Does Incomputable Mean Not Engineerable?

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Self-referential systems have some remarkable properties. The processes of life and mind are not only self-referential, but self-reference turns out to be a crucial property of both. However, they are difficult to understand. From a given starting point, both endogenous systems (self-referential natural systems) and impredicative systems (self-referential formal systems) have infinitely many logically consistent consequences. Both are incomputable; neither halts after a finite number of steps. Therefore, neither can produce an exact prediction of the behavior of the other in finitely many steps. Despite the fact that all engineering decisions are based on incomplete information, this inherent inability of ... continued below

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Kercel, SW August 15, 2001.

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Self-referential systems have some remarkable properties. The processes of life and mind are not only self-referential, but self-reference turns out to be a crucial property of both. However, they are difficult to understand. From a given starting point, both endogenous systems (self-referential natural systems) and impredicative systems (self-referential formal systems) have infinitely many logically consistent consequences. Both are incomputable; neither halts after a finite number of steps. Therefore, neither can produce an exact prediction of the behavior of the other in finitely many steps. Despite the fact that all engineering decisions are based on incomplete information, this inherent inability of an impredicative model to produce exact predictions of an endogenous system is troubling to some engineers. Nevertheless, self-reference leads to a more general, but no less rational, form of modeling than that provided by traditional reductionism. Although the mathematics of self-reference is unfamiliar to engineers, its power is dramatic. For example, it resolves the apparent paradox of how a brain/mind possessing freewill can operate in a deterministic Universe.

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  • Annie 2001, St. Louis, Mo (US), 11/04/2001--11/07/2001

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  • Report No.: P01-111552
  • Grant Number: AC05-00OR22725
  • Office of Scientific & Technical Information Report Number: 788588
  • Archival Resource Key: ark:/67531/metadc720926

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  • August 15, 2001

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  • Sept. 29, 2015, 5:31 a.m.

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  • Jan. 19, 2016, 12:53 p.m.

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Kercel, SW. Does Incomputable Mean Not Engineerable?, article, August 15, 2001; Tennessee. (digital.library.unt.edu/ark:/67531/metadc720926/: accessed September 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.