QUANTITATIVE LANGUAGES FOR COMPLEX SYSTEMS

Mark A. Smith, Yaneer Bar-Yam and William Gelbart

We believe that many fields of scientific study are hampered by the lack of precise language to describe the structure, behavior, and dynamics of complex systems. New quantitative languages are needed. The challenge is to develop intuitive, and yet precise and systematic mechanisms for description. Such languages will merge the strength of human language in specifying objects, attributes, relationships and processes with the ability of computer systems to display and manipulate numerical aspects of systematic description. They will also serve as bridges between experimental observations and theoretical treatments.

The creation of a particular language involves connecting qualitative terms and quantitative representations of the system. We illustrate the development of such languages using the structure of drosophila (fruit fly) wings. In this language, the description of a wing is composed of descriptions of veins (structural support elements of the wing), and the structural constraints on these veins. The veins are described as mathematical curves which capture their shape. The constraints that are satisfied by these curves as parts of the wing are incorporated in the description of the wing. The nature of a "wing" as a class of objects is captured by the set of curves and their constraints. A description of a particular wing is captured by the specific values of parameters which can be captured for individual real wings.

Graphical illustration of a quantitative wing model
Overlay of default quantitative wing model on real wing
After capture of real wing structure—quantitative description of the real wing

Short paper describing the quantitative language

Papers:

M. A. Smith, Y. Bar-Yam and W. Gelbart: Quntitative languages for complex systems applied to biological structure, Nonlinear Dynamics in the Life and Social Sciences, W. Sulis and I. Trofimova, eds., NATO Science Series A/320, pp.65-71, 2001, IOS Press. PDF file

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