The structure definitions wiki page

Structure and Structure Definitions

Members: Tanja Gesell, Alexander Moffet, YunQiXue, Walter Zesk, Adam Campbell, Meritxell Vinyals, Peter Graff, Laura Feeney, David Papo and Craig Hayenga.

Email: csss08-structuredefinitions@googlegroups.com

At first sight, it seems obvious what a structure is. Recently, there has been a lot of literature -- e.g. in poststructuralist (e.g. Deleuze, 1973). However, it seems that there is no possibility in forming or there is a lack of a clear, general definition. Indeed, the lack of consensus within this literature raises a number of questions regarding the possibility of providing a single general definition of structure. Is there a single concept of structure or just different concepts of structure found in different disciplines? Are structures discovered or are they invented? Are they simply patterns, or do they offer a more profound understanding of the properties of different entities? Is there a single, correct structure with which each entity is associated, or is there a range of different potential structures, with pragmatic considerations determining the assignment of particular structures to particular entities? Is there a general challenge in thinking about structure? How scientist apply structure today? What is a structure?

One way in which to improve our understanding of the concept of structure is to consider its use in and between a wide range of disciplines. In our project, we propose to consider different definitions of structure as they are found in information theory, philosophy, linguistics, computer science, logic, software engineering, molecular biology, physics, psychology, and architecture. In comparing the concepts employed within these different disciplines, we shall attempt to elaborate the shared features of these definitions -- e.g. considering their modularity, functionality, levels of abstraction and time. We shall likewise study the history of this concept as it has evolved within these different disciplines, so as to develop an additional perspective for the comparative analysis of this concept.

In addition to the variance in concepts of structure from different disciplines, we are also interested in the similarity of structure, especially how scientists apply structures to conceptual modeling, on a higher level (Dalen, 2004). Logic, the formal reasoning language, is considered as a fundamental rule in building structure in different disciplines. For example, logical structure was used intensively by mathematicians to prove theorems, and later in all kinds of mathematical modeling. Do other disciplines also choose their modeling language, define the syntax and semantics of the language, and derive axioms in order to have a structural approach in finding new results? If they do, is it precisely like how a logician would do it or do we need to 'translate' them? If not, how far is this from the logic approach of structure?

On the basis of this analysis, we hope to elucidate a general concept of structure. This might be done through reference to the capacity of a universal Turing machine operating upon sequences of characters. Koppel (Koppel,1994) and Wiener (Wiener, 1994) have suggested that the structures of a given sequence might be associated with those Turing machines that are capable of producing the sequence as output. This computational approach offers a useful foundation upon which to base a general understanding of structure. In order to build upon this foundation, we shall attempt to specify the sequences/data and machines/programs that are present in those disciplines in which the concept of structure is used, thus offering a general framework for the comparison of such uses. In addition, the methodology of conceptual modeling may provide a useful set of tools with which to clarify this concept.

The global aim of this summer school project is the try to clarify the meaning of structure in general and between scientists of different disciplines. It is an cross-disciplinary issue. However, in the end we want to take structure on a higher human level into account. We will see if our discussions need and come up with some new terms and visualizations.

References:

Deleuze, G: Woran erkent man den Strukturalismus? Berlin: Merve Verlag 1973.

Dalen, D: Logic and Structure (Universitext), Kindle Edition, 2004

Koppel M: Structure. In The Univeral Turing Machine, A Half-Century Survey. Edited by Herken R., New York: Springer Verlag 1994: 403-419.

Wiener, O: Form and Content in Thinking Turing Machines. In The Univeral Turing Machine, A Half-Century Survey. Edited by Herken R., New York: Springer Verlag 1994: 403-419.