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Protein Folding, Spin Glass and Computational Complexity
 In Proceedings of the 3rd DIMACS Workshop on DNA Based Computers, held at the University of Pennsylvania, June 23 – 25
, 1997
"... . A reduction from "Ground State of Spin Glass" in statistical mechanics to a minimumenergy model of protein folding is made, which shows that the latter is NPcomplete (high complexity) . The reduction approximates true folding of a protein. The method also enables to show that even if th ..."
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. A reduction from "Ground State of Spin Glass" in statistical mechanics to a minimumenergy model of protein folding is made, which shows that the latter is NPcomplete (high complexity) . The reduction approximates true folding of a protein. The method also enables to show that even if the backbone of the protein is fixed, the folding of the sidechains is NPcomplete. In a separate second part, the possibility of synthesizing proteins to solve arbitrary instances of the spin glass problem is speculated upon. 1. Introduction The motivation for this work is the speculation of exploiting nature's capability of protein folding to solve computationally intractable problems. One way of investigating this idea is to encode known NPcomplete problems in terms of protein folding. The main content of this paper is to do this for the spin glass problem. We construct a protein that achieves the encoding, i.e., the folded protein provides a solution to spin glass. More precisely, albeit incident...
On the Inherent Incompleteness of Scientific Theories
, 2005
"... We examine the question of whether scientific theories can ever be complete. For two closely related reasons, we will argue that they cannot. The first reason is the inability to determine what are “valid empirical observations”, a result that is based on a selfreference Gödel/Tarskilike proof. Th ..."
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We examine the question of whether scientific theories can ever be complete. For two closely related reasons, we will argue that they cannot. The first reason is the inability to determine what are “valid empirical observations”, a result that is based on a selfreference Gödel/Tarskilike proof. The second reason is the existence of “metaempirical ” evidence of the inherent incompleteness of observations. These reasons, along with theoretical incompleteness, are intimately connected to the notion of belief and to theses within the philosophy of science: the QuineDuhem (and underdetermination) thesis and the observational/theoretical distinction failure. Some puzzling aspects of the philosophical theses will become clearer in light of these connections. Other results that follow are: no absolute measure of the informational content of empirical data, no absolute measure of the entropy of physical systems, and no complete computer simulation of the natural world are possible. The connections with the mathematical theorems of Gödel and Tarski reveal the existence of other connections between scientific and mathematical incompleteness: computational irreducibility, complexity, infinity, arbitrariness and selfreference. Finally, suggestions will be offered of where a more rigorous (or formal) “proof ” of scientific incompleteness can be found.