In this brief paper we research systems with respect to their abstract properties as structure and organization. In our approach important significance has theory of ordered sets and fixed points of morphism. We present state of art in this field and some new results based on retracts of posets. We point also the importance of methods to represent, manipulate and measure poset.
Retracts and fixed points have a crucial significance for recursion and computation.?Well know is that fixed points are important because they exactly characterize solutions to recursive definitions. It’s convenient to describe functions using recursion, certainly in programming languages, also tempting in semantics. The problem is, are they well defined? Idea is successive approximations. The approximation process yields a fixed point, that give us a solutions to the recursive equations.
We use morphisms for processing posets. In our paper we check out different measures of poset morphisms. We define a new concept: the energy of a morphism. The energy of the morphism of order set is a scale-invariant of morphism: function from morphism to rational numbers. Intuitively, the connection between the complexity of the morphism of an order set and its energy is simple: the more complicated morphism, the higher energy.
This kind of research have many application: for networking (portable knowledge management environments), cybernetic, for AGI and many other novel problem area: appearance of large, combinatorial data objects.
- Robert Balthasar Lisek is an artist and mathematician who focuses on systems and processes (computer, biological and social), draws upon conceptual art, radical art strategies, hacktivism, bioart, software art and artificial intelligence his work defies categorization. Lisek is a pioneer of art based on AI and bioinformatics. He explores the relationship between bio-molecular technology, code and issues arising from network technologies. In the project Das Gespenst the artist represented the self-replicating behavior of new original bacteria in order to draw out its wider bio-political significance in an imagined scenario of bioterrorism attack of Warsaw. Lisek is also researching problems of security and privacy in networked societies. He build NEST – Citizens Intelligent Agency, advanced software for searching hidden patterns and links between people, groups, events, objects and places. Lisek is also a scientist focused on the complexity, graph and order theory. Lisek is a founder of IRSA, FRL and ACCESS art symposium. Author of many exhibitions and actions, among others: NGRU – FILE, Sao Paulo; NEST – ARCO Art Fair, Madrid; Float – DMAC Harvestworks and Lower Manhattan Cultural Council, NYC; WWAI – Siggraph, Los Angeles; Falsecodes – Red Gate Gallery, Beijing; Gengine – National Gallery, Warsaw; Flextex – Byzantine Museum, Athens, FXT– ACA Media Festival, Tokyo and ISEA, Nagoya; SSSpear –17th Meridian, WRO Center, Wroclaw. fundamental.art.pl lisek.art.pl/gespenst.html
Full text (PDF) p. 1563-1567