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Microscopic self‐organization and self‐referential systems: A progress report
Author(s) -
Brändas Erkki J.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.22377
Subject(s) - dissipative system , quantum , factorization , code (set theory) , order (exchange) , computer science , encoding (memory) , theoretical physics , physics , algebra over a field , pure mathematics , mathematics , quantum mechanics , algorithm , artificial intelligence , programming language , set (abstract data type) , finance , economics
It is contended that (the classical canonical form of) Jordan blocks, play a role analogous to those of paradoxes and self‐referential contradictions in philosophy and mathematical logic. As examples we will briefly discuss the occurrence of such triangular units in appropriately generalized quantum theory of microscopic as well as open dissipative systems with structures appearing on both the fundamental as well as in higher order levels of organization. The mathematical structure centers on specific transformations within coherent‐dissipative ensembles that exhibit certain factorization properties allowing prime number algorithms, cf. the Gödel encoding system used to derive the celebrated incompleteness theorem. This prompts the suggestion that an additional meta‐code, cf. the genetic code, might be a‐scripted for the mapping between the genotype and phenotype spaces. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009