Structural science
The term structural sciences is used to summarize areas of knowledge which generally consider functionally effective forms and which neither generally nor specifically deal with objects of nature or social reality. This limitation serves as an alternative to the classification according to subject area, as in the classification as natural , human or social sciences .
The use of the term structural science is often associated with the claim that these areas of knowledge represent meta theories of the subject areas or even refer to a single science of structures and forms. There is a certain relationship and overlap to the extent claimed with formal sciences or the classical rationalistic conception of a pure rational science . The idea of structural science then includes the idea of a unity of the sciences , which overcomes a division of the individual sciences so that in the end only the structural sciences and the respective empirical sciences in which it is applied face each other. One of the goals of structural science is to trace the origin of the diversity of organized and complex structures found in nature back to uniform, abstract fundamental laws. As part of the division of the sciences into individual sciences , a segmentation into structural sciences, natural sciences, human sciences (i.e. the humanities and social sciences), and engineering sciences is occasionally made. The term is often filled by giving basic and sub-disciplines of certain established sciences the rank of structural science.
scope
The proponents of this division of science include various research areas as structural sciences, some of which are listed as examples in the table on the right.
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| Thousands of individual disciplines are now counted among the structural sciences. |
Comparatively new branches, for example in the area between applied mathematics and the classical natural and engineering sciences, have opened up in the application areas of systems sciences or cybernetics.
Russian universities explicitly have their own faculties for applied mathematics and cybernetics. The Technical University of Ilmenau also describes its technical cybernetics and systems theory course as follows: “Technical cybernetics is an interdisciplinary science. It is located between engineering and applied mathematics and deals with the description, analysis and control of dynamic processes. Cybernetic methods enable z. B. the automatic navigation of ships, can describe complex processes in cell organisms or help to optimize logistical processes, such as timetables or energy networks. "
“Nowadays the structural sciences are the basic sciences for understanding complex phenomena. ... The fact that the proportion of structural sciences is constantly increasing can be seen, among other things, from the fact that computer simulation is increasingly displacing classic experiments in the natural sciences. ... In fact, the structural sciences seem to lead to a unified understanding of reality, that is, to an objective context of meaning and an objective whole, which now includes all forms of scientific knowledge. And it may seem downright paradoxical that it is precisely the multifaceted science of the complex that leads back to the unity of knowledge and thus to the unity of reality. "
development
mathematics
“The popular question of whether mathematics is a natural science or a humanities is based on an incomplete classification. It is a structural science. "
The structural-scientific concept of structure comes from the endeavor at the turn of the 20th century to find a common basis for all mathematics . Significant steps for this were the development of naive set theory , formal logic , the Hilbert program , the group theory of algebra and the work of the Nicolas Bourbaki group .
The formal predicate logic is based on the set theory formalized by Georg Cantor ( naive set theory ). George Boole's An Investigation of the Laws of Thought already compared the linkage structures of logical thinking with numerical algebra and its arithmetic methods. Gottlob Frege dropped the " Begriffsschrift before" the first purely formal axiomatic logic system with which it into the basic laws of arithmetic tried to found mathematics on a purely logical axioms, by trying the concept of number based on extents and mapping relations define. Frege's system, however, allowed the derivation of Russell's antinomy . This problem was met on the one hand with type theory and on the other hand with additions to the axiomatics of set theory.
Conversely, based on David Hilbert and Wilhelm Ackermann, logic was algebraized . For the position of formalism, roughly every set that formally satisfies the Peano axioms (represents a model of the axioms) corresponds to the natural numbers. The model theory is concerned in particular with such structures corresponding to axiomatised languages or theories. A model is a set provided with certain structures to which the axioms of the system apply. Formally, models are structures based on an elementary language in which the axioms are formulated. In proof theory , the structural proof procedure forms an important calculus basis as proof theory. Evidence is usually represented as inductively defined data structures , such as lists or trees. Formal logic forms one of the historical starting points of theoretical computer science through the theory of computability (see also computability ).
