure for substation and feeder equipment.

25. URL:, 20.06.2006.

26. Standard IEC 61499-1:2005. Function blocks, Part 1: Architecture (prep. by IEC TC65).

27. Standard ISA-95.00.01-2000. Enterprise-Control System Integration, Part 1: Models and Terminology.

28. Standard ISA-88.01-1995 (Rev. 2006). Bach Control, Part 1: Models and Terminology.

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