[ISEA2011] Paper: Robert Balthasar Lisek – Retracts And Fixed Points In Theory Of Ordered Sets: Towards Combinatorial Computer Science


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