With the help of the abstract group concept, the abstract algebraic structure could be defined by one or more basic sets (of objects, elements or symbols) and the operations, relations and functions on these basic sets. “It was the undisputed merit of Emmy Noether , [Emil] Artin and the algebraists of their school, such as Hasse, Krull, Schreier, van der Waerden, to have fully implemented the conception of modern algebra as a theory of algebraic structures in the 1920s . “These structures were ultimately independent of the decision of the fundamental debate between Platonists, formalists and intuitionists.
Already in Frege's system the predicates themselves can become the object of the predication through predicates of a higher level (and so on). On this basis, large areas of mathematics can already be expressed in mathematical logic. The relation signs, function signs or constants then form the type of language, equivalent to the type of an algebraic structure. During the fundamental debate in mathematics and logic around 1940, a "structural standpoint" emerged which declared mathematics to be a structural science in relation to mathematics didactics and which became didactically effective in Germany from 1955.
The group Nicolas Bourbaki finally declared in a published article in 1950 structures for appropriate means to secure the entire unit of mathematics.
Computer science
The development of theoretical computer science began around the 1930s. The fundamental concept in computer science is the mathematical concept of the algorithm , which is a rule of action consisting of a finite number of steps to solve a mathematical problem. The concept of computability is associated with the concept of algorithms , for which various mathematical formalizations and analysis methods have been developed in computability theory . In computer science, too, structural properties of object classes are researched on a formal level, without taking into account which specific objects are subordinate to this structure and whether these can be constructed in reality at all, although a requirement for constructibility can certainly be made depending on the discipline.
A concept that is alien to classical mathematics is that of data structure , which is of central importance in computer science, alongside that of algorithms. The representation of the algorithms, data structures and investigations over time and space, which are necessary for the execution and storage, is a separate contribution of the theoretical computer science to the structural sciences.
Specific basic structures of computer science are in the area of computer structures u. A. the Von Neumann architecture (since 1945) or its opposite, the non-Von Neumann architectures (e.g. parallel computers ).
The basis of all structured programming that is still valid today are the three control structures of sequence, branching and loop. Flow charts or structured charts (since 1972) are used for visualization .
Structural science owes further important impulses to the subject areas of computability theory , the question of decidability and complexity theory . The investigations into automaton theory , especially those of cellular automatons , show a progressive character to this day, not least also in the field of scientific explanatory models.
Complexity Research and Systems Theory
In 1971, Carl Friedrich von Weizsäcker coined an expanded term for the structural sciences: “Structural sciences will not only refer to pure and applied mathematics, but also the area of the sciences, which is not yet fully understood in its structure and which is known by names such as systems analysis, information theory, cybernetics , Called game theory. They are, as it were, the mathematics of temporal processes that are controlled by human decision, by planning, by structures, [...] or finally by chance. So they are structural theories of change over time. Your most important practical aid is the computer, the theory of which is itself one of the structural sciences. Anyone who wants to promote the progress of science in a country must promote these sciences as a matter of priority, because they denote a new level of consciousness. "
In the 1970s and 1980s, synergetics , the theory of self-organization and chaos theory, other areas that can be assigned to the structural sciences, experienced a rapid rise. In the context of complexity research , the concept of the system plays a central role. Systems initially organize and maintain themselves through structures. The structure describes the pattern of the system elements and their network of relationships through which a system is created, functions and is maintained. The structure of a system is understood to mean the entirety of the elements of a system, their function and their interrelations. But in systems theory , system structure , system behavior and system development are mutually dependent . Therefore, in addition to structure, further axioms are introduced within system theory, which define the system boundaries (the distinction between system and environment), but above all the system attributes such as stability, dynamics, linearity, etc. A. include. Furthermore, it is constitutive for a system that the respective system elements fulfill a system function (system purpose, system objective) and thereby have a functional differentiation. The first formalized system theories were developed around 1950. The application of such model theories enables the simulation of complex processes and was therefore aimed at in many individual sciences, but above all in biology in the 1970s and 1980s.
“The structural sciences… are today powerful instruments for researching the complex structures of reality. They are structured according to the general organizational and functional features that structure reality and that we describe with generic terms such as system, organization, self-control, information and the like. In addition to the classic disciplines of cybernetics, game theory, information theory and systems theory, structural sciences have produced such important branches of science as synergetics, network theory, complexity theory, semiotics, chaos theory, catastrophe theory, theory of fractals, decision theory and the theory of self-organization. The theory of boundary conditions that I am aiming for may one day develop into an independent structural science. "
Idea, formalization and examples of mathematical structures
On the concept of mathematical structure
First of all, the "conception of modern algebra as a theory of algebraic structures" was formed, which is still often taught today as structural mathematics. Then the Bourbaki group developed all of mathematics as a "doctrine of structures" in the sense of a comprehensive structural science. However, the concept of a mathematical structure only has something to do with the colloquial term structure. Mathematics formulates this term much more precisely as part of its formalization. The hierarchy of mathematical structures contains, for example, the algebraic structures and the topological structures .
Every mathematical structure is based on a set M, the elements of which are initially not related to one another, for example the set M = {1,2,3,4,5}, whereby the elements are not necessarily numbers. A structure S is now impressed on this set M, which is called the carrier set. A mathematical structure can therefore be represented with (M, S) as an ordered pair for the system "the set M provided with the structure S". For this one can use an order relation, for example, which shows which elements are related to which others, or which remain isolated. The set M then has a certain structure S.
The formal definition of a mathematical structure is:
- A structure is a 4-tuple from a set A, as well as a family of basic relations I, one of basic functions J and one of constants K.
I, J and K can also be empty or infinite . A structure without I, J, and K is then again, trivially, the carrier set itself. Pure sets of relations without associated sets are therefore not defined as mathematical structures, but can only be analyzed separately as elementary structural components.
Complex structures and systems science
Relatively young branches of structural sciences nowadays deal with complex and hyper-complex structures. The interest in these structures was not primarily motivated by the desire for new mathematical models, but by the desire to understand natural structures. At the moment, therefore, many corresponding areas are located “between” applied mathematics and traditional natural and engineering sciences. Some areas are now quite well-formalized and others are more semi-formalized.
Examples of this are parts of systems science ( system dynamics , sustainability ), systems schools of thought ( Vester , Senge ), the sensor-motor stage model of emergent systems from the control, function and situation circles , as well as the viable system model or the approaches of cybernetics Consider order .
Relation to the natural, human and social sciences
Natural sciences
Abstract mathematical model formations can also be found nowadays in every branch of natural science, so that it can seem sensible to make these structural sciences a general component of the methodology . For physics, for example, it is then important to fish out of the most general possible structures those that are required for the description of experimental processes. Mathematical conclusions can then be drawn from the respective structure, which correspond to verifiable consequences for the object of investigation.
From the perspective of differential geometry , physical theories are differentiable manifolds with a finite number of dimensions. From a mathematical point of view, even the phase space is a special manifold. This knowledge then allows investigations such as the difference between integrable and non-integrable dynamic systems, and this has been investigated in more detail for some years now in the form of chaos theory .
Furthermore, the concept of the group has become extremely important in modern physics. The group theory , the mathematical tools available with which symmetries can be examined. A physical system is called symmetric with respect to a transformation if it does not change due to the application of the transformation. Symmetries are particularly important within the framework of Noether's theorem (formulated in 1918 by Emmy Noether ) because they result in invariances and thus conserved quantities.
The chemical can be used as application for the structure Sciences, since 1865 is the structure of theory (based on Friedrich August Kekule prevailed) in chemistry. According to this, chemical properties are explained by the internal structure of the molecules (an important application in chemistry is therefore the establishment of structural formulas ). This also created the basis for a special proximity to physics, which made it possible to interpret the chemical bonds as the ability of atoms to connect. Insofar as chemistry examines the bonds of atoms through their outer electron shell, which can realize very different bond strengths and types within chemical bonds due to their atomic and molecular structure, it deals with given structures within nature.
Within biology , structural biology deals with the creation of hierarchically organized structures in living beings, from macromolecules to cells , organs , organisms , biocenoses and biospheres . Both the individual building blocks of living beings and the individuals within populations or other communities are in a relational exchange with each other and with the physical-chemical environment.
In this context, the question of the extent to which certain structures are carriers of emergent properties is particularly relevant . While the structural analysis on the one hand promises to illuminate the transition between basic physical forces, chemical compounds and organic life, on the other hand there are also systems science approaches that can also be understood in structural terms.
Systems physics is carried out, for example, in the context of research into the physics of complex systems at the Max Planck Institute for the Physics of Complex Systems. Areas of non-linear system dynamics are researched, the physical fundamentals often provided by the models of statistical physics .
The systems biology is a branch of biological science that seeks to understand biological organisms as a whole. The aim is to get an integrated picture of all regulatory processes across all levels, from the genome to the proteome , to the organelles, to the behavior and biomechanics of the entire organism. Essential methods for this purpose come from systems theory and its sub-areas. However, since the mathematical-analytical side of systems biology is not perfect, computer simulations and heuristics are often used as research methods. Attempts to mathematically formalize life can be found among others. a. with Robert Rosen , who describes metabolism and repair or replication as the main characteristics of living beings in the context of his relational biology .
Examples of the integrative achievements of the structural sciences to support the natural sciences in describing the emergence of organized structures in nature are the research results of Manfred Eigen , which started in molecular biology, as well as the structural scientific results of Illya Prigogine and Herman Haken which began with considerations on thermodynamics. The paradigm of self-organization ( Ilya Prigogine ) and synergetics ( Hermann Haken ) made it possible to connect biological evolution as the evolution of structures to physics. Previously, the 2nd law of thermodynamics , which predicts an increase in entropy , seemed to contradict a spontaneous formation of structures. The starting point for the considerations of Haken on synergetics was therefore the question of why complex structures could develop in the universe if only the second law of thermodynamics applies. He writes about it:
“Physics claims to be the fundamental natural science par excellence. But if you had asked a physicist in the past whether, for example, the origin of life could be reconciled with the fundamental laws of physics, the honest answer should have been no. According to the basic laws of thermodynamics, the disorder of the world should increase more and more. All regulated functional processes would have to cease in the long term, all order would fall apart. The only way out, which many physicists saw, was to view the formation of states of order in nature as a gigantic fluctuation phenomenon, which, according to the rules of probability theory, should also be arbitrarily improbable. A truly absurd idea, but it seemed the only acceptable one in the context of so-called statistical physics. Had physics reached an impasse by claiming that biological processes are based on physical laws, but that the origin of life itself contradicts physical laws? The results of the synergetics enable us to uncover the limits of thermodynamics and to prove classic misinterpretations. "
Humanities and Social Sciences
In the philosophy above all the schools of thought of making structuralism and the structures realism of structure scientific bases use. Structuralism is a collective term for interdisciplinary methods and research programs that investigate structures and relationships in the largely unconsciously functioning mechanisms of cultural symbol systems. Structuralism asserts a logical priority of the whole over the parts and tries to grasp an internal connection of phenomena as structure. The philosophical area of structural realism in its epistemic variant proposes the theory that all scientific theories refer to structures in the world, the ontic variant claims that the world consists only of structures and examines the possibilities of the existence and the emergence of relations and ( physical) objects, or also asks whether there can be only relations without their own slide.
The central structural science theory within philology is linguistics or linguistics. From the perspective of structural science, this is a sub-area of semiotics . Linguists, however, also partly hold the opinion that linguistics has already developed from this sub-area into an independent structural science. From a structural science perspective, linguistics assumes that its object, language , is structured. To this end, she develops methodological procedures to uncover these structures and constructs theories that are intended to depict these structures.
In sociology , the sociological systems theory of Niklas Luhmann counts as a structural-scientific theory building, which in turn goes back to the considerations of structural functionalism and system functionalism of Talcott Parsons . For the structural and functional analysis of social systems, Parsons developed the AGIL scheme , which systematizes the functions necessary for maintaining the structure. The system theory according to Niklas Luhmann is a philosophical-sociological communication theory with universal claim, with which society is to be described and explained as a complex system of communication. Communications are the operations that allow various social systems of society to emerge, let them pass, maintain, terminate, differentiate, interpenetrate and connect through structural coupling . According to Luhmann, social systems are systems that process meaning. According to Luhmann, "sense" is the name given to the way in which social (and psychological) systems reduce complexity. The boundary of a social system thus marks a complexity gradient between the environment and the social system. Social systems are the most complex systems systems theories can handle. In a social system, the reduction of complexity compared to the environment creates a higher order with fewer possibilities. By reducing complexity, social systems mediate between the indefinite world complexity and the complexity-processing capacity of psychic systems.
The Gestalt psychology of the Leipzig School, a direction founded by Felix Krueger at the beginning of the 20th century, saw itself as the antithesis of mechanical-materialistic psychophysics . An approach to psychology that is more driven by the basics of computer science can be found in constructivism .
Web links
- Homepage of the Frege Center for Structural Sciences at the Friedrich Schiller University Jena
- Competence Center for Pure and Applied Structural Sciences
Individual evidence
- ^ Helmut Balzert: Scientific work. 2008, p. 46.
- ↑ See for example http://cs.bsu.edu.az/en/content/faculty_of_applied_mathematics_and_cybernetics .
- ↑ http://www.tu-ilmenau.de/studieninteressierte/studieren/bachelor/technische-kybernetik-und-systemtheorie/
- ↑ in: B.-O. Küppers (Ed.), The Unit of Reality, Munich 2000: pp.89-105., Online (PDF; 206 kB); Pp. 20-22
- ↑ CF v. Weizsäcker: The unity of nature. 1971, p. 22.
- ↑ Reiner Winter: Fundamentals of formal logic. 2001, pp. 3-6.
- ↑ Wußling, Hans: Lectures on the history of mathematics; 1998, p. 281
- ↑ Köck, Michael: Mathematics - a product of natural history ?; 2011, p. 31
- ^ Bourbaki, Nicolas: The Architecture of Mathematics. Amer. Math. Monthly 67; 1950, pp. 221-232
- ↑ CF v. Weizsäcker: The unity of nature; 1971, p. 22
- ↑ Bernd-Olaf Küppers: Only knowledge can dominate knowledge 2008, p. 314
- ↑ Wußling, Hans: Lectures on the History of Mathematics 1998, p. 281.
- ↑ Wußling, Hans: Lectures on the History of Mathematics 1998, p. 283
- ↑ Brock, William, 1992; Vieweg's History of Chemistry, p. 163
- ^ Homepage of the Max Planck Institute for the Physics of Complex Systems
- ↑ Rosen, Robert; 1991, Life Itself: A Comprehensive Inquiry into the Nature, Origin, and Fabrication of Life , Columbia University Press
- ↑ Glandsdorff, Prigogine; 1971: Thermodynamics of Structure, Stability and Fluctuations
- ↑ Haken, Hermann; 1978: Synergetics, Nonequilibrium Phase Transitions and Selforganisation in Physics, Chemistry and Biology
- ↑ Haken, Hermann; 1995, Nature's secrets of success, p. 